Vieri Benci
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Measure Theory
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Mathematics
Vieri Benci's Degrees
- PhD Mathematics University of Florence
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(Suggest an Edit or Addition)Vieri Benci'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
- Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity (1983) (773)
- An eigenvalue problem for the Schrödinger-Maxwell equations (1998) (587)
- Critical point theorems for indefinite functionals (1979) (456)
- SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS (2002) (343)
- On critical point theory for indefinite functionals in the presence of symmetries (1982) (276)
- Positive solutions of some nonlinear elliptic problems in exterior domains (1987) (265)
- The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems (1991) (249)
- Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology (1994) (223)
- Solitons in Several Space Dimensions:¶Derrick's Problem and¶Infinitely Many Solutions (2000) (196)
- Existence of positive solutions of the equation −Δu + a(x)u = u(N + 2)(N − 2) in RN (1990) (182)
- A new approach to the Morse-Conley theory and some applications (1991) (97)
- Towards a Unified Field Theory for Classical Electrodynamics (2004) (96)
- Soliton Like Solutions of a Lorentz Invariant Equation in Dimension 3 (1998) (93)
- A geometrical index for the group S1 and some applications to the study of periodic solutions of ordinary differential equations (1981) (86)
- Non-Archimedean Probability (2011) (84)
- On the existence of multiple geodesics in static space-times (1991) (83)
- Numerosities of labelled sets: a new way of counting (2003) (81)
- Solitons and the electromagnetic field (1999) (72)
- Periodic solutions of Lagrangian systems on a compact manifold (1986) (67)
- Infinitesimal Probabilities* (2016) (65)
- Alpha-theory: An elementary axiomatics for nonstandard analysis (2003) (65)
- Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systems (1984) (63)
- Compression and diffusion: a joint approach to detect complexity (2002) (59)
- On the existence of infinitely many geodesics on space-time manifolds (1994) (56)
- The eightfold path to Nonstandard Analysis (2004) (54)
- The Semiclassical Limit of the Nonlinear Schrödinger Equation in a Radial Potential (2002) (52)
- Weighted sobolev spaces and the nonlinear dirichlet problem in unbounded domains (1979) (50)
- On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds (2007) (50)
- An Aristotelian notion of size (2006) (49)
- Existence of static solutions of the semilinear Maxwell equations (2006) (48)
- Discreteness conditions of the spectrum of Schrödinger operators (1978) (47)
- A nonlinear elliptic equation with singular potential and applications to nonlinear field equations (2007) (45)
- Bending and stretching energies in a rectangular plate modeling suspension bridges (2014) (45)
- The nonlinear Klein–Gordon equation coupled with the Maxwell equations (2001) (44)
- An Eigenvalue Problem for a Quasilinear Elliptic Field Equation (2001) (42)
- Existence and non existence of the ground state solution for the nonlinear Schroedinger equations with $V(\infty)=0$ (2005) (42)
- Variational Methods in Nonlinear Field Equations (2014) (41)
- Hylomorphic solitons in the nonlinear Klein-Gordon equation (2008) (40)
- Some critical point theorems and applications (1980) (40)
- Normal modes of a Lagrangian system constrained in a potential well (1984) (39)
- Solitons for the Nonlinear Klein-Gordon Equation (2007) (39)
- On the existence of closed geodesics on noncompact Riemannian manifolds (1992) (39)
- Existence of Solutions for the Nonlinear Schrödinger Equation with V (∞) = 0 (2005) (39)
- The dual method in critical point theory. Multiplicity results for indefinite functional (1982) (39)
- Dynamical systems and computable information (2002) (36)
- A note on the existence of multiple brake orbits (1993) (36)
- Introduction to Morse Theory a New Approach (1995) (35)
- Nonlinear analysis and applications to physical sciences (2004) (35)
- Solitary Waves in Abelian Gauge Theories (2007) (35)
- Information and dynamical systems: a concrete measurement on sporadic dynamics (2002) (34)
- Periodic bounce trajectories with a low number of bounce points (1989) (31)
- Spinning Q-Balls for the Klein-Gordon-Maxwell Equations (2010) (31)
- Ultrafunctions and Generalized Solutions (2012) (30)
- Solitary Waves with Non-Vanishing Angular Momentum (2003) (29)
- On a filtration problem through a porous medium (1974) (29)
- On the existence of stable charged Q-balls (2010) (29)
- Existence of hylomorphic solitary waves in Klein-Gordon and in Klein-Gordon-Maxwell equations (2009) (28)
- Hylomorphic solitons (2009) (28)
- An Euclidean measure of size for mathematical universes (2007) (27)
- Solitons in Schrödinger-Maxwell equations (2014) (27)
- Does bifurcation from the essential spectrum occur (1981) (26)
- Variational Methods in Nonlinear Field Equations: Solitary Waves, Hylomorphic Solitons and Vortices (2014) (25)
- Periodic Trajectories for the Lorentz-Metric of a Static Gravitational Field (1990) (25)
- Solutions in Exterior Domains of Null Mass Nonlinear Field Equations (2006) (25)
- Homoclinic orbits on compact manifolds (1991) (25)
- Periodic solutions of asymptotically linear dynamical systems (1994) (25)
- Solitary waves: physical aspects and mathematical results. (2004) (23)
- An algebraic approach to nonstandard analysis (2000) (23)
- Existence of geodesics for the Lorentz metric of a stationary gravitational field (1990) (23)
- A New Variational Principle for the Fundamental Equations of Classical Physics (1998) (22)
- Three dimensional vortices in Abelian Gauge Theories (2007) (22)
- from the disk into the euclidean n-sphere (1985) (21)
- Hylomorphic solitons and charged Q-balls: Existence and stability (2012) (21)
- Remarks on topological solitons (1996) (21)
- A remark on the nodal regions of the solutions of some superlinear elliptic equations (1989) (21)
- Ultrafunctions and Applications (2014) (21)
- Variational and Topological Methods in the Study of Nonlinear Phenomena (2012) (20)
- Solitary waves in the nolinear wave equation and in gauge theories (2007) (19)
- Morse theory for symmetric functionals on the sphere and an application to a bifurcation problem (1985) (18)
- The nonlinear Schroedinger equation: Solitons dynamics (2008) (18)
- Data compression and genomes: a two-dimensional life domain map. (2008) (18)
- A purely algebraic characterization of the hyperreal numbers (2005) (18)
- Solitary waves in classical field theory (2004) (18)
- Positive Solutions of Some Eigenvalue Problems in the Theory of Variational Inequalities (1977) (17)
- A non-archimedean algebra and the Schwartz impossibility theorem (2014) (17)
- On the geodesic connectedeness of Lorentzian manifolds (1994) (17)
- A model problem for ultrafunctions (2012) (16)
- Three Dimensional Vortices in the Nonlinear Wave Equation (2009) (16)
- Morse theory for $C^1$-functions and Conley blocks (1994) (16)
- A “Birkhoff-Lewis” type result for a class of Hamiltonian systems (1987) (15)
- Hylomorphic solitons on lattices (2010) (15)
- A minimization method and applications to the study of solitons (2011) (15)
- An elementary approach to Stochastic Differential Equations using the infinitesimals (2008) (15)
- Elementary numerosity and measures (2012) (15)
- Basic properties of ultrafunctions (2013) (15)
- Geodesics on static Lorentz manifolds with convex boundary (1992) (14)
- A Morse index for geodesics in static Lorentz manifolds (1992) (14)
- Estimate of the Number of Periodic Solutions via the Twist Number (1997) (14)
- Generalized functions beyond distributions (2014) (14)
- Periodic Solutions of Hamiltonian Systems of Prescribed Period. (1983) (13)
- On the Dynamics of Solitons in the Nonlinear Schrödinger Equation (2011) (13)
- Some properties of the spectral flow in Semiriemannian geometry (1998) (13)
- Determinism, Holism, and Complexity (2010) (12)
- A ring homomorphism is enough to get nonstandard analysis (2003) (12)
- A REMARK ON A PRIORI BOUNDS AND EXISTENCE FOR PERIODIC SOLUTIONS OF HAMILTONIAN SYSTEMS (1987) (11)
- Information, complexity and entropy: a new approach to theory and measurement methods (2001) (11)
- The Direct Method in the Study of Periodic Solutions of Hamiltonian Systems with Prescribed Period (1983) (11)
- Existence, multiplicity and concentration of bound states for a quasilinear elliptic field equation (2001) (10)
- Solitons and Relativistic Dynamics (2000) (10)
- Solitary Waves and Vortices in Non-Abelian Gauge Theories with Matter (2011) (10)
- Quantum Phenomena in a Classical Model (1999) (10)
- Existence of 3D-Vortices in Abelian Gauge Theories (2006) (10)
- A strongly degenerate elliptic equation arising from the semilinear Maxwell equations (2004) (9)
- Solitons and Bohmian mechanics (2002) (9)
- Existence of solitons in the nonlinear beam equation (2011) (9)
- On a discreteness condition of the spectrum of Schrödinger operators with unbounded potential from below (1978) (8)
- Hamiltonian formulation of the Klein-Gordon-Maxwell equations (2011) (8)
- Existence of Torsional Solitons in a Beam Model of Suspension Bridge (2016) (8)
- Semiclassical limit for a quasilinear elliptic field equation: one-peak and multipeak solutions (2001) (8)
- Su un problema di autovalori per disequazioni variazionali (1975) (7)
- Some nonlinear elliptic problems with asymptotic conditions (1979) (7)
- On asymptotically quadratic Hamiltonian systems (1983) (7)
- A priori bounds for periodic solutions of a class of Hamiltonian systems (1988) (7)
- A Unitarian Approach to Classical Electrodynamics: The Semilinear Maxwell Equations (2005) (7)
- On the Morse inequalities for geodesics on Lorentzian manifolds (2003) (7)
- Some Remarks on the Semilinear Wave Equation (2003) (7)
- A generalization of Gauss' divergence theorem (2014) (6)
- Infinitesimal and infinite numbers as an approach to quantum mechanics (2019) (6)
- Generalized solutions in PDE's and the Burgers' equation (2016) (6)
- Solitary waves and Bohmian mechanics (2002) (6)
- Morse Theory for functionals of class C^1 (1992) (6)
- A "birkhoff-lewis" type result for non autonomous differential equations (1988) (6)
- The Euclidean numbers (2017) (6)
- Lusternik–Schnirelman and Morse Theory for the Van der Waals–Cahn–Hilliard equation with volume constraint (2020) (6)
- On the existence of hylomorphic vortices in the nonlinear Klein-Gordon equation (2012) (6)
- Some applications of numerosities in measure theory (2014) (6)
- Periodic Solutions of Dissipative Dynamical Systems (1990) (6)
- Hausdorff Nonstandard Extensions - doi: 10.5269/bspm.v20i1-2.7519 (2009) (5)
- Periodic solutions of a class of Hamiltonian systems (1982) (5)
- Generalized solutions of variational problems and applications (2018) (5)
- Hylomorphic Vortices in Abelian Gauge Theories (2009) (5)
- A generalization of the Conley-index theory (1986) (5)
- Axioms for non-Archimedean probability (NAP) (2012) (4)
- Stability and instability in evolution. (1998) (4)
- The algorithmic numbers in non-archimedean numerical computing environments (2021) (4)
- Multiple solutions for the Van der Waals–Allen–Cahn–Hilliard equation with a volume constraint (2019) (4)
- The Caccioppoli ultrafunctions (2017) (3)
- Matter and electromagnetic fields: remarks on the dualistic and unitarian standpoints (2005) (3)
- Non–Standard Analysis Revisited: An Easy Axiomatic Presentation Oriented Towards Numerical Applications (2022) (3)
- Periodic orbits of a one-dimensional non-autonomous Hamiltonian system (2006) (3)
- The Nonlinear Schroedinger Equation: Existence, Stability and Dynamics of Solitons (2010) (3)
- Some Applications of the Morse-Conley Theory to the Study of Periodic Solutions of Second Order Conservative Systems (1987) (3)
- Spectral properties of some differential and pseudodifferential operators. Applications to some quark models (1981) (3)
- The General Principles (2014) (3)
- Stability properties for solitary waves in 3 space dimensions (1996) (3)
- Exponential decay and regularity properties of the Hartree approximation to the bound state wavefunctions of the helium atom (1976) (3)
- A topological approach to non-Archimedean Mathematics (2014) (3)
- Maximal Poincaré polynomials and minimal Morse functions (2001) (2)
- On the existence of geodesics in static Lorentz manifolds with singular boundary (2012) (2)
- Hylomorphic solitons for the Benjamin-Ono and the fractional KdV equations (2016) (2)
- Index theory and stability of periodic solutions of Lagrangian systems (1992) (2)
- A variational problem for manifold valued functions (2000) (2)
- About emergent properties and complexity in biological theories. (2004) (2)
- The Nonlinear Klein-Gordon Equation (2014) (2)
- Some Remarks on the Theory of Relativity and the Naïve Realism (2002) (2)
- Some Remarks on the Definition of Boltzmann, Shannon and Kolmogorov Entropy (2005) (2)
- On the Existence of Stable Isolated Ecosystems outside the Earth (1997) (1)
- Rotation numbers for Lagrangian systems and Morse theory (1996) (1)
- How to Measure the Infinite: Numerosities and Nonstandard Analysis (2019) (1)
- An Improved Setting for Generalized Functions: Fine Ultrafunctions (2021) (1)
- The Nonlinear Klein-Gordon-Maxwell Equations (2014) (1)
- Non-Archimedean Mathematics and the formalism of Quantum Mechanics (2018) (1)
- On the spectrum of some differential and pseudodifferential operators (1979) (1)
- The Euclidean Universe (2021) (1)
- Optimal information measures for weakly chaotic dynamical systems (2005) (1)
- Hylomorphic solitons for the generalized KdV equation (2014) (1)
- Solitons in Schr\"odinger-Maxwell equations (2013) (1)
- Euclidean numbers and numerosities (2021) (1)
- The Nonlinear Schrödinger-Maxwell Equations (2014) (1)
- Some Remarks on the Arrow of Time and the Notion of Information (2003) (1)
- Generalized functions beyond distributions (2014) (0)
- A non-archimedean algebra and the Schwartz impossibility theorem (2014) (0)
- On Perturbations of Z sub 2 Symmetric Functionals. (1987) (0)
- Towards a Morse theory on Banach spaces via ultrafunctions (2015) (0)
- The Nonlinear Beam Equation (2014) (0)
- Neboǰsa MUDRINSKI THE LARGEST HIGHER COMMUTATOR SEQUENCE (2019) (0)
- Solitary Waves and Solitons: Abstract Theory (2014) (0)
- Existence of positive solutions of the equation $-Delta u+a(x)u=usp {(N+2)/(N-2)}$ in $Rsp N$ (1990) (0)
- Existence of solitons in the nonlinear beam equation (2012) (0)
- Matter and electromagnetic fields: remarks on the dualistic and unitarian point of view (2005) (0)
- The Nonlinear Schrödinger Equation (2014) (0)
- Future Directions for Logic (2012) (0)
- Some results on the existenceof geodesics in static Lorentz manifolds with nonsmooth boundary (1991) (0)
- A Model for the Maxwell Equations Coupled with Matter Based on Solitons (2021) (0)
- On a second order boundary value problem with singular nonlinearity (2006) (0)
- Preface: Applications of mathematical analysis to problems in theoretical physics (2021) (0)
- Computable Information Content and a Simple Application to the Study of DNA (2003) (0)
- A classical model for the Maxwell equations coupled with matter (2020) (0)
- An abstract theorem on the existence of hylomorphic solitons (2011) (0)
- Why is the Gravitational Mass Equal to the Inertial Mass (2000) (0)
- Tempered ultrafunctions (2015) (0)
- O ct 2 00 2 Dynamical systems and computable information (0)
- Solitons in Schrödinger-Maxwell equations (2014) (0)
- Abstracts of the talks (2017) (0)
- The Arrow of Time and Information Theory (2014) (0)
- On the Dynamics of Solitons in the Nonlinear Schrödinger Equation (2012) (0)
- Multiple solutions for the Van der Waals–Allen–Cahn–Hilliard equation with a volume constraint (2020) (0)
- Computable Information Content and Boolean Networks Dynamics (2005) (0)
- Existence of Torsional Solitons in a Beam Model of Suspension Bridge (2017) (0)
- An Euclidean Measure of Size for Mathematical (2007) (0)
- A “Birkhoff-Lewis” Type Result for Nonautonomous Hamiltonian Systems (1987) (0)
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