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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
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2015, Volume 428, Issue 2, pp. 1054 - 1069
In this paper, we are concerned with the following Schrödinger–Kirchhoff-type problem:(P){−(a+b∫RN|∇u|pdx)p−1Δpu+λV(x)|u|p−2u=f(x,u),x∈RN,u∈W1,p(RN), where... 
P-Laplacian | Infinitely many solutions | Schrödinger–Kirchhoff-type | Schrödinger-Kirchhoff-type | MATHEMATICS | MATHEMATICS, APPLIED | R-N | STATES | Schrodinger-Kirchhoff-type | POSITIVE SOLUTIONS | ELLIPTIC EQUATION
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 01/2018, Volume 35, Issue 1, pp. 65 - 100
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 02/2019, Volume 88, pp. 21 - 27
This paper is concerned with a gauged nonlinear Schrödinger equation −Δu+ωu+h2(|x|)|x|2+∫|x|∞h(s)su2(s)dsu=f(|x|,u)inR2.Under some suitable conditions on the... 
Infinitely many solutions | Gauged Schrödinger equation | Superlinear | Variational methods | SYSTEM | MATHEMATICS, APPLIED | Gauged Schrodinger equation | STANDING WAVES
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 03/2017, Volume 151, pp. 126 - 144
This paper is concerned the existence of infinitely many solutions for perturbed sublinear indefinite elliptic equations involving the nonlocal operator. By... 
Infinitely many solutions | Nonlocal operator | Broken symmetry | Sublinear indefinite elliptic equation | Rabinowitz’s perturbation method | Rabinowitz's perturbation method | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | CRITICAL-POINTS
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 12/2019, Volume 64, Issue 12, pp. 2077 - 2090
In this paper, we prove the existence of infinitely many solutions and least energy solutions for the following nonhomogeneous Klein-Gordon equation coupled... 
35J65 | Infinitely many solutions | 35J20 | Born-Infeld theory | Klein-Gordon equation | least energy solution | MATHEMATICS | MAXWELL SYSTEMS | Formulas (mathematics)
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 09/2019, Volume 186, pp. 33 - 54
In this paper, we consider the following nonlinear Kirchhoff type problem: −a+b∫R3|∇u|2Δu+V(x)u=f(u),inR3,u∈H1(R3),where a,b>0 are constants, the nonlinearity... 
Kirchhoff type problems | Infinitely many sign-changing solutions | Invariant sets | Descending flow | Nonlinearity | Minimax technique | Infinity | Coercivity
Journal Article
by Li, HY and Liao, JF
COMPUTERS & MATHEMATICS WITH APPLICATIONS, ISSN 0898-1221, 12/2016, Volume 72, Issue 12, pp. 2900 - 2907
In this article, we consider a class of superlinear Kirchhoff-type equations with critical growth [GRAPHICS] where lambda, mu > 0, N >= 4, 2 <= q < 2*, 2* =... 
Kirchhoff-type equation | MATHEMATICS, APPLIED | Positive solutions | CRITICAL GROWTH | Infinitely many solutions | Critical exponent | Variational method | GROUND-STATE SOLUTIONS
Journal Article
Boundary Value Problems, ISSN 1687-2762, 2012, Volume 2012, Issue 1, pp. 1 - 10
Journal Article
Nonlinearity, ISSN 0951-7715, 01/2016, Volume 29, Issue 2, pp. 357 - 374
The aim of this paper is to establish the multiplicity of weak solutions for a Kirchhoff-type problem driven by a fractional p-Laplacian operator with... 
symmetric mountain pass theorem | fractional p-Laplacian | infinitely many solutions | genus theory | Kirchhoff-type problem | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | EXPONENT | PHYSICS, MATHEMATICAL | NONLOCAL OPERATORS | Mountains | Operators | Dirichlet problem | Texts | Nonlinearity | Boundary conditions | Boundaries | Symmetry
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 03/2019, Volume 89, pp. 22 - 27
This paper discusses the quasilinear Schrödinger equation −Δu+V(x)u−Δ[(1+u2)12]u2(1+u2)12=K(x)f(u),x∈RN,where N⩾3. Under appropriate assumptions on the... 
Infinitely many nontrivial solutions | Local sublinear term | Variational methods | Quasilinear Schrödinger equation | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS | THEOREM | Quasilinear Schrodinger equation
Journal Article
by Yang, Z and Yuan, GX
JOURNAL OF MATHEMATICAL ECONOMICS, ISSN 0304-4068, 10/2019, Volume 84, pp. 94 - 100
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 07/2019, Volume 93, pp. 1 - 7
This paper is concerned with the following Kirchhoff type problems (0.1)−(a+b∫Ω|∇u|2dx)Δu=λ|u|q−2u+|u|p−2u,x∈Ω,u=0,x∈∂Ω,where constants a,b>0, the parameter... 
Kirchhoff type problems | Infinitely many solutions | Bound states | Genus | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | CONCAVE | POSITIVE SOLUTIONS | EQUATIONS
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 12/2016, Volume 32, pp. 242 - 259
In this paper, under some superquadratic conditions made on the nonlinearity f, we use variational approaches to establish the existence of infinitely many... 
Infinitely many solutions | Soliton solution | Quasilinear Schrödinger equation | ([formula omitted])-Laplacian | (p,q)-Laplacian | REACTION-DIFFUSION EQUATIONS | SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | (p, q)-Laplacian | SOLITON-SOLUTIONS | POSITIVE SOLUTIONS | Quasilinear Schrodinger equation | Q-LAPLACIAN
Journal Article
by Ge, Bin
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 08/2016, Volume 30, pp. 236 - 247
In this paper we are devoted to a time-independent fractional Schrödinger equation (−Δ)αu+V(x)u=f(x,u)in  RN, where (−Δ)α stands for the fractional Laplacian... 
Infinitely many solutions | Fractional Laplacian | Nonlinear Schrödinger equation | EXISTENCE | MATHEMATICS, APPLIED | Nonlinear Schrodinger equation | Supports | Asymptotic properties | Images | Nonlinearity | Complement | Schroedinger equation | Stands
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 09/2014, Volume 24, Issue 9, pp. 1450118 - 1-1450118-28
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2015, Volume 270, pp. 794 - 801
In this paper, we study a class of damped vibration problems with superquadratic terms at infinity. By using variational methods, we obtain infinitely many... 
Superquadratic | Infinitely many nontrivial periodic solutions | Variational methods | Damped vibration problems | MATHEMATICS, APPLIED | THEOREMS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 11/2018, Volume 291, Issue 16, pp. 2476 - 2488
In this paper, we study a class of sublinear or superlinear p(x)‐Laplacian equations in RN. Some new criteria to guarantee that the existence of multiple... 
Morse theory | 35D05 | 58E05 | symmetric version of mountain pass lemma | 35J60 | 35J92 | sign‐changing potential | p(x)‐Laplacian equations | infinitely many nontrivial solutions | p(x)-Laplacian equations | sign-changing potential | Registered nurses
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 01/2014, Volume 94, pp. 171 - 184
We consider the perturbed nonlinear elliptic system as following {−Δuj+λjuj=∑i=12βijui2uj+αj(x),uj∈H01(Ω),j=1,2, where Ω is a bounded smooth domain in RN(N≤3)... 
Bose–Einstein system | Infinitely many solutions | Perturbed symmetric | Minimax methods | Bose-Einstein system | MORSE INDEXES | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | MULTIPLE CRITICAL-POINTS | MATHEMATICS | R-N | WAVES | SYMMETRY | ELLIPTIC-SYSTEMS | FUNCTIONALS
Journal Article
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