Applied Mathematics Letters, ISSN 0893-9659, 04/2020, Volume 102, p. 106148

We consider a class of generalized quasilinear Schrödinger equations where is a parameter, , , , is the real function. Under mild conditions posed on and...

Ground state | Generalized quasilinear Schrödinger equations | Asymptotic behavior

Ground state | Generalized quasilinear Schrödinger equations | Asymptotic behavior

Journal Article

Applicable Analysis, ISSN 0003-6811, 2019, pp. 1 - 16

Journal Article

Communications on Pure and Applied Analysis, ISSN 1534-0392, 05/2016, Volume 15, Issue 3, pp. 853 - 870

We establish the existence of nontrivial solutions for the following quasilinear Schrodinger equation with critical Sobolev exponent: -Delta u + V(x)u -...

Generalized | Critical exponents | Quasilinear Schrodinger equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | generalized | SOLITON-SOLUTIONS | GROUND-STATE | POSITIVE SOLUTIONS | critical exponents

Generalized | Critical exponents | Quasilinear Schrodinger equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | generalized | SOLITON-SOLUTIONS | GROUND-STATE | POSITIVE SOLUTIONS | critical exponents

Journal Article

Applicable Analysis, ISSN 0003-6811, 2019, pp. 1 - 24

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2017, Volume 14, Issue 5

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2017, Volume 14, Issue 5, pp. 1 - 20

In this paper, we study the following generalized quasilinear Schrödinger equation: $$\begin{aligned} -\text {div}(g^2(u)\nabla u)+g(u)g'(u)|\nabla...

ground state solutions | Mathematics, general | Mathematics | periodic potential | Primary 35J60 | bounded potential | Secondary 35J20 | Generalized quasilinear Schrödinger equation

ground state solutions | Mathematics, general | Mathematics | periodic potential | Primary 35J60 | bounded potential | Secondary 35J20 | Generalized quasilinear Schrödinger equation

Journal Article

Far East Journal of Mathematical Sciences, ISSN 0972-0871, 05/2016, Volume 99, Issue 9, pp. 1283 - 1295

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 12/2017, Volume 19, Issue 4, pp. 3127 - 3149

We investigate the existence of ground state sign-changing solutions for the following elliptic equation of Kirchhoff type: $$\begin{aligned}...

ground state sign-changing solutions | Mathematical Methods in Physics | Analysis | Generalized quasilinear Schrödinger equations | Mathematics, general | Mathematics | non-Nehari manifold method | Kirchhoff-type perturbation | Primary 35J60 | Secondary 35J20 | EXISTENCE | MATHEMATICS, APPLIED | Generalized quasilinear Schrodinger equations | HIGH-ENERGY SOLUTIONS | NEHARI-MANIFOLD METHOD | INFINITY | MATHEMATICS | LOCAL SUBLINEAR NONLINEARITIES | R-N | SOLITON-SOLUTIONS | NODAL SOLUTIONS | BOUNDED DOMAINS | ELLIPTIC-EQUATIONS

ground state sign-changing solutions | Mathematical Methods in Physics | Analysis | Generalized quasilinear Schrödinger equations | Mathematics, general | Mathematics | non-Nehari manifold method | Kirchhoff-type perturbation | Primary 35J60 | Secondary 35J20 | EXISTENCE | MATHEMATICS, APPLIED | Generalized quasilinear Schrodinger equations | HIGH-ENERGY SOLUTIONS | NEHARI-MANIFOLD METHOD | INFINITY | MATHEMATICS | LOCAL SUBLINEAR NONLINEARITIES | R-N | SOLITON-SOLUTIONS | NODAL SOLUTIONS | BOUNDED DOMAINS | ELLIPTIC-EQUATIONS

Journal Article

9.
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 where , , , and are 1-periodic on . By using a change of variable, we obtain...

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

Complex Variables and Elliptic Equations, ISSN 1747-6933, 06/2016, Volume 61, Issue 6, pp. 817 - 842

We study the existence of standing wave solutions for a class of quasilinear Schrödinger equations with subcritical or critical growth where is a given...

35J20 | critical exponents | generalized | 35J62 | quasilinear Schrödinger equations | Minimax methods | EXISTENCE | MATHEMATICS | R-N | quasilinear Schrodinger equations | SPACE DIMENSION | CRITICAL GROWTH | Standing waves | Theorems | Variational methods | Mathematical analysis | Images | Combing | Schroedinger equation | Complex variables

35J20 | critical exponents | generalized | 35J62 | quasilinear Schrödinger equations | Minimax methods | EXISTENCE | MATHEMATICS | R-N | quasilinear Schrodinger equations | SPACE DIMENSION | CRITICAL GROWTH | Standing waves | Theorems | Variational methods | Mathematical analysis | Images | Combing | Schroedinger equation | Complex variables

Journal Article

MEDITERRANEAN JOURNAL OF MATHEMATICS, ISSN 1660-5446, 10/2017, Volume 14, Issue 5, p. 1

In this paper, we study the following generalized quasilinear Schrodinger equation: -div(g(2)(u)del u) + g(u)g'(u)|del u|(2) + V(x)u = f(x, u), x is an element...

EXISTENCE | POSITIVE SOLUTION | MATHEMATICS, APPLIED | Generalized quasilinear Schrodinger equation | CALCULUS | ground state solutions | CONCENTRATION-COMPACTNESS PRINCIPLE | INFINITY | MATHEMATICS | SOLITON-SOLUTIONS | GROWTH | periodic potential | bounded potential

EXISTENCE | POSITIVE SOLUTION | MATHEMATICS, APPLIED | Generalized quasilinear Schrodinger equation | CALCULUS | ground state solutions | CONCENTRATION-COMPACTNESS PRINCIPLE | INFINITY | MATHEMATICS | SOLITON-SOLUTIONS | GROWTH | periodic potential | bounded potential

Journal Article

Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 6/2018, Volume 44, Issue 3, pp. 691 - 705

This paper focuses on the following generalized quasilinear Schrödinger equations: $$\begin{aligned} -\,\mathrm{div}(\textit{g}^{2}(u)\nabla...

35J20 | Perturbation methods | 35J60 | Finite depth potential well | Generalized quasilinear Schrödinger equations | Mathematics, general | Mathematics | EXISTENCE | Generalized quasilinear Schrodinger equations | POSITIVE SOLUTIONS | FRACTIONAL EQUATIONS | PERTURBATION METHOD | MATHEMATICS | SOLITON-SOLUTIONS | PLASMA | CRITICAL GROWTH | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS | PARAMETER

35J20 | Perturbation methods | 35J60 | Finite depth potential well | Generalized quasilinear Schrödinger equations | Mathematics, general | Mathematics | EXISTENCE | Generalized quasilinear Schrodinger equations | POSITIVE SOLUTIONS | FRACTIONAL EQUATIONS | PERTURBATION METHOD | MATHEMATICS | SOLITON-SOLUTIONS | PLASMA | CRITICAL GROWTH | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS | PARAMETER

Journal Article

13.
Full Text
Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems

Boundary Value Problems, ISSN 1687-2762, 12/2018, Volume 2018, Issue 1, pp. 1 - 17

This paper is concerned with the existence of ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems in R3 $\mathbb {R}^{3}$...

35J20 | 35J60 | 35J92 | Ground state | Mathematics | Generalized quasilinear | Mountain-pass theorem | Ordinary Differential Equations | Analysis | Variational principle | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Partial Differential Equations | EXISTENCE | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | EQUATIONS | SCALAR FIELD | MATHEMATICS | SOLITON-SOLUTIONS | Plasma physics | Functionals | Sobolev space | Plasma (physics)

35J20 | 35J60 | 35J92 | Ground state | Mathematics | Generalized quasilinear | Mountain-pass theorem | Ordinary Differential Equations | Analysis | Variational principle | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Partial Differential Equations | EXISTENCE | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | EQUATIONS | SCALAR FIELD | MATHEMATICS | SOLITON-SOLUTIONS | Plasma physics | Functionals | Sobolev space | Plasma (physics)

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

Computers and 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 Schrödinger-Maxwell system where , and...

Non-Nehari manifold method | Generalized quasilinear Schrödinger-Maxwell system | Ground state sign-changing solutions

Non-Nehari manifold method | Generalized quasilinear Schrödinger-Maxwell system | Ground state sign-changing solutions

Journal Article

Few-Body-Systems, ISSN 0177-7963, 5/2004, Volume 34, Issue 1, pp. 57 - 62

Quasilinear solutions of the radial Schrödinger equation for different potentials are compared with corresponding WKB solutions. For this study, the...

Physics | PHYSICS, MULTIDISCIPLINARY | LINEARIZATION METHOD | QUANTUM-MECHANICS | Mathematical analysis | Research methodology | Comparative analysis | Estimates | Generalized linear models | Quantum theory

Physics | PHYSICS, MULTIDISCIPLINARY | LINEARIZATION METHOD | QUANTUM-MECHANICS | Mathematical analysis | Research methodology | Comparative analysis | Estimates | Generalized linear models | Quantum theory

Journal Article

Russian Mathematics, ISSN 1066-369X, 1/2018, Volume 62, Issue 1, pp. 50 - 57

In the present work we develop approximation approach to evaluation of solutions to boundary-value problems for quasilinear equations of the elliptic type on...

generalized solutions | quasilinear elliptic equations | noncompact Riemannian manifolds | approximation approach | Mathematics, general | Mathematics | boundary-value problem

generalized solutions | quasilinear elliptic equations | noncompact Riemannian manifolds | approximation approach | Mathematics, general | Mathematics | boundary-value problem

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 10/2019, Volume 70, Issue 5, pp. 1 - 19

A class of generalised Schrödinger elliptic problems involving concave–convex and other types of nonlinearities is studied. A reasonable overview about the set...

35J10 | Engineering | Mathematical Methods in Physics | Generalised Schrödinger elliptic problems | Variational methods | 35J60 | Multiplicity of solutions | Theoretical and Applied Mechanics | 35J25 | EXISTENCE | MATHEMATICS, APPLIED | Generalised Schrodinger elliptic problems | SOLITON-SOLUTIONS | PLASMA | EQUATIONS

35J10 | Engineering | Mathematical Methods in Physics | Generalised Schrödinger elliptic problems | Variational methods | 35J60 | Multiplicity of solutions | Theoretical and Applied Mechanics | 35J25 | EXISTENCE | MATHEMATICS, APPLIED | Generalised Schrodinger elliptic problems | SOLITON-SOLUTIONS | PLASMA | EQUATIONS

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 3/2006, Volume 25, Issue 3, pp. 361 - 393

We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be...

Degenerate parabolic equation | Systems Theory, Control | Analysis | Mathematical and Computational Physics | Calculus of Variations and Optimal Control | Mathematics | Generalized sobolev spaces | Optimization | Global bifurcation | Global attractor | REACTION-DIFFUSION EQUATIONS | SCHRODINGER-EQUATIONS | degenerate parabolic equation | MATHEMATICS, APPLIED | global attractor | POSITIVE SOLUTIONS | INHOMOGENEOUS-MEDIUM | global bifurcation | MATHEMATICS | R-N | LINEAR EVOLUTION EQUATIONS | generalized sobolev spaces | GINZBURG-LANDAU EQUATION | KOHN-NIRENBERG INEQUALITIES | ELLIPTIC-EQUATIONS | JOSEPHSON-JUNCTIONS

Degenerate parabolic equation | Systems Theory, Control | Analysis | Mathematical and Computational Physics | Calculus of Variations and Optimal Control | Mathematics | Generalized sobolev spaces | Optimization | Global bifurcation | Global attractor | REACTION-DIFFUSION EQUATIONS | SCHRODINGER-EQUATIONS | degenerate parabolic equation | MATHEMATICS, APPLIED | global attractor | POSITIVE SOLUTIONS | INHOMOGENEOUS-MEDIUM | global bifurcation | MATHEMATICS | R-N | LINEAR EVOLUTION EQUATIONS | generalized sobolev spaces | GINZBURG-LANDAU EQUATION | KOHN-NIRENBERG INEQUALITIES | ELLIPTIC-EQUATIONS | JOSEPHSON-JUNCTIONS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 73, Issue 8, pp. 2686 - 2698

We derive some new results concerning the Cauchy problem and the existence of bound states for a class of coupled nonlinear Schrödinger-gKdV systems. In...

Bound states | Schrödinger-gKdV | Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | GENERALIZED KORTEWEG-DEVRIES | STABILITY | WAVE INTERACTIONS | EQUATIONS | SCATTERING | Schrodinger-gKdV

Bound states | Schrödinger-gKdV | Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | GENERALIZED KORTEWEG-DEVRIES | STABILITY | WAVE INTERACTIONS | EQUATIONS | SCATTERING | Schrodinger-gKdV

Journal Article

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