Martin Schechter | Academic Influence

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Martin Schechter

Mathematics

#3217

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#4799

Historical Rank

#1208

USA Rank

Measure Theory

#658

World Rank

#899

Historical Rank

#266

USA Rank

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Mathematics

Martin Schechter 's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Martin Schechter Influential?

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According to Wikipedia, Martin Schechter was an American mathematician whose work concerned mathematical analysis . He was a professor at the University of California, Irvine. Schechter did his undergraduate studies at the City University of New York.

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Martin Schechter 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Principles of Functional Analysis (1971) (466)
Spectra of partial differential operators (1986) (304)
Critical point theory and its applications (2006) (300)
Linking methods in critical point theory (1999) (218)
Semigroups of operators and measures of noncompactness (1971) (173)
General boundary value problems for elliptic partial differential equations (1959) (153)
On the essential spectrum of an arbitrary operator. I (1966) (142)
On the Solvability of Semilinear Gradient Operator Equations (1977) (121)
An Introduction to Nonlinear Analysis (2004) (116)
WEAK LINKING THEOREMS AND SCHR¨ ODINGER EQUATIONS WITH CRITICAL SOBOLEV EXPONENT (2003) (104)
A Variation of the Mountain Pass Lemma and Applications (1991) (100)
Operator methods in quantum mechanics (1981) (98)
Superlinear Problems (2004) (86)
A generalization of the problem of transmission (1960) (83)
Embedding theorems and quasi-linear elliptic boundary value problems for unbounded domains (1972) (82)
On the Brézis–Nirenberg Problem (2010) (69)
Unique continuation for Schrodinger operators with unbounded potentials (1980) (65)
On L p Estimates and Regularity, I (1963) (61)
Periodic non-autonomous second-order dynamical systems (2006) (61)
The Fučík Spectrum (1999) (58)
Global solutions of nonlinear Schrödinger equations (2017) (58)
Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems (1992) (54)
Basic theory of Fredholm operators (1967) (52)
Invariance of the essential spectrum (1965) (51)
Riesz operators and Fredholm perturbations (1968) (51)
Negative Norms and Boundary Problems (1960) (51)
Integral inequalities for partial differential operators and functions satisfying general boundary conditions (1959) (50)
Minimax Systems and Critical Point Theory (2009) (50)
On the spectra of operators on tensor products (1969) (47)
The existence of wave operators in scattering theory (1977) (47)
On $L^p$ Estimates and Regularity II. (1963) (46)
Superlinear elliptic boundary value problems (1995) (40)
Superlinear Schrödinger operators (2012) (39)
Remarks on elliptic boundary value problems (1959) (38)
Non-autonomous second order Hamiltonian systems (2014) (37)
The spectrum of the Schrödinger operator (1989) (36)
Multiplication Operators (1989) (36)
Sign-changing critical points from linking type theorems (2006) (35)
A generalization of the saddle point method with applications (1992) (35)
Modern methods in partial differential equations (1977) (34)
Spectral theory for operators generated by elliptic boundary problems with eigenvalue parameter in boundary conditions, II (1965) (33)
Scattering theory for elliptic operators of arbitrary order (1974) (33)
A bounded mountain pass lemma without the (PS) condition and applications (1992) (32)
Type II regions between curves of the Fučik spectrum and critical groups (1998) (32)
New linking theorems (1998) (31)
New Saddle Point Theorems (1993) (31)
Hamiltonians for Singular Potentials (1972) (31)
Mixed boundary problems for general elliptic equations (1960) (29)
Periodic solutions of second-order nonautonomous dynamical systems (2006) (28)
Double resonance problems with respect to the Fucik spectrum (2003) (28)
The Use of Cerami Sequences in Critical Point Theory (2007) (27)
BEST FREDHOLM PERTURBATION THEOREMS (1988) (27)
Spectral theory for Fredholm operators (1963) (25)
Various types of boundary conditions for elliptic equations (1960) (25)
Infinitely many solutions to perturbed elliptic equations (2005) (25)
The Fucik spectrum and critical groups (2001) (25)
Solution of nonlinear equations having asymptotic limits at zero and infinity (2001) (24)
Resonance problems with respect to the Fucík spectrum (2000) (23)
Essential self-adjointness of the Schrödinger operator with magnetic vector potential (1975) (23)
The Klein-Gordon equation and scattering theory (1976) (22)
On the dirichlet problem for second order elliptic equations with coefficients singular at the boundary (1960) (22)
Existence solutions for second order Hamiltonian systems (2016) (22)
Sandwich pairs in critical point theory (2008) (22)
Nonlinear elliptic boundary value problems at resonance (1990) (21)
On the invariance of the essential spectrum of an arbitrary operator. III (1968) (21)
On Estimating Elliptic Partial Differential Operators in the L 2 Norm (1957) (21)
Homoclinic orbits for Schrödinger systems (2003) (20)
Joint Spectra and Interpolation of Operators (1968) (20)
Coerciveness of linear partial differential operators for functions satisfying zero dirichlet‐type boundary data (1958) (20)
Type (II) regions between curves of the Fucik spectrum (1997) (20)
A new criterion for scattering theory (1977) (19)
A generalized operational calculus developed from Fredholm operator theory (1973) (19)
Double linking theorem and multiple solutions (2003) (18)
Spherical maxima in Hilbert space and semilinear elliptic eigenvalue problems (1990) (18)
Nonlinear Elliptic Boundary Value Problems at Strong Resonance (1990) (18)
ROTATIONALLY INVARIANT PERIODIC SOLUTIONS OF SEMILINEAR WAVE EQUATIONS (1998) (18)
A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities (2000) (18)
The Hampwile theorem for nonlinear eigenvalues (1989) (17)
Non-periodic discrete Schrödinger equations: ground state solutions (2016) (17)
On the essential spectrum of an elliptic operator perturbed by a potential (1969) (17)
Some notes on a superlinear second order Hamiltonian system (2017) (17)
New Linking Theorem and Sign-Changing Solutions (2005) (16)
The intrinsic mountain pass (1995) (16)
Elliptic Problems in Nonsmooth Domains (P. Grisvard) (1986) (16)
A Theorem on the Existence of Dyon Solutions (1981) (16)
The invariance principle (1979) (15)
Cut-off potentials and forms extensions (1976) (14)
Periodic second order superlinear Hamiltonian systems (2015) (14)
SOLUTION OF THE NONLINEAR PROBLEM Au = N(u) IN A BANACH SPACE (1978) (14)
Topics in Critical Point Theory (2012) (13)
Nonlinear Schrödinger operators with zero in the spectrum (2015) (13)
Splitting subspaces and saddle points (1993) (13)
Modern methods in partial differential equations : an introduction (1977) (13)
Bounded resonance problems for semilinear elliptic equations (1995) (13)
Imbedding estimates involving new norms and applications (1984) (12)
On Perturbations of Essential Spectra (1969) (11)
Nonautonomous second order Hamiltonian systems (2011) (11)
The mountain pass alternative (1991) (11)
Multiple solutions of second order Hamiltonian systems (2017) (10)
Solution of the dirichlet problem for systems not necessarily strongly elliptic (1959) (10)
Eigenvalues for semilinear boundary value problems (1991) (10)
Critical points over splitting subspaces (1993) (10)
Review: Enrico G. Beltrametti and Gianni Cassinelli, The logic of quantum mechanics (1983) (10)
Coerciveness in L p (1963) (10)
SCATTERING THEORY FOR PSEUDODIFFERENTIAL OPERATORS (1976) (10)
A nonlinear elliptic boundary value problem (1973) (10)
On the existence, uniqueness and regularity of solutions to general elliptic boundary-value problems (1974) (10)
Infinite Dimensional Linking (1998) (9)
16 – Trace Class Operators (1981) (9)
Discreteness of the singular spectrum for Schrödinger operators (1976) (9)
Systems of partial differential equations in a half‐space (1964) (8)
Nontrivial solutions of elliptic semilinear equations¶at resonance (2000) (8)
Nonlocal elliptic boundary value problems (1966) (8)
Morse index estimates in saddle point theorems without a finite dimensional closed loop (1998) (8)
Schrödinger Equations (2020) (8)
An infinite-dimensional linking theorem and applications (2004) (8)
Families of “first eigenfunctions” for semilinear elliptic eigenvalue problems (1991) (8)
On the spectra of singular elliptic operators (1976) (7)
Ground state solutions for non-autonomous dynamical systems (2014) (7)
Non-periodic Schrödinger lattice systems with perturbed and asymptotically linear terms: Negative energy solutions (2019) (7)
Points of Spherical Maxima and Solvability of Semilinear Elliptic Equations (1991) (7)
On the dominance of partial differential operators II (1964) (7)
Sandwich pairs for p-Laplacian systems (2009) (7)
Steady state solutions for Schrödinger equations governing nonlinear optics (2012) (7)
Asymptotically linear elliptic boundary value problems (1994) (7)
CRITICAL POINT THEORY WITH WEAK-TO-WEAK LINKING (1998) (6)
Sandwich pairs in $p$-Laplacian problems (2007) (6)
Nonlinear eigenvalues and mountain pass methods (1993) (6)
$L_p$ embedding and nonlinear eigenvalue problems for unbounded domains (1970) (6)
Saddle point techniques (2005) (6)
Semi-Classical Analysis for the Schrodinger Operator and Applications (Bernard Helffer) (1989) (6)
Wave operators for oscillating potentials (1977) (6)
On the theory of differential boundary problems (1963) (6)
On the dominance of partial differential operators (1963) (5)
Partial differential operators on $L^p \left( {E^n } \right)$ (1969) (5)
Computation of critical groups in Fučı́k resonance problems (2003) (5)
Eigenfunction expansions for the Schrödinger operator (1976) (5)
Critical points when there is no saddle point geometry (1995) (5)
INFINITE-DIMENSIONAL SANDWICH PAIRS (2008) (5)
Self-Adjoint Realizations in Another Hilbert Space (1984) (5)
Derivatives of mappings with applications to nonlinear differential equations (1986) (5)
Elliptic resonance problems with unequal limits at infinity (1994) (5)
Differentiation in abstract spaces (1984) (5)
Interpolation spaces by complex methods (1966) (5)
Multiple solutions for non-periodic Schrödinger lattice systems with perturbation and super-linear terms (2019) (5)
Completeness of wave operators in two Hilbert spaces (1979) (5)
The conjugate of a product of operators (1970) (5)
The Saddle Point Alternative (1995) (5)
Nonhomogeneous elliptic systems and scattering (1975) (4)
Multiple homoclinic solutions for discrete Schrödinger equations with perturbed and sublinear terms (2021) (4)
Homoclinic solutions of nonlinear second-order Hamiltonian systems (2016) (4)
Wave operators for pairs of spaces and the Klein-Gordon equation (1978) (4)
Weighted norm inequalities for potential operators (1988) (4)
Strong Sandwich Pairs (2008) (4)
Scattering theory for second order elliptic operators (1975) (4)
Boundary value problems for semilinear elliptic equations of arbitrary order in unbounded domains (1988) (4)
Solution of the Dirichlet problem for equations not necessarily strongly elliptic (1958) (4)
Critical Point Theory (2020) (3)
The spectrum of operators on $L^p (E^n)$ (1970) (3)
Periodic solutions of semilinear higher dimensional wave equations (2001) (3)
Resonance Problems Which Intersect Many Eigenvalues (1997) (3)
Multiple solutions for semilinear elliptic problems (2000) (3)
On the solvability of semilinear operator equations and elliptic boundary value problems (1972) (3)
Scattering theory for elliptic systems (1976) (3)
Essential spectra of elliptic partial differential equations (1967) (3)
Existence of the solution to electromagnetic wave scattering problem for an impedance body of an arbitrary shape (2015) (3)
Critical Groups in Saddle Point Theorems without a Finite Dimensional Closed Loop (2002) (3)
The schrodinger operator with vector potential (1977) (3)
Multiple nontrivial solutions of elliptic semilinear equations (2000) (3)
The continuous singular spectrum of the Schrödinger operator (1980) (2)
Remarks on a previous paper (1976) (2)
Semilinear boundary value problems of the strong resonance type (1993) (2)
Schrödinger operators in the uniform norm (1977) (2)
The Mountain Cliff Theorem (1992) (2)
Proper boundary points of the spectrum (1975) (2)
Multiple periodic solutions for damped vibration systems with general nonlinearities at infinity (2019) (2)
A general approach to boundary problems (1960) (2)
Exact estimates for potentials (1988) (2)
Methods in Classical and Functional Analysis.@@@Functional Analysis in Historical Perspective.@@@Principles of Functional Analysis. (1977) (2)
The role of core functions in semilinear elliptic problems (2011) (2)
The spectra of non-elliptic operators (1968) (2)
On Functionals Bounded Below (2003) (2)
Spectral and Scattering Theory for Propagative Systems (1981) (2)
Reflexive Banach spaces (2001) (2)
Critical point methods (2008) (2)
Noncooperative elliptic systems (2011) (2)
Landesman-Lazer resonance problems and saddle point methods (1994) (2)
ON LP ESTIMATES AND REGULARITY, I.* 1 (2016) (2)
Potential estimates in Orlicz spaces. (1988) (2)
Norms on quotient spaces (1969) (2)
REMARKS ON A LIMITING CASE IN THE TREATMENT OF NONLINEAR PROBLEMS WITH MOUNTAIN PASS GEOMETRY (2010) (2)
Another look at scattering theory (1978) (2)
Review: Aleksei A. Dezin, Partial differential equations: An introduction to a general theory of linear boundary value problems, and J. Wloka, Partial differential equations (1988) (1)
Semilinear elliptic equations having asymptotic limits at zero and infinity (1999) (1)
Ordinary Differential Equations (1984) (1)
Linking sandwich pairs (2009) (1)
Flows and Critical Points (2008) (1)
Sign-Changing Solutions to Equations of Elliptic Type (2010) (1)
Book Review: Spectral theory of linear operators---and spectral systems in Banach algebras (2004) (1)
Fredholm operators and the essential spectrum (2011) (1)
Two space scattering theory using the subspace of continuity (1979) (1)
Some $L^p $ estimates for partial differential equations (1962) (1)
Schrödinger Equations in Nonlinear Optics (2020) (1)
Systems of sandwich pairs (2009) (1)
Coerciveness in $L\sp{p}$ (1963) (1)
Scattering in Two Hilbert Spaces (1979) (1)
Semi-classical bound states of Schrödinger equations (2013) (1)
Observations concerning a paper of peetre (1961) (1)
Linking in Hilbert space (2005) (1)
Weighted norm estimates for Sobolev spaces (1987) (1)
Nonlinear Differential Equations and Applications NoDEA Flows and Critical Points (2008) (1)
2 – The Spectrum (1981) (1)
8 – Time-Independent Theory (1981) (1)
Rigorous results on the existence of dyon solutions (1980) (1)
Selfadjoint Operators, Spectral and Scattering Theory, Variational Technioues, Non-Linear Phenomena, Linear and Non-Linear Partial Differential Eouations, and Related Topics (1984) (1)
Monotonicity methods for noncooperative elliptic systems (2012) (1)
Applications of Morse theory to the solution of semilinear problems depending on C 1 functionals (2001) (1)
Variant sandwich pairs (2010) (1)
Critical Points of Functionals (2009) (0)
12 – Eigenfunction Expansions (1981) (0)
13 – Restricted Particles (1981) (0)
A free boundary problem for pseudo-analytic functions (1959) (0)
Topics in Critical Point Theory: Sandwich pairs (2012) (0)
Dyons Solutions to Yang-Mills Equations (1981) (0)
An Introduction to Nonlinear Analysis: Preface (2005) (0)
Semilinear boundary value problems for unbounded domains. (1987) (0)
Weak Sandwich Pairs (2009) (0)
Bounded Saddle Point Methods (1999) (0)
An Introduction to Nonlinear Analysis: Concepts from functional analysis (2005) (0)
Wave operators tor pairs of spaces and the Klein-Gordon equation (1978) (0)
Spectral Theory of Linear Operators (2006) (0)
Research Article The Use of Cerami Sequences in Critical Point Theory (2007) (0)
4 – The Negative Eigenvalues (1981) (0)
Theory of Perturbations of Partial Differential Operators (2010) (0)
Radially Symmetric Wave Equations (2020) (0)
Infinite-dimensional singularity theory and bifurcation from equilibria for certain nonlinear evolution equations (1994) (0)
Canonical Systems of Partial Differential Equations (2021) (0)
Zero in the Spectrum (2020) (0)
Differential Equations (2020) (0)
An infinite-dimensional linkingtheorem and applications (2004) (0)
We present the most general definition of the linking of sets in a Banach space and discuss necessary and sufficient conditions for sets to link. (2006) (0)
Semilinear problems with bounded nonlinear term (2005) (0)
EXISTENCE OF PERIODIC SOLUTIONS OF COMPLETE SECOND ORDER HAMILTONIAN SYSTEMS (2014) (0)
Applications to semilinear problems (2012) (0)
Fučík Spectrum: Resonance (2009) (0)
Two space scattering and propagative systems (1987) (0)
Complex interpolation (2019) (0)
Complex interpolation (2019) (0)
Spectral Theory of Ordinary Differential Operators (Erich Muller-Pfeiffer) (1982) (0)
Homoclinic solutions of nonlinear second-order Hamiltonian systems (2015) (0)
Eigenvalue Problems for Semilinear Equations (1998) (0)
Custom sandwich pairs (2009) (0)
An Introduction to Nonlinear Analysis: Metric spaces (2005) (0)
Applications of a Theorem of Brezis-Nirenberg (2018) (0)
Applied Functional Analysis (Jean-Pierre Aubin) (1982) (0)
7 – Long-Range Potentials (1981) (0)
Semilinear problems in unbounded domains (2007) (0)
Boundary value problems (2005) (0)
15 – The Invariance Principle (1981) (0)
A Course in Functional Analysis (John B. Conway) (1986) (0)
Nonlinear Optics (2020) (0)
OF PARTIAL DIFFERENTIAL OPERATORS(1) (2016) (0)
Critical Point Theory in Infinite Dimensional Spaces Using the Leray–Schauder Index (2021) (0)
The Method Using Flows (2009) (0)
BOUNDARY VALUE PROBLEMS FOR SEMILINEAR ELLIPTIC EQUATIONS OF ARBITRARY ORDER IN U N B O U N D E D DOMAINS (2008) (0)
Book Review: Systems of equations of composite type (1991) (0)
Applications of sandwich pairs (2009) (0)
Linking in infinite dimensional spaces using the Leray-Schauder index (2021) (0)
Semilinear Boundary Value Problems (1999) (0)
Notes, Remarks and References (1999) (0)
Second Order Hamiltonian Systems (2020) (0)
THE METHOD OF WEAK LINKING (2004) (0)
The Semilinear Wave Equation (2020) (0)
3 – The Essential Spectrum (1981) (0)
Intermediate extensions in $L^p$ (1967) (0)
5 – Estimating the Spectrum (1981) (0)
ON A DISCRETENESS CONDITION OF THE SPECTRUM OF SCHRÖDINGER OPERATORS WITH UNBOUNDED POTENTIAL FROM BELOW1 (2010) (0)
New Techniques in Critical Point Theory (2017) (0)
Non-periodic discrete Schrödinger equations: ground state solutions (2016) (0)
Global solutions of nonlinear Schrödinger equations (2017) (0)
Finding Link Sets (2005) (0)
Eigenfunc t ion expans ions for Schr 6 dinger operator (2006) (0)
OPERATORS IN THE L2 NORM. (2016) (0)
1 – One-Dimensional Motion (1981) (0)
Review: A. Dzhuraev, Systems of equations of composite type (1991) (0)
Estimates on Subspaces (1999) (0)
The Monotonicity Trick (2020) (0)
Theory of Partial Differential Equations (H. Melvin Lieberstein) (1973) (0)
Finding linking sets (2006) (0)
Morse theory applied to semilinear problems (2012) (0)
Advanced Problems: 6126-6131 (1977) (0)
Rotationally Invariant Solutions (2009) (0)
Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms (2021) (0)
14 – Hard-Core Potentials (1981) (0)
An Introduction to Nonlinear Analysis: Bibliography (2005) (0)
10 – Strong Completeness (1981) (0)
Solving Linear Partial Differential Equations (2020) (0)
Some notes on a superlinear second order Hamiltonian system (2016) (0)
Semilinear Wave Equations (2009) (0)
Type (II) Regions (2009) (0)
Book Review: Partial differential equations: An introduction to a general theory of linear boundary value problems (1988) (0)
Nonlinear Schrödinger operators with zero in the spectrum (2015) (0)
Appendix Sobolev spaces (2012) (0)
Elliptic problems in which the boundary conditions do not form a normal set (1960) (0)
6 – Scattering Theory (1981) (0)
Carathéodory Functions in Partial Differential Equations (2016) (0)
Partial Differential Equations. An Introduction (B. Epstein) (1963) (0)
Examples of Minimax Systems (2009) (0)
The Riesz theory for compact operators (2001) (0)
Second-Order Periodic Systems (2009) (0)
11 – Oscillating Potentials (1981) (0)
Spectral Theory and Wave Operators for the Schrödinger Equation (A. M. Berthier) (1984) (0)
Topics in Critical Point Theory: Bibliography (2012) (0)
Linking Sandwich Sets (2020) (0)
An Introduction to Nonlinear Analysis: Conditional extrema (2005) (0)
SELF-ADJOINT REALIZATIONS IN (2016) (0)
Sign-changing critical points via Sandwich Pair theorems (2013) (0)
Measures of operators (2001) (0)
Differential Equations, Partial (2003) (0)
Saddle Point Problems (2006) (0)

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