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Science China Mathematics, ISSN 1674-7283, 2015, Volume 58, Issue 4, pp. 715 - 728
We consider the semilinear Schrodinger equation where f is a superlinear, subcritical nonlinearity. We mainly study the case where V(x) = V (0)(x) + V (1)(x),... 
non-Nehari manifold method | ground state solutions of Nehari-Pankov type | asymptotically periodic | Schrödinger equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | SUPER | Schrodinger equation | GROUND-STATE | NONLINEARITY | INDEFINITE LINEAR PART
Journal Article
Journal of the Australian Mathematical Society, ISSN 1446-7887, 02/2015, Volume 98, Issue 1, pp. 104 - 116
We consider the semilinear Schrodinger equation {-Delta u + V(x)u = f(x, u), x is an element of R-N, u is an element of H-1 (R-N), where f (x, u) is... 
non-Nehari-manifold method | Schrodinger equation | ground state solutions of Nehari-Pankov type | asymptotically linear | MATHEMATICS | SUPER | PART
Journal Article
Taiwanese Journal of Mathematics, ISSN 1027-5487, 12/2014, Volume 18, Issue 6, pp. 1957 - 1979
We consider the boundary value problem where Ω ⊂ ℝ is a bounded domain, info ( ) > −∞, is a superlinear, subcritical nonlinearity. Inspired by previous work of... 
Mathematical manifolds | Ground state | Boundary value problems | Mathematical theorems | Critical points | Nontrivial solutions | Superlinear | Boundary value problem | Strongly indefinite functional | Diagonal method | Ground state solutions of Nehari-Pankov type | Schrödinger equation | EXACT MULTIPLICITY | EXISTENCE | MATHEMATICS | Schrodinger equation | POSITIVE SOLUTIONS
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 12/2017, Volume 196, Issue 6, pp. 2043 - 2062
By using the penalization method and the Ljusternik–Schnirelmann theory, we investigate the multiplicity of positive solutions of the following fractional... 
Penalization method | 35A15 | 35J60 | Multiplicity of solutions | 35R11 | Mathematics, general | Mathematics | Nehari manifold | Supercritical problems | Fractional Laplacian | 45G05 | MATHEMATICS | MATHEMATICS, APPLIED | GROUND-STATES
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 05/2004, Volume 29, Issue 5-6, pp. 879 - 901
For a class of quasilinear Schrödinger equations we establish the existence of both one-sign and nodal ground states of soliton type solutions by the Nehari... 
Standing waves | 35J10 | 35J20 | The Nehari method | Quasilinear Schrödinger equations | 35J60 | One-sign and nodal solutions | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | WAVES | SOLITON-SOLUTIONS | quasilinear Schrodinger equations | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | one-sign and nodal solutions | standing waves | the Nehari method
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 12/2017, Volume 74, pp. 20 - 26
In this paper, we study the following generalized quasilinear Schrödinger equation −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=f(x,u),x∈RN,where N≥3, 2∗=2NN−2,... 
Non-Nehari manifold method | Periodic potential | Generalized quasilinear Schrödinger equation | Ground state solutions | MATHEMATICS, APPLIED | Generalized quasilinear Schrodinger equation | SOLITON-SOLUTIONS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 11/2012, Volume 75, Issue 16, pp. 6009 - 6033
This paper is devoted to the existence of a solution for a (p,q)-gradient elliptic system. The main tool employed consists of an application of the fibering... 
Conditional critical point | Fibering method | Critical point | Multiplicity | Gradient elliptic system | [formula omitted]-system | (p, q) -system | (p, q)-system | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | POSITIVE SOLUTIONS | NEHARI MANIFOLD | Tools | Nonlinearity
Journal Article
Journal of Nonlinear Science and Applications, ISSN 2008-1898, 2016, Volume 9, Issue 5, pp. 3018 - 3030
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 10/2018, Volume 25, Issue 5, pp. 1 - 18
In this work we prove some abstract results about the existence of a minimizer for locally Lipschitz functionals, over a set which has its definition inspired... 
35J62 | Bounded variation functions | 35J93 | Analysis | 1-Biharmonic | Mathematics | Nehari method | 1-Laplacian | EIGENVALUE PROBLEM | MATHEMATICS, APPLIED | LINEAR GROWTH | EQUATION | 1-BIHARMONIC OPERATOR | 1-LAPLACE OPERATOR
Journal Article
Topological Methods in Nonlinear Analysis, ISSN 1230-3429, 2017, Volume 49, Issue 2, pp. 683 - 714
Journal Article
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, ISSN 1230-3429, 06/2017, Volume 49, Issue 2, pp. 683 - 714
We study applicability conditions of the Nehari manifold method to the equation of the form DuT(u) - lambda DuF(u) = 0 in a Banach space W, where lambda is a... 
EXISTENCE | MATHEMATICS | CONCAVE | POSITIVE SOLUTIONS | Nehari manifold | ELLIPTIC-EQUATIONS | nonlinear system of equations | Rayleigh's quotient
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 06/2017, Volume 14, Issue 3, p. 1
In this paper, we consider a class of elliptic equation with dependence on the gradient. The existence of sign-changing solutions is established via the Nehari... 
Nehari method | Semilinear elliptic equations | iterative technique | sign-changing solutions | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | QUASI-LINEAR EQUATIONS | EXISTENCE THEOREMS | DIVERGENCE FORM | VARIATIONAL-INEQUALITIES | MATHEMATICS | DU | MOUNTAIN-PASS TECHNIQUES
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 06/2018, Volume 75, Issue 12, pp. 4427 - 4437
We study a class of critical Sobolev exponent problems involving Kirchhoff-type nonlocal term −a+b∫Ω|∇u|2dxΔu=u5+g(x,u)+λuq−1,x∈Ω,u=0,x∈∂Ω,where Ω⊂R3 is a... 
Variational method | Nehari method | Positive solutions | Critical Sobolev exponent | Kirchhoff-type nonlocal term
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 02/2013, Volume 254, Issue 3, pp. 1529 - 1547
For a C2-functional J defined on a Hilbert space X, we consider the set N={x∈A:projVx∇J(x)=0}, where A⊂X is open and Vx⊂X is a closed linear subspace, possibly... 
Critical point theory | Nehari manifold | Singularly perturbed domains | Systems of elliptic PDE | EXISTENCE | DOMAIN SHAPE | STATES | ENERGY | POSITIVE SOLUTIONS | STANDING WAVES | ELLIPTIC SYSTEM | MATHEMATICS | SOLITONS | NONLINEAR EQUATIONS | NEUMANN BOUNDARY-CONDITIONS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 08/2016, Volume 261, Issue 4, pp. 2384 - 2402
In the present paper, we consider the existence of ground state sign-changing solutions for a class of Kirchhoff-type... 
Non-Nehari manifold method | Kirchhoff-type problem | Ground state energy sign-changing solutions | EXISTENCE | MATHEMATICS | NODAL SOLUTIONS | MULTIPLICITY | POSITIVE SOLUTIONS | NONTRIVIAL SOLUTIONS | ELLIPTIC-EQUATIONS
Journal Article
COMPUTERS & MATHEMATICS WITH APPLICATIONS, ISSN 0898-1221, 08/2017, Volume 74, Issue 3, pp. 466 - 481
In this paper, we study the existence of ground state sign-changing solutions for the following generalized quasilinear Schrodinger-Maxwell system... 
Non-Nehari manifold method | INFINITY | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS | Ground state sign-changing solutions | BOUNDED DOMAINS | ELLIPTIC-EQUATIONS | Schrodinger-Maxwell system | Generalized quasilinear | NEHARI-MANIFOLD METHOD
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2017, Volume 40, Issue 14, pp. 5056 - 5067
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 02/2020, Volume 79, Issue 4, pp. 889 - 907
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2018, Volume 265, Issue 5, pp. 1894 - 1921
We study a p-Laplacian equation involving a parameter λ and a concave-convex nonlinearity containing a weight which can change sign. By using the Nehari... 
Bifurcation | Fibering method | p-Laplacian | Concave-convex | Nehari manifold | Variational methods | EXISTENCE | MATHEMATICS | MULTIPLICITY | REGULARITY | LINEAR ELLIPTIC-EQUATIONS | SOBOLEV | Mathematics - Analysis of PDEs
Journal Article
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