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

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

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

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

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

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

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Full Text
Non-Nehari manifold method for a class of generalized quasilinear Schrödinger equations

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

Non-Nehari manifold method | Periodic potential | Generalized quasilinear Schrödinger equation | Ground state solutions | MATHEMATICS, APPLIED | Generalized quasilinear Schrodinger equation | SOLITON-SOLUTIONS

Journal Article

Acta Mathematica Sinica, English Series, ISSN 1439-8516, 4/2016, Volume 32, Issue 4, pp. 463 - 473

We consider the nonlinear difference equations of the form $$Lu = f\left( {n,u} \right),\;n \in Z,$$ where L is a Jacobi operator given by (Lu)(n) =...

Discrete nonlinear Schrödinger equation | superlinear | 58E05 | 39A12 | ground state solutions of Nehari–Pankov type | Mathematics, general | 70H05 | Mathematics | non-Nehari manifold method | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | GAP SOLITONS | SATURABLE NONLINEARITY | HAMILTONIAN-SYSTEMS | DIFFERENCE-EQUATIONS | ground state solutions of Nehari-Pankov type | HOMOCLINIC SOLUTIONS | Discrete nonlinear Schrodinger equation | Studies | Nonlinear equations | Theorems | Schrodinger equation | Topological manifolds | Applied mathematics | Mathematical models | Manifolds | Operators | Energy use | Difference equations | Mathematical analysis | Texts | Ground state | Schroedinger equation

Discrete nonlinear Schrödinger equation | superlinear | 58E05 | 39A12 | ground state solutions of Nehari–Pankov type | Mathematics, general | 70H05 | Mathematics | non-Nehari manifold method | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | GAP SOLITONS | SATURABLE NONLINEARITY | HAMILTONIAN-SYSTEMS | DIFFERENCE-EQUATIONS | ground state solutions of Nehari-Pankov type | HOMOCLINIC SOLUTIONS | Discrete nonlinear Schrodinger equation | Studies | Nonlinear equations | Theorems | Schrodinger equation | Topological manifolds | Applied mathematics | Mathematical models | Manifolds | Operators | Energy use | Difference equations | Mathematical analysis | Texts | Ground state | Schroedinger equation

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

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

We consider the semilinear Schrodinger equation [GRAPHICS] where N >= 4, 2* := 2N/(N - 2) is the critical Sobolev exponent, V, K, f is 1 -periodic in x(j) for...

Critical sobolev exponent | Non-Nehari-manifold method | Ground state solutions of Nehari-Pankov type | Schrödinger equation | non-Nehari-manifold method | MATHEMATICS | MATHEMATICS, APPLIED | STATES | Schrodinger equation | SEMICLASSICAL SOLUTIONS | NONLINEARITY | ground state solutions of Nehari-Pankov type | POTENTIALS | critical Sobolev exponent

Critical sobolev exponent | Non-Nehari-manifold method | Ground state solutions of Nehari-Pankov type | Schrödinger equation | non-Nehari-manifold method | MATHEMATICS | MATHEMATICS, APPLIED | STATES | Schrodinger equation | SEMICLASSICAL SOLUTIONS | NONLINEARITY | ground state solutions of Nehari-Pankov type | POTENTIALS | critical Sobolev exponent

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

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

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

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

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

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

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

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

In this paper, we prove the existence of ground state sign‐changing solutions for the following class of elliptic equation:...

ground state sign‐changing solutions | p‐Laplacian equations | non‐Nehari manifold method | ground state sign-changing solutions | p-Laplacian equations | non-Nehari manifold method | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | NODAL SOLUTIONS | HIGH-ENERGY SOLUTIONS | ELLIPTIC-EQUATIONS | NEHARI-MANIFOLD METHOD | Ground state | Energy use | Helium | Mathematical analysis | Continuity (mathematics)

ground state sign‐changing solutions | p‐Laplacian equations | non‐Nehari manifold method | ground state sign-changing solutions | p-Laplacian equations | non-Nehari manifold method | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | NODAL SOLUTIONS | HIGH-ENERGY SOLUTIONS | ELLIPTIC-EQUATIONS | NEHARI-MANIFOLD METHOD | Ground state | Energy use | Helium | Mathematical analysis | Continuity (mathematics)

Journal Article

19.
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Ground states for a class of critical quasilinear coupled superlinear elliptic systems

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2020, Volume 79, Issue 4, pp. 889 - 907

In this work we consider the following class of quasilinear coupled systems...

Nehari method | Variational methods | Ground states | Quasilinear Schrödinger elliptic systems | SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS | PLASMA | Quasilinear Schrodinger elliptic systems | STANDING WAVES | Infinity | Continuity (mathematics)

Nehari method | Variational methods | Ground states | Quasilinear Schrödinger elliptic systems | SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS | PLASMA | Quasilinear Schrodinger elliptic systems | STANDING WAVES | Infinity | Continuity (mathematics)

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

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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