Applied Mathematics Letters, ISSN 0893-9659, 04/2019, Volume 90, pp. 188 - 193

This paper is concerned with the following Klein–Gordon–Maxwell system −△u+V(x)u−(2ω+ϕ)ϕu=f(x,u),x∈R3,△ϕ=(ω+ϕ)u2,x∈R3,where ω>0 is a constant, V and f are...

Variational methods | Klein–Gordon–Maxwell system | Geometrically distinct solutions | EQUATIONS | MATHEMATICS, APPLIED | Klein-Gordon-Maxwell system | GROUND-STATE SOLUTIONS

Variational methods | Klein–Gordon–Maxwell system | Geometrically distinct solutions | EQUATIONS | MATHEMATICS, APPLIED | Klein-Gordon-Maxwell system | GROUND-STATE SOLUTIONS

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 04/2019, Volume 90, pp. 175 - 180

In this paper, we study the following Klein–Gordon–Maxwell system −Δu+(λa(x)+1)u−(2ω+ϕ)ϕu=f(x,u),inR3,−Δϕ=−(ω+ϕ)u2,inR3.Using variational methods, we obtain...

Klein–Gordon–Maxwell system | Ground state solution | Variational methods | Steep potential well | MATHEMATICS, APPLIED | Klein-Gordon-Maxwell system

Klein–Gordon–Maxwell system | Ground state solution | Variational methods | Steep potential well | MATHEMATICS, APPLIED | Klein-Gordon-Maxwell system

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2017, Volume 455, Issue 2, pp. 1152 - 1177

In this paper, we consider the critical Klein–Gordon–Maxwell system with external potential. When the potential well is steep, by using the penalization...

Klein–Gordon–Maxwell system | Variational method | Critical growth | EXISTENCE | MATHEMATICS, APPLIED | EXPONENTS | MULTIPLICITY | NONEXISTENCE | POSITIVE SOLUTIONS | WELL | GROUND-STATE SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | MATHEMATICS | ELLIPTIC PROBLEMS | SOLITARY WAVES | Klein-Gordon-Maxwell system

Klein–Gordon–Maxwell system | Variational method | Critical growth | EXISTENCE | MATHEMATICS, APPLIED | EXPONENTS | MULTIPLICITY | NONEXISTENCE | POSITIVE SOLUTIONS | WELL | GROUND-STATE SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | MATHEMATICS | ELLIPTIC PROBLEMS | SOLITARY WAVES | Klein-Gordon-Maxwell system

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 12/2014, Volume 65, Issue 6, pp. 1153 - 1166

We prove the existence of least energy nodal solution for a class of Schrödinger–Poisson system in a bounded domain $${\Omega \subset {\mathbb{R}}^3}$$ Ω ⊂ R 3...

35J65 | Engineering | 35J20 | Mathematical Methods in Physics | Schrödinger–Poisson systems Nodal solution | Variational methods | Theoretical and Applied Mechanics | EQUATIONS | MATHEMATICS, APPLIED | Schrodinger-Poisson systems Nodal solution | KLEIN-GORDON-MAXWELL | GROUND-STATE | Mathematical analysis | Nonlinearity | Energy of solution

35J65 | Engineering | 35J20 | Mathematical Methods in Physics | Schrödinger–Poisson systems Nodal solution | Variational methods | Theoretical and Applied Mechanics | EQUATIONS | MATHEMATICS, APPLIED | Schrodinger-Poisson systems Nodal solution | KLEIN-GORDON-MAXWELL | GROUND-STATE | Mathematical analysis | Nonlinearity | Energy of solution

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 01/2019, Volume 60, Issue 1, p. 11503

In this paper, we prove the existence of a positive solution with minimal energy for a planar Schrödinger-Poisson system, where the nonlinearity is a...

EQUATIONS | PHYSICS, MATHEMATICAL | KLEIN-GORDON-MAXWELL | Continuity (mathematics)

EQUATIONS | PHYSICS, MATHEMATICAL | KLEIN-GORDON-MAXWELL | Continuity (mathematics)

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 11/2014, Volume 110, pp. 157 - 169

In this paper, a nonlinear Klein–Gordon–Maxwell System with solitary wave solution is considered. Using critical point theory, we establish sufficient...

Variational methods | Critical point theorem | Klein–Gordon–Maxwell System | Klein-Gordon-Maxwell System | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLICITY | NONEXISTENCE | SOLITARY WAVES | SCHRODINGER-POISSON EQUATIONS | GROUND-STATE SOLUTIONS | Nonlinearity | Complement | Critical point | Solitary waves

Variational methods | Critical point theorem | Klein–Gordon–Maxwell System | Klein-Gordon-Maxwell System | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLICITY | NONEXISTENCE | SOLITARY WAVES | SCHRODINGER-POISSON EQUATIONS | GROUND-STATE SOLUTIONS | Nonlinearity | Complement | Critical point | Solitary waves

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2016, Volume 437, Issue 1, pp. 160 - 180

In this paper, we consider the following Schrödinger–Poisson system with singularity{−Δu+ηϕu=μu−r,inΩ,−Δϕ=u2,inΩ,u>0,inΩ,u=ϕ=0,on∂Ω, where Ω⊂R3 is a smooth...

Singularity | Schrödinger–Poisson system | Multiplicity | Uniqueness | Schrödinger-Poisson system | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | NONLINEARITY | EQUATIONS | GROUND-STATE SOLUTIONS | MATHEMATICS | SIGN-CHANGING SOLUTIONS | R-3 | SEMILINEAR ELLIPTIC PROBLEM

Singularity | Schrödinger–Poisson system | Multiplicity | Uniqueness | Schrödinger-Poisson system | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | NONLINEARITY | EQUATIONS | GROUND-STATE SOLUTIONS | MATHEMATICS | SIGN-CHANGING SOLUTIONS | R-3 | SEMILINEAR ELLIPTIC PROBLEM

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 05/2018, Volume 75, Issue 9, pp. 3358 - 3366

This paper is concerned with the following Klein–Gordon–Maxwell system: −△u+V(x)u−(2ω+ϕ)ϕu=f(x,u),x∈R3,△ϕ=(ω+ϕ)u2,x∈R3,where ω>0 is a constant, V∈C(R3,R),...

Klein–Gordon–Maxwell system | Infinitely many solutions | Least energy solutions | Sign-changing potential | EXISTENCE | MATHEMATICS, APPLIED | NONEXISTENCE | SOLITARY WAVES | EQUATIONS | Klein-Gordon-Maxwell system | GROUND-STATE SOLUTIONS | POTENTIALS

Klein–Gordon–Maxwell system | Infinitely many solutions | Least energy solutions | Sign-changing potential | EXISTENCE | MATHEMATICS, APPLIED | NONEXISTENCE | SOLITARY WAVES | EQUATIONS | Klein-Gordon-Maxwell system | GROUND-STATE SOLUTIONS | POTENTIALS

Journal Article

9.
Full Text
Positive solutions for a Schrödinger-Poisson system with singularity and critical exponent

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2020, Volume 483, Issue 2, p. 123647

We study multiplicity of positive solutions for a class of Schrödinger-Poisson system with singularity and critical exponent, and obtain two positive solutions...

Schrödinger-Poisson systems | Critical exponent | Singular nonlinearity | Perturbation approach | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | Schrodinger-Poisson systems | EQUATIONS | GROUND-STATE SOLUTIONS | MATHEMATICS | SOLITARY WAVES | BOUND-STATES | CONCAVE

Schrödinger-Poisson systems | Critical exponent | Singular nonlinearity | Perturbation approach | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | Schrodinger-Poisson systems | EQUATIONS | GROUND-STATE SOLUTIONS | MATHEMATICS | SOLITARY WAVES | BOUND-STATES | CONCAVE

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 07/2020, Volume 196, p. 111771

This paper is concerned with two classes of critical Klein–Gordon–Maxwell systems as follows −Δu+V(x)u−(2ω+ϕ)ϕu=μf(u)+u5,x∈R3,Δϕ=(ω+ϕ)u2,x∈R3and...

Klein–Gordon–Maxwell | Critical growth | Ground state solution | Semiclassical states

Klein–Gordon–Maxwell | Critical growth | Ground state solution | Semiclassical states

Journal Article

Nonlinearity, ISSN 0951-7715, 08/2017, Volume 30, Issue 9, pp. 3492 - 3515

In this paper, we are concerned with the Schrodinger-Poisson system {-Delta u + u + empty set u = vertical bar u vertical bar(p-2)u in R-d, Delta empty set -...

variational methods | logarithmic convolution potential | SchrödingerPoisson system | ground state solutions | EXISTENCE | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | WAVES | SCALAR FIELD-EQUATIONS | PRESCRIBED NORM | PHYSICS, MATHEMATICAL

variational methods | logarithmic convolution potential | SchrödingerPoisson system | ground state solutions | EXISTENCE | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | WAVES | SCALAR FIELD-EQUATIONS | PRESCRIBED NORM | PHYSICS, MATHEMATICAL

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 05/2018, Volume 38, Issue 5, pp. 2333 - 2348

This paper is concerned with the following Klein-Gordon-Maxwell system. [graphic] [graphic] where 0 < omega <= m(0) and f is an element of C(R, R). By...

Klein-Gordon-Maxwell system | Zero mass case | Ground state solutions | EXISTENCE | MATHEMATICS, APPLIED | zero mass case | NONEXISTENCE | ground state solutions | EQUATIONS | GROUND-STATE SOLUTIONS | POTENTIALS | MATHEMATICS | SOLITARY WAVES | HAMILTONIAN ELLIPTIC SYSTEM | SIGN-CHANGING SOLUTIONS | AMBROSETTI-RABINOWITZ CONDITION

Klein-Gordon-Maxwell system | Zero mass case | Ground state solutions | EXISTENCE | MATHEMATICS, APPLIED | zero mass case | NONEXISTENCE | ground state solutions | EQUATIONS | GROUND-STATE SOLUTIONS | POTENTIALS | MATHEMATICS | SOLITARY WAVES | HAMILTONIAN ELLIPTIC SYSTEM | SIGN-CHANGING SOLUTIONS | AMBROSETTI-RABINOWITZ CONDITION

Journal Article

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, ISSN 1417-3875, 2019, Volume 2019, Issue 40, pp. 1 - 12

In this paper, we consider the following nonhomogeneous Klein-Gordon-Maxwell system {-Delta u + V(x)u - (2 omega + phi)phi u = f(x,u) +h(x), x is an element of...

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | nonhomogeneous | NONEXISTENCE | SOLITARY WAVES | Mountain Pass Theorem | EQUATIONS | Klein-Gordon-Maxwell system | GROUND-STATE SOLUTIONS | Ekeland's variational principle | klein–gordon–maxwell system | mountain pass theorem | ekeland's variational principle

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | nonhomogeneous | NONEXISTENCE | SOLITARY WAVES | Mountain Pass Theorem | EQUATIONS | Klein-Gordon-Maxwell system | GROUND-STATE SOLUTIONS | Ekeland's variational principle | klein–gordon–maxwell system | mountain pass theorem | ekeland's variational principle

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2016, Volume 2016, Issue 1, pp. 1 - 11

In this paper, we study the existence of solutions for the following nonhomogeneous Schrodinger-Poisson systems: (*) {-Delta u + V(x) u + K(x)phi(x) u = f (x,...

variational methods | concave and convex nonlinearities | Schrödinger-Poisson systems | sublinear nonlinearities | CONVEX NONLINEARITIES | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | MULTIPLE SOLUTIONS | POSITIVE SOLUTIONS | Schrodinger-Poisson systems | EQUATIONS | INDEFINITE NONLINEARITY | GROUND-STATE SOLUTIONS | MATHEMATICS | SOLITARY WAVES | THOMAS-FERMI | R-3 | Space and time | Usage | Schrodinger equation | Analysis | Critical point | Research | Quantum theory | Tests, problems and exercises | Texts | Boundary value problems | Mathematical analysis

variational methods | concave and convex nonlinearities | Schrödinger-Poisson systems | sublinear nonlinearities | CONVEX NONLINEARITIES | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | MULTIPLE SOLUTIONS | POSITIVE SOLUTIONS | Schrodinger-Poisson systems | EQUATIONS | INDEFINITE NONLINEARITY | GROUND-STATE SOLUTIONS | MATHEMATICS | SOLITARY WAVES | THOMAS-FERMI | R-3 | Space and time | Usage | Schrodinger equation | Analysis | Critical point | Research | Quantum theory | Tests, problems and exercises | Texts | Boundary value problems | Mathematical analysis

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 10/2010, Volume 198, Issue 1, pp. 349 - 368

This paper is motivated by the study of a version of the so-called Schrödinger–Poisson–Slater problem: $$- \Delta u + \omega u + \lambda \left( u^2 \star...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | KLEIN-GORDON-MAXWELL | STATES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYMMETRY | SOLITARY WAVES | MODELS | STABILITY | EQUATIONS | STANDING WAVES | POTENTIALS | Mathematics - Analysis of PDEs

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | KLEIN-GORDON-MAXWELL | STATES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYMMETRY | SOLITARY WAVES | MODELS | STABILITY | EQUATIONS | STANDING WAVES | POTENTIALS | Mathematics - Analysis of PDEs

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2019, Volume 473, Issue 1, pp. 87 - 111

In the present paper, we consider the following nonlinear Schrödinger–Poisson system with convolution...

Schrödinger–Poisson system | Choquard equation | Convolution nonlinearity | Nonlinear problem | Ground state solutions | EXISTENCE | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | CLASSICAL LIMIT | BOSE-EINSTEIN CONDENSATION | MATHEMATICS | WAVES | CHOQUARD-EQUATIONS

Schrödinger–Poisson system | Choquard equation | Convolution nonlinearity | Nonlinear problem | Ground state solutions | EXISTENCE | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | CLASSICAL LIMIT | BOSE-EINSTEIN CONDENSATION | MATHEMATICS | WAVES | CHOQUARD-EQUATIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 03/2020, Volume 268, Issue 6, pp. 2672 - 2716

In this paper, we study the following singularly perturbed Schrödinger-Poisson system{−ε2△u+V(x)u+ϕu=f(u)+u5,x∈R3,−ε2△ϕ=u2,x∈R3, where ε is a small positive...

Concentration | Critical growth | Schrödinger-Poisson system | Semiclassical state | EXISTENCE | Schrodinger-Poisson system | HARTREE | KLEIN-GORDON-MAXWELL | EQUATIONS | STANDING WAVES | MATHEMATICS | THOMAS-FERMI | BOUND-STATES | ATOMS

Concentration | Critical growth | Schrödinger-Poisson system | Semiclassical state | EXISTENCE | Schrodinger-Poisson system | HARTREE | KLEIN-GORDON-MAXWELL | EQUATIONS | STANDING WAVES | MATHEMATICS | THOMAS-FERMI | BOUND-STATES | ATOMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2014, Volume 411, Issue 2, pp. 787 - 793

We consider a Schrödinger–Poisson system in R3 with potential indefinite in sign and a general nonlinearity. We use the direct variational method and Morse...

Morse theory | Palais–Smale condition | Schrödinger–Poisson system | Schrödinger-Poisson system | Palais-Smale condition | MATHEMATICS | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | BOUND-STATES | EQUATIONS | GROUND-STATE SOLUTIONS

Morse theory | Palais–Smale condition | Schrödinger–Poisson system | Schrödinger-Poisson system | Palais-Smale condition | MATHEMATICS | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | BOUND-STATES | EQUATIONS | GROUND-STATE SOLUTIONS

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 02/2018, Volume 18, Issue 1, pp. 55 - 63

We study a Klein-Gordon-Maxwell system in a bounded spatial domain under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling...

Ljusternik-Schnirelmann Theory | Static Solutions | Variational Methods | Klein-Gordon-Maxwell Systems | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | GROUND-STATE SOLUTIONS | Mathematics - Analysis of PDEs

Ljusternik-Schnirelmann Theory | Static Solutions | Variational Methods | Klein-Gordon-Maxwell Systems | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | GROUND-STATE SOLUTIONS | Mathematics - Analysis of PDEs

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 11/2018, Volume 38, Issue 11, pp. 5461 - 5504

In this paper, we study the following nonlinear Schrodinger-Poisson system { -Delta u + u + epsilon K(x)Phi(x)u = f(u), x is an element of R-3, -Delta Phi =...

Schrödinger-Poisson system | Nonsymmetric potential | Reduction | nonsymmetric potential | EXISTENCE | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | NONEXISTENCE | SPHERES | EQUATIONS | NEUMANN PROBLEM | MOLECULES | MATHEMATICS | SOLITARY WAVES | BOUND-STATES | NONSYMMETRIC POTENTIALS | reduction

Schrödinger-Poisson system | Nonsymmetric potential | Reduction | nonsymmetric potential | EXISTENCE | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | NONEXISTENCE | SPHERES | EQUATIONS | NEUMANN PROBLEM | MOLECULES | MATHEMATICS | SOLITARY WAVES | BOUND-STATES | NONSYMMETRIC POTENTIALS | reduction

Journal Article

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