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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 345, Issue 1, pp. 90 - 108
In this paper we study the nonlinear Schrödinger–Maxwell equations { − Δ u + V ( x ) u + ϕ u = | u | p − 1 u in R 3 , − Δ ϕ = u 2 in R 3 . If V is a positive... 
Nonlinear Schrödinger–Maxwell equations | Ground state solutions | Nonlinear Schrödinger-Maxwell equations
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 02/2016, Volume 260, Issue 3, pp. 2119 - 2149
In this paper, we consider the following nonlinear Schrödinger–Poisson system{−Δu+V(x)u+ϕu=f(x,u),inR3,−Δϕ=u2,inR3, where the nonlinearity f is superlinear at... 
Ground state | Schrödinger–Poisson systems | Nehari manifold | Critical exponent | Schrödinger-Poisson systems | EXISTENCE | MATHEMATICS | BOUND-STATES | POSITIVE SOLUTIONS | Schrodinger-Poisson systems | EQUATIONS | MULTIBUMP SOLUTIONS
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2017, Volume 56, Issue 4, pp. 1 - 25
This paper is dedicated to studying the following Kirchhoff-type problem 0.1 $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} -\left( a+b\int _{\mathbb... 
35J65 | 35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLICITY | POSITIVE SOLUTIONS | NONTRIVIAL SOLUTIONS | SIGN-CHANGING SOLUTIONS | ELLIPTIC-EQUATIONS
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 8/2016, Volume 67, Issue 4, pp. 1 - 18
This paper is dedicated to studying the following Schrödinger–Poisson system $${\left\{ \begin{array}{ll}-\triangle u+V(x)u+\lambda\phi u=K(x)f(u),& \quad x\in... 
35J65 | Engineering | 35J20 | Mathematical Methods in Physics | Schrödinger–Poisson system | Sign-changing solution | Ground state | Theoretical and Applied Mechanics | SYSTEM | EXISTENCE | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | MULTIPLE SOLUTIONS | SUPER | SEMICLASSICAL SOLUTIONS | POSITIVE SOLUTIONS | EQUATIONS | SOLITARY WAVES
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2012, Volume 252, Issue 5, pp. 3365 - 3380
In this paper, we study the Schrödinger–Poisson system ( SP) { − Δ u + u + K ( x ) ϕ ( x ) u = a ( x ) f ( u ) , in R 3 , − Δ ϕ = K ( x ) u 2 , in R 3 , and... 
Ground state | Lack of compactness | Variational methods | Non-autonomous Schrödinger–Poisson system | Asymptotically linear | Non-autonomous Schrödinger-Poisson system | EXISTENCE | MATHEMATICS | HAMILTONIAN-SYSTEMS | Non-autonomous Schrodinger-Poisson system | HOMOCLINIC ORBITS | EQUATION | Universities and colleges
Journal Article
by Li, GB and Ye, HY
JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, 07/2014, Volume 257, Issue 2, pp. 566 - 600
In this paper, we study the following nonlinear problem of Kirchhoff type with pure power nonlinearities: {-(a + b integral(R3) vertical bar Du vertical... 
MATHEMATICS | Kirchhoff equation | R-N | MULTIPLICITY | Variational methods | REGULARITY | MAXWELL EQUATIONS | GROWTH | QUASILINEAR ELLIPTIC-EQUATIONS | Pohozaev type identity | Ground state solutions
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 09/2017, Volume 37, Issue 9, pp. 4973 - 5002
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2014, Volume 412, Issue 1, pp. 435 - 448
In this paper, we study the existence of ground state solutions for the following Schrödinger–Poisson equation{−Δu+V(x)u+λϕu=μ|u|q−1u+|u|4u,inR3,−Δϕ=u2,inR3,... 
Schrödinger–Poisson equations | Variational method | Critical growth | Ground state solutions | Schrödinger-Poisson equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | MAXWELL EQUATIONS | SYSTEMS | Schrodinger-Poisson equations
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2019, Volume 473, Issue 1, pp. 87 - 111
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 04/2019, Volume 60, Issue 4, p. 41501
We prove that under some mild assumptions, the nonlinear fractional Schrödinger equation (−Δ)su+V(x)u=f(u) (x∈RN), where V(x) is an indefinite potential, has... 
EXISTENCE | ELLIPTIC PROBLEMS | SIGN-CHANGING SOLUTIONS | PHYSICS, MATHEMATICAL | POSITIVE SOLUTIONS | UNIQUENESS | Ground state | Schroedinger equation
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2017, Volume 456, Issue 2, pp. 927 - 945
In this paper, we study the following generalized quasilinear Schrödinger equations−div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=h(x,u),x∈RN, where N≥3,g:R→R+ is an even... 
Quasilinear Schrödinger equations | [formula omitted] condition | Ground state solutions | (AR) condition | EXISTENCE | POSITIVE SOLUTION | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | SCALAR FIELD-EQUATIONS | Quasilinear Schrodinger equations | MATHEMATICS | R-N | SOLITON-SOLUTIONS | PLASMA | CRITICAL GROWTH | ELLIPTIC-EQUATIONS
Journal Article
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2015, Volume 428, Issue 1, pp. 387 - 404
In this paper, we study the Schrödinger–Poisson equation with a nonlinearity in the critical growth. By using variational methods, the existence of ground... 
Schrödinger–Poisson equations | Nodal solutions | Critical growth | Ground state solutions | Schrödinger-Poisson equations | EXISTENCE | SYSTEM | MATHEMATICS | POSITIVE SOLUTION | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | SOLITARY WAVES | Schrodinger-Poisson equations
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2017, Volume 56, Issue 4, pp. 1 - 25
In this paper, we study the following fractional Schrödinger–Poisson system 0.1 $$\begin{aligned} \left\{ \begin{array}{ll} \varepsilon ^{2s}(-\Delta )^s u... 
35J50 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35R11 | 35Q55 | Mathematics | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE BOUND-STATES | REGULARITY | EQUATIONS | STANDING WAVES | SEMICLASSICAL LIMITS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 07/2014, Volume 257, Issue 2, pp. 566 - 600
In this paper, we study the following nonlinear problem of Kirchhoff type with pure power... 
Kirchhoff equation | Variational methods | Pohoz̆aev type identity | Ground state solutions | Pohožaev type identity
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 06/2013, Volume 54, Issue 6, p. 61504
This paper is devoted to a time-independent fractional Schrödinger equation of the form \documentclass[12pt]{minimal}\begin{document}$(-\Delta )^s... 
LAPLACIAN | R-N | REGULARITY | FIELD | PHYSICS, MATHEMATICAL | OPERATORS | ELLIPTIC PROBLEM | Supports | Variational methods | Infinity | Asymptotic properties | Mathematical analysis | Ground state | Schroedinger equation | Stands
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
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2017, Volume 40, Issue 6, pp. 2165 - 2176
Journal Article