Edward Norman Dancer
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(Suggest an Edit or Addition)According to Wikipedia, Edward Norman Dancer FAA is an Australian mathematician, specializing in nonlinear analysis. Dancer received in 1969 a Bachelor of Science with Honours from the Australian National University and in 1972 a PhD from the University of Cambridge with thesis advisor Frank Smithies and thesis Bifurcation in Banach Spaces. As a postdoc Dancer was from 1971 to 1972 at the University of Newcastle-upon-Tyne, UK and from 1972 to 1973 at the Institute of Advanced Studies at the Australian National University. At the University of New England in New South Wales, he was from 1973 to 1975 a lecturer, from 1976 to 1981 a senior lecturer, from 1981 to 1987 an associate professor, and from 1987 to 1993 a full professor. From 1993 to the present, he has been a full professor and chair of the school of mathematics and statistics at the University of Sydney.
Edward Norman Dancer's Published Works
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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
- MINIMAX METHODS IN CRITICAL POINT THEORY WITH APPLICATIONS TO DIFFERENTIAL EQUATIONS (CBMS Regional Conference Series in Mathematics 65) (1987) (360)
- On the Dirichlet problem for weakly non-linear elliptic partial differential equations (1977) (258)
- A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system (2010) (231)
- On the indices of fixed points of mappings in cones and applications (1983) (219)
- The effect of domain shape on the number of positive solutions of certain nonlinear equations, II (1990) (197)
- On positive solutions of some pairs of differential equations (1984) (178)
- Some notes on the method of moving planes (1992) (169)
- ELLIPTIC PROBLEMS IN DOMAINS WITH PIECEWISE SMOOTH BOUNDARIES (de Gruyter Expositions in Mathematics 13) (1996) (156)
- MULTIPEAK SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM (1999) (151)
- Stability of fixed points for order-preserving discrete-time dynamical systems. (1991) (140)
- On positive solutions of semilinear elliptic equations (1987) (128)
- Boundary-value problems for weakly nonlinear ordinary differential equations (1976) (117)
- Spatial segregation limit of a competition–diffusion system (1999) (113)
- A Note on an Equation with Critical Exponent (1988) (110)
- Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability (1999) (109)
- Global solution branches for positive mappings (1973) (108)
- Competing Species Equations with Diffusion, Large Interactions, and Jumping Nonlinearities (1994) (107)
- Finite Morse index solutions of an elliptic equation with supercritical exponent (2011) (105)
- On the Number of Positive Solutions of Weakly Non‐Linear Elliptic Equations when a Parameter is Large (1986) (105)
- On positive solutions of some pairs of differential equations, II (1985) (103)
- Domain Perturbation for Elliptic Equations Subject to Robin Boundary Conditions (1997) (91)
- Effects of Certain Degeneracies in the Predator-Prey Model (2002) (89)
- Bifurcation from Simple Eigenvalues and Eigenvalues of Geometric Multiplicity One (2002) (87)
- The limit equation for the Gross–Pitaevskii equations and S. Terraciniʼs conjecture (2012) (84)
- Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions (2004) (81)
- On the existence and uniqueness of positive solutions for competing species models with diffusion (1991) (76)
- The Regularity and Local Bifurcation of¶Steady Periodic Water Waves (2000) (75)
- Degenerate critical points, homotopy indices and Morse inequalities. II. (1984) (75)
- On the use of asymptotics in nonlinear boundary value problems (1982) (72)
- On sign-changing solutions of certain semilinear elliptic problems (1995) (72)
- Global Structure of the Solutions of Non‐Linear Real Analytic Eigenvalue Problems (1973) (72)
- Uniform Hölder estimate for singularly perturbed parabolic systems of Bose–Einstein condensates and competing species (2011) (66)
- On Stability and Hopf Bifurcations for Chemotaxis Systems (2001) (61)
- On the superlinear Lazer-McKenna conjecture (2005) (59)
- Dynamics of Lotka–Volterra Competition Systems with Large Interaction (2002) (59)
- ON THE CLASSIFICATION OF SOLUTIONS OF −∆u = e ON R : STABILITY OUTSIDE A COMPACT SET AND APPLICATIONS (2008) (59)
- Stable and finite Morse index solutions on Rn or on bounded domains with small diffusion, II (2004) (56)
- On the Uniqueness of the Positive Solution of a Singularly Perturbed Problem (1995) (54)
- Bifurcation Theory for Analytic Operators (1973) (52)
- Interior and Boundary Peak Solutions for a Mixed Boundary Value Problem (1999) (48)
- Calculus of Variations and Partial Differential Equations: Topics On Geometrical Evolution Problems And Degree Theory (2000) (48)
- A new degree for $S^1$-invariant gradient mappings and applications (1985) (48)
- Fucik Spectrum, Sign-Changing, and Multiple Solutions for Semilinear Elliptic Boundary Value Problems with Resonance at Infinity (2000) (47)
- Existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero (1994) (46)
- New solutions of equations on $\mathbb {R}^n$ (2001) (46)
- Degenerate critical points, homotopy indices and Morse inequalities. (1984) (45)
- Some remarks on a boundedness assumption for monotone dynamical systems (1998) (45)
- On the classification of solutions of $-\Delta u= e^u$ on $\mathbb {R}^N$: Stability outside a compact set and applications (2008) (45)
- Dynamics of strongly competing systems with many species (2012) (45)
- On the existence of a maximal weak solution for a semilinear elliptic equation (1989) (43)
- A singularly perturbed elliptic problem in bounded domains with nontrivial topology (1999) (43)
- Multiple fixed points of positive mappings. (1986) (42)
- A note on asymptotic uniqueness for some nonlinearities which change sign (2000) (42)
- On the existence of multipeak solutions for nonlinear field equations on $R^N$ (1999) (41)
- On the effect of domain topology in a singular perturbation problem (1998) (40)
- A Note on Multiple Solutions of Some Semilinear Elliptic Problems (1997) (40)
- On multi-bump semi-classical bound states of nonlinear Schrödinger equations with electromagnetic fields (2006) (39)
- A minimization problem associated with elliptic systems of FitzHugh–Nagumo type (2004) (39)
- Finite Morse index solutions of supercritical problems (2008) (38)
- Global breaking of symmetry of positive solutions on two-dimensional annuli (1992) (37)
- On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem (1997) (37)
- The G-invariant implicit function theorem in infinite dimensions II (1986) (37)
- Bifurcation Theory in Real Banach Space (1971) (36)
- Generic domain dependence for non-smooth equations and the open set problem for jumping nonlinearities (1993) (36)
- Boundary‐Value Problems for Ordinary Differential Equations on Infinite Intervals (1975) (35)
- On Non-Radially Symmetric Bifurcation (1979) (35)
- Infinitely many turning points for some supercritical problems (2000) (34)
- Superlinear problems on domains with holes of asymptotic shape and exterior problems (1998) (33)
- Multiple solutions of asymptotically homogeneous problems (1988) (33)
- A counterexample to the Lazer-McKenna conjecture (1988) (33)
- Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian manifolds (2009) (32)
- Some remarks on classical problems and fine properties of Sobolev spaces (1996) (32)
- Finite Morse index solutions of exponential problems (2008) (32)
- On the influence of domain shape on the existence of large solutions of some superlinear problems (1989) (32)
- Multiple Solutions of Some Semilinear Elliptic Equations via the Generalized Conley Index (1995) (32)
- Realization of vector fields and dynamics of spatially homogeneous parabolic equations (1999) (32)
- Uniqueness and Nonexistence of Positive Solutions to Semipositone Problems (2006) (32)
- Multi-layer solutions for an elliptic problem☆ (2003) (32)
- On the Superlinear Lazer–McKenna Conjecture: Part II (2005) (32)
- Some remarks on Liouville type results for quasilinear elliptic equations (2002) (30)
- Remarks on Jumping Nonlinearities (1999) (30)
- The Lazer–McKenna conjecture and a free boundary problem in two dimensions (2008) (29)
- Positivity of Maps and Applications (1995) (29)
- On positive solutions of some singularly perturbed problems where the nonlinearity changes sign (1995) (28)
- On stable solutions of quasilinear periodic-parabolic problems (1987) (27)
- On long-time dynamics for competition-diffusion systems with inhomogeneous Dirichlet boundary conditions (2007) (26)
- A new type of concentration solutions for a singularly perturbed elliptic problem (2006) (26)
- A note on periodic solutions of autonomous Hamiltonian systems emanating from degenerate stationary solutions (1999) (26)
- Upper and lower stability and index theory for positive mappings and applications (1991) (24)
- Symmetries, degree, homotopy indices and asymptotically homogeneous problems (1982) (24)
- Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem (1999) (24)
- The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations (1998) (24)
- Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains (2000) (23)
- On the existence of bifurcating solutions in the presence of symmetries (1980) (23)
- On Uniqueness and Stability for Solutions of Singularly Perturbed Predator-Prey Type Equations with Diffusion (1993) (22)
- The structure of a nonlinear elliptic operator (1993) (22)
- Liouville‐type results for non‐cooperative elliptic systems in a half‐space (2012) (22)
- Counterexamples to some conjectures on the number of solutions of nonlinear equations (1985) (21)
- On a free boundary problem arising from population biology (2003) (21)
- Some remarks on half space problems (2009) (21)
- On the number of positive solutions of some weakly nonlinear equations on annular regions (1991) (21)
- Non-radial singular solutions of Lane-Emden equations in $R^N$ (2012) (21)
- Stable Subharmonic Solutions in Periodic Reaction-Diffusion Equations (1994) (20)
- On the existence of solutions of certain asymptotically homogeneous problems (1981) (20)
- A NOTE ON BIFURCATION FROM INFINITY (1974) (19)
- On a nonlinear elliptic boundary-value problem (1975) (19)
- On the principal eigenvalue of linear cooperating elliptic systems with small diffusion (2009) (19)
- On the spectrum of some linear noncooperative elliptic systems with radial symmetry (1995) (19)
- On the Hardy–Sobolev equation (2015) (18)
- On the superlinear Lazer-McKenna conjecture: the non-homogeneous case (2007) (18)
- Domain variation for certain sets of solutions and applications (1996) (16)
- The symmetry of positive solutions of periodic-parabolic problems (1994) (16)
- On the ranges of certain damped nonlinear differential equations (1979) (16)
- Perturbation of zeros in the presence of symmetries (1984) (15)
- A counterexample on competing species equations (1996) (15)
- The generalized Conley index and multiple solutions of semilinear elliptic problems (1996) (15)
- Singularly perturbed elliptic problems in exterior domains (2000) (15)
- Addendum to “The limit equation for the Gross–Pitaevskii equations and S. Terraciniʼs conjecture” [J. Funct. Anal. 262 (3) (2012) 1087–1131]☆ (2013) (15)
- Solution branches for mappings in cones, and applications (1974) (15)
- Weak star separability (1979) (15)
- On the profile of the changing sign mountain pass solutions for an elliptic problem (2002) (14)
- The Index Change and Global Bifurcation for Flows with a First Integral (1993) (14)
- Quasilinear Elliptic Equations on Half- and Quarter-spaces (2013) (14)
- The G-invariant implicit function theorem in infinite dimensions (1982) (14)
- Some Singularly Perturbed Problems on Annuli and a Counterexample to a Problem of Gidas, Ni and Nirenberg (1997) (14)
- Behaviour of a semilinear periodic-parabolic problem when a parameter is small (1990) (14)
- Multipeak solutions for an elliptic system of Fitzhugh-Nagumo type (2006) (13)
- Singular perturbed problems in the zero mass case: asymptotic behavior of spikes (2010) (13)
- Stable solutions on $\R^n$ and the primary branch of some non-self-adjoint convex problems (2004) (13)
- Asymptotic behavior of positive solutions of some elliptic problems (2003) (12)
- On the global bifurcation diagram for the one-dimensional Ginzburg–Landau model of superconductivity (1999) (12)
- On the resonance set in a fourth-order equation with jumping nonlinearity (2001) (12)
- Degree theory on convex sets and applications to bifurcation (2000) (12)
- Breaking of symmetries for forced equations (1983) (11)
- Least energy nodal solution of a singular perturbed problem with jumping nonlinearity (2011) (11)
- Order intervals of selfadjoint linear operators and nonlinear homeomorphisms (1984) (11)
- Weakly Nonlinear Dirichlet Problems on Long or Thin Domains (1993) (11)
- Multipeak Solutions for the Neumann Problem of an Elliptic System of Fitzhugh–Nagumo Type (2005) (11)
- On the Lazer-McKenna Conjecture Involving Critical and Super-critical Exponents (2008) (10)
- On the least point of the spectrum of certain cooperative linear systems with a large parameter (2011) (10)
- Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions (2007) (10)
- An implicit function theorem with symmetries and its application to nonlinear eigenvalue equations (1980) (10)
- Solutions with interior and boundary peaks for the neumann problem of an elliptic system of fitzhugh-nagumo type (2006) (10)
- SOME REMARKS ON THE STABILITY OF SIGN CHANGING SOLUTIONS (1995) (9)
- Poincaré-Hopf type formulas on convex sets of Banach spaces (2009) (9)
- On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients (1991) (9)
- Asymptotic behavior of the least energy solution of a problem with competing powers (2011) (8)
- Elementary Stability and Bifurcation Theory (Gerard Iooss and Daniel D. Joseph) (1991) (8)
- Corrigendum: On the Dirichlet problem for weakly non-linear elliptic partial differential equations (1981) (8)
- Highly nonlinear large-competition limits of elliptic systems (2010) (8)
- A uniqueness theorem for a free boundary problem (2006) (8)
- Some mountain-pass solutions for small diffusion (2003) (7)
- Some bifurcation results for rapidly growing nonlinearities (2012) (7)
- Degenerate critical points, homotopy indices and morse inequalities III (1989) (7)
- Some results for jumping nonlinearities (2002) (6)
- On the existence of zeros of perturbed operators (1983) (6)
- Quasinormal cones in Banach spaces (1983) (6)
- BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS ON INFINITE INTERVALS II (1977) (5)
- Uniform convergence of solutions to elliptic equations on domains with shrinking holes (2015) (5)
- A Note on a Paper of Fučik and Nečas (1976) (5)
- Degree Theory for Orbits of Prescribed Period of Flows with a First Integral (1990) (5)
- A Variational Theory of Stokes Waves and their Sub-Harmonic Bifurcations (1998) (5)
- A CONLEY INDEX CALCULATION (2009) (5)
- A Liouville theorem for $$p$$p-harmonic functions on exterior domains (2014) (5)
- On connecting orbits for competing species equations with large interactions (2004) (4)
- On domain perturbation for super-linear Neumann problems and a question of Y. Lou,W-M Ni and L. Su (2012) (4)
- Interior peak solutions for an elliptic system of FitzHugh–Nagumo type (2006) (4)
- On Multiple Radial Solutions of a Singularly Perturbed Nonlinear Elliptic System (2007) (4)
- Critical point, anti-maximum principle and semipositone p-laplacian problems (2005) (4)
- Non-uniqueness for nonlinear boundary-value problems (1983) (4)
- Some near critical problems (2003) (3)
- Equilibrium States in the Degree Theory of Periodic Orbits with a First Integral (1991) (3)
- Turing instabilities for systems of two equations with periodic coefficients (1994) (3)
- Stable and Finite Morse Index Solutions for Dirichlet Problems with Small Diffusion in a Degenerate Case and Problems with Infinite Boundary Values (2009) (3)
- Liouville‐type results for a class of quasilinear elliptic systems and applications (2018) (3)
- Proofs of the Results in “Boundary-Value Problems for Weakly Nonlinear Ordinary Differential Equations” (2010) (3)
- Connectedness of the branch of positive solutions of some weakly nonlinear elliptic equations (1993) (3)
- Existence of stable and unstable periodic solutions for semilinear parabolic problems (1997) (2)
- Remarks on the pure critical exponent problem (1998) (2)
- Spatial Independence of Invariant Sets of Parabolic Systems (2002) (2)
- Certain weakly nonlinear partial differential equations on annuli (1990) (2)
- Some remarks on a theorem of Kachurovskii (1978) (2)
- Conley indices on convex sets, attractor-repeller pairs and applications to multiple solutions of nonlinear elliptic equations (2007) (2)
- Peak solutions for the Dirichlet problem of an elliptic system (2009) (2)
- Asymptotics applied to nonlinear boundary-value problems (1978) (2)
- Supercritical finite Morse index solutions (2007) (2)
- Real transformations with polynomial invariants (1996) (1)
- A Note on Multiple Solutions of Some (1997) (1)
- Remarks on Nonlinear Elliptic Problems on Long Domains (2005) (1)
- Morse inequalities and estimates for the number of solutions of nonlinear equations (1984) (1)
- Some slightly subcritical or slightly supercritical problems (1999) (1)
- Solvability of some asymptotically homogeneous elliptic problems (1982) (1)
- DEFORMATION RETRACTS TO THE FAT DIAGONAL AND APPLICATIONS TO THE EXISTENCE OF PEAK SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS (2012) (1)
- New Results for Finite Morse Index Solutions on ℝN and applications (2010) (1)
- Functions of asymptotic expansions (1971) (1)
- Bifurcation under Continuous Groups of Symmetries (1983) (1)
- Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations (2007) (1)
- Remarks on multiple solutions of nonlinear equations (1986) (1)
- On a degree associated with the Gross-Pitaevskii system with a large parameter (2019) (1)
- Finite Morse Index and Linearized Stable Solutions on Bounded and Unbounded Domains (2011) (1)
- Competition systems with strong interaction on a subdomain (2011) (1)
- Recent progress on nonlinear elliptic and parabolic problems and related abstract methods (2008) (0)
- On the number of stable positive solutions of weakly nonlinear elliptic equations when the diffusion is small (2021) (0)
- Infinitely many bifurcations for rapidly growing nonlinearities (2014) (0)
- A remark on stable solutions of nonlinear elliptic equations on $\mathbb R^3$ or $\mathbb R^4$ (2014) (0)
- Retracts , fixed point index and differential equations Rafael (2008) (0)
- Addendum to: Stable and Finite Morse Index Solutions for Dirichlet Problems with Small Diffusion in a Degenerate Case and Problems with Infinite Boundary Values (2013) (0)
- Existence and multiplicity of solutions for a weakly coupled radial system in a ball (2008) (0)
- A note on uniqueness for the plasma problem (1992) (0)
- Some examples on solution structures for weakly nonlinear elliptic equations (2005) (0)
- Two notes on supercritical problems on long domains (1994) (0)
- Topological and Variational Methods for Partial Differential Equations (2009) (0)
- Domain Variation and Non-Uniqueness of Homoclinic Solutions of Some Partial Differential Equations on Strips (2007) (0)
- ON SPIKES ON LINES FOR A NEUMANN SUPERLINEAR AMBROSETTI-PRODI TYPE PROBLEM (2020) (0)
- On Stable and Meta-stable Solutions of the Shadow System For the Geirer-Meinhardt Equation (2006) (0)
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