Applied Mathematics Letters, ISSN 0893-9659, 06/2017, Volume 68, pp. 8 - 12

The aim of this paper is to study the following Schrödinger–Poisson problem (SP)−△u+V(x)u+εϕ(x)u=λf(u),inR3,−△ϕ=u2,lim|x|→+∞ϕ(x)=0,inR3,u>0,inR3.We prove...

Variational methods | Schrödinger–Poisson system | Priori estimate | Schrodinger-Poisson system | MATHEMATICS, APPLIED | MULTIPLICITY | EQUATIONS | RADIAL POTENTIALS | KIRCHHOFF TYPE PROBLEMS

Variational methods | Schrödinger–Poisson system | Priori estimate | Schrodinger-Poisson system | MATHEMATICS, APPLIED | MULTIPLICITY | EQUATIONS | RADIAL POTENTIALS | KIRCHHOFF TYPE PROBLEMS

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

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

3.
Full Text
Existence and concentration behavior of positive solutions for a Kirchhoff equation in R 3

Journal of Differential Equations, ISSN 0022-0396, 2012, Volume 252, Issue 2, pp. 1813 - 1834

We study the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem { − ( ε 2 a + ε b ∫ R 3 | ∇ u |...

Kirchhoff type equation | Positive solutions | Variational methods | MATHEMATICS | NONLINEAR SCHRODINGER-EQUATIONS | MULTIPLICITY | REGULARITY | SEMICLASSICAL STATES | QUASILINEAR ELLIPTIC-EQUATIONS | PRINCIPLE

Kirchhoff type equation | Positive solutions | Variational methods | MATHEMATICS | NONLINEAR SCHRODINGER-EQUATIONS | MULTIPLICITY | REGULARITY | SEMICLASSICAL STATES | QUASILINEAR ELLIPTIC-EQUATIONS | PRINCIPLE

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 02/2013, Volume 254, Issue 4, pp. 2015 - 2032

In this paper we consider the quasilinear Schrödinger equation−Δu+V(x)u−Δ(u2)u=g(x,u),x∈RN, where g and V are periodic in x1,…,xN and g is odd in u,...

Multiplicity of solutions | Quasilinear Schrödinger equation | Nehari manifold | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Multiplicity of solutions | Quasilinear Schrödinger equation | Nehari manifold | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Journal Article

Results in Mathematics, ISSN 1422-6383, 6/2019, Volume 74, Issue 2, pp. 1 - 34

We consider parametric Dirichlet problems driven by the sum of a p-Laplacian ($$p>2$$ p>2 ) and a Laplacian ((p, 2)-equation) and with a reaction term which...

constant sign and nodal solutions | 35J20 | 58E05 | 35J60 | critical groups | 35J92 | Competing nonlinearities | concave term | Mathematics, general | multiplicity theorems | Mathematics | resonance | MATHEMATICS, APPLIED | MATHEMATICS | NODAL SOLUTIONS | NONLINEAR ELLIPTIC-EQUATIONS | GROWTH | CONSTANT SIGN | Q)-EQUATIONS | Computer science

constant sign and nodal solutions | 35J20 | 58E05 | 35J60 | critical groups | 35J92 | Competing nonlinearities | concave term | Mathematics, general | multiplicity theorems | Mathematics | resonance | MATHEMATICS, APPLIED | MATHEMATICS | NODAL SOLUTIONS | NONLINEAR ELLIPTIC-EQUATIONS | GROWTH | CONSTANT SIGN | Q)-EQUATIONS | Computer science

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 7110 - 7124

In this paper, our main purpose is to establish the existence results of positive solutions for a p−q‐Laplacian system involving concave‐convex nonlinearities:...

critical nonlinearities | positive solutions | p−q‐Laplacian | critical exponent | Critical exponent | Critical nonlinearities | Positive solutions | P − q-Laplacian | MATHEMATICS, APPLIED | NUMBER | MULTIPLICITY | CONCAVE-CONVEX NONLINEARITIES | NEHARI MANIFOLD | ELLIPTIC PROBLEMS | CRITICAL GROWTH | DOMAIN TOPOLOGY | p - q-Laplacian | CRITICAL SOBOLEV EXPONENTS | CHANGING WEIGHT FUNCTION | EQUATION | Variational methods

critical nonlinearities | positive solutions | p−q‐Laplacian | critical exponent | Critical exponent | Critical nonlinearities | Positive solutions | P − q-Laplacian | MATHEMATICS, APPLIED | NUMBER | MULTIPLICITY | CONCAVE-CONVEX NONLINEARITIES | NEHARI MANIFOLD | ELLIPTIC PROBLEMS | CRITICAL GROWTH | DOMAIN TOPOLOGY | p - q-Laplacian | CRITICAL SOBOLEV EXPONENTS | CHANGING WEIGHT FUNCTION | EQUATION | Variational methods

Journal Article

JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, 02/2013, Volume 254, Issue 4, pp. 2015 - 2032

In this paper we consider the quasilinear Schrodinger equation -Delta u + V(x)u - Delta(u(2))u = g(x, u), x is an element of R-N, where g and V are periodic in...

SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS | SOLITON-SOLUTIONS | Multiplicity of solutions | Nehari manifold | Quasilinear Schrodinger equation

SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS | SOLITON-SOLUTIONS | Multiplicity of solutions | Nehari manifold | Quasilinear Schrodinger equation

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 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

MATHEMATICS | Kirchhoff equation | R-N | MULTIPLICITY | Variational methods | REGULARITY | MAXWELL EQUATIONS | GROWTH | QUASILINEAR ELLIPTIC-EQUATIONS | Pohozaev type identity | Ground state solutions

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 04/2019, Volume 266, Issue 9, pp. 5912 - 5941

In this paper we study the following type of the Schrödinger–Poisson–Slater equation with critical growth−△u+(u2⋆1|4πx|)u=μ|u|p−1u+|u|4u,inR3, where μ>0 and...

Concentration-compactness principle | Perturbation technique | Schrödinger–Poisson–Slater problem | Positive solution | SYSTEM | MATHEMATICS | MULTIPLICITY | BOUND-STATES | SPHERES | SIGN-CHANGING SOLUTIONS | ATOMS | Schrodinger-Poisson-Slater problem

Concentration-compactness principle | Perturbation technique | Schrödinger–Poisson–Slater problem | Positive solution | SYSTEM | MATHEMATICS | MULTIPLICITY | BOUND-STATES | SPHERES | SIGN-CHANGING SOLUTIONS | ATOMS | Schrodinger-Poisson-Slater problem

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 04/2014, Volume 232, pp. 313 - 323

•The model we study is much closer to real situation compared to existing research.•Conditions of solution existence are more easily to be obtained by our...

Multiplicity of solutions | Leray–Schauder degree theory | Upper and lower solutions | Fractional differential equations | Integral boundary value problems | Leray-Schauder degree theory | EXISTENCE | MATHEMATICS, APPLIED | REVERSED ORDER | MONOTONE ITERATIVE METHOD | SOLVABILITY | 1ST-ORDER | Differential equations

Multiplicity of solutions | Leray–Schauder degree theory | Upper and lower solutions | Fractional differential equations | Integral boundary value problems | Leray-Schauder degree theory | EXISTENCE | MATHEMATICS, APPLIED | REVERSED ORDER | MONOTONE ITERATIVE METHOD | SOLVABILITY | 1ST-ORDER | Differential equations

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 12/2019, Volume 267, Issue 12, pp. 7411 - 7461

In this paper, we study the existence of localized nodal solutions for a class of semiclassical quasilinear Schrödinger equations including, as a special case,...

Nodal solutions | Variational perturbation method | Modified nonlinear Schrödinger equation (MNLS) | Semiclassical states | EXISTENCE | Modified nonlinear Schrodinger equation (MNLS) | MULTIPLICITY | STABILITY | STANDING WAVES | CRITICAL FREQUENCY | MATHEMATICS | SOLITON-SOLUTIONS | PROFILE | BOUND-STATES | ELLIPTIC-EQUATIONS

Nodal solutions | Variational perturbation method | Modified nonlinear Schrödinger equation (MNLS) | Semiclassical states | EXISTENCE | Modified nonlinear Schrodinger equation (MNLS) | MULTIPLICITY | STABILITY | STANDING WAVES | CRITICAL FREQUENCY | MATHEMATICS | SOLITON-SOLUTIONS | PROFILE | BOUND-STATES | ELLIPTIC-EQUATIONS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2016, Volume 437, Issue 1, pp. 160 - 180

In this paper, we consider the following Schrödinger–Poisson system with singularity{−Δu+ηϕu=μu−r,inΩ,−Δϕ=u2,inΩ,u>0,inΩ,u=ϕ=0,on∂Ω, where Ω⊂R3 is a smooth...

Singularity | Schrödinger–Poisson system | Multiplicity | Uniqueness | Schrödinger-Poisson system | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | NONLINEARITY | EQUATIONS | GROUND-STATE SOLUTIONS | MATHEMATICS | SIGN-CHANGING SOLUTIONS | R-3 | SEMILINEAR ELLIPTIC PROBLEM

Singularity | Schrödinger–Poisson system | Multiplicity | Uniqueness | Schrödinger-Poisson system | Schrodinger-Poisson system | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | NONLINEARITY | EQUATIONS | GROUND-STATE SOLUTIONS | MATHEMATICS | SIGN-CHANGING SOLUTIONS | R-3 | SEMILINEAR ELLIPTIC PROBLEM

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2015, Volume 429, Issue 2, pp. 1153 - 1172

In this paper, we study the following nonlinear Kirchhoff-type equation where is nonnegative. By using the variational method, we obtain the existence of...

Kirchhoff-type equation | Zero mass | Critical exponent | Variational methods | EXISTENCE | MATHEMATICS, APPLIED | STATES | MULTIPLICITY | CRITICAL NONLINEARITY | MATHEMATICS | CRITICAL GROWTH | R-3 | CRITICAL SOBOLEV EXPONENTS | ELLIPTIC-EQUATIONS

Kirchhoff-type equation | Zero mass | Critical exponent | Variational methods | EXISTENCE | MATHEMATICS, APPLIED | STATES | MULTIPLICITY | CRITICAL NONLINEARITY | MATHEMATICS | CRITICAL GROWTH | R-3 | CRITICAL SOBOLEV EXPONENTS | ELLIPTIC-EQUATIONS

Journal Article

14.
Full Text
Positive solutions of generalized nonlinear logistic equations via sub-super solutions

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2019, Volume 471, Issue 1-2, pp. 653 - 670

Let Ω be a smooth bounded domain in RN, N≥1, let m,n be two nonnegative functions defined in Ω, and let ϕ:RN→RN be a continuous and strictly monotone mapping....

Orlicz–Sobolev spaces | ϕ-Laplacian | Logistic equations | Sub and supersolutions | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | phi-Laplacian | Orlicz-Sobolev spaces | MULTIPLICITY RESULT | DIRICHLET PROBLEM | UNIQUENESS

Orlicz–Sobolev spaces | ϕ-Laplacian | Logistic equations | Sub and supersolutions | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | phi-Laplacian | Orlicz-Sobolev spaces | MULTIPLICITY RESULT | DIRICHLET PROBLEM | UNIQUENESS

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 12

In this paper, we investigate the existence and multiplicity of nontrivial weak solutions for a class of nonlinear impulsive (q, p)-Laplacian dynamical...

(q, p) -Laplacian | variational methods | existence | multiplicity | nontrivial solution | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | P-LAPLACIAN | 2ND-ORDER DIFFERENTIAL-SYSTEMS | EQUATIONS | (q, p)-Laplacian | Theorems (Mathematics) | Usage | Variational principles | Laplacian operator | Nonlinear systems | Dynamical systems | Critical point | ( q , p ) $(q,p)$ -Laplacian

(q, p) -Laplacian | variational methods | existence | multiplicity | nontrivial solution | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | P-LAPLACIAN | 2ND-ORDER DIFFERENTIAL-SYSTEMS | EQUATIONS | (q, p)-Laplacian | Theorems (Mathematics) | Usage | Variational principles | Laplacian operator | Nonlinear systems | Dynamical systems | Critical point | ( q , p ) $(q,p)$ -Laplacian

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2017, Volume 455, Issue 2, pp. 1559 - 1578

We study the existence and asymptotic behavior of the least energy sign-changing solutions to a gauged nonlinear Schrödinger...

Gauged Schrödinger equation | Asymptotic behavior | Least energy sign-changing solutions | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | WAVES | SCALAR FIELD-EQUATIONS | NODAL SOLUTIONS | MULTIPLICITY | Gauged Schrodinger equation | POSITIVE SOLUTIONS

Gauged Schrödinger equation | Asymptotic behavior | Least energy sign-changing solutions | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | WAVES | SCALAR FIELD-EQUATIONS | NODAL SOLUTIONS | MULTIPLICITY | Gauged Schrodinger equation | POSITIVE SOLUTIONS

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

Journal of Mathematical Physics, ISSN 0022-2488, 01/2019, Volume 60, Issue 1, p. 11506

In this paper, we study the existence of infinitely many solutions for a fractional Kirchhoff–Schrödinger–Poisson system. Based on variational methods,...

EXISTENCE | MULTIPLICITY | PHYSICS, MATHEMATICAL | EQUATION | Consumer goods | Variational methods | Theorems

EXISTENCE | MULTIPLICITY | PHYSICS, MATHEMATICAL | EQUATION | Consumer goods | Variational methods | Theorems

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2019, Volume 45, pp. 542 - 556

In this paper, the problem of periodic solutions is studied for Liénard equations with anindefinite singularity x′′(t)+f(x(t))x′(t)+φ(t)xm(t)−α(t)xμ(t)=0,where...

Singularity | Continuation theorem | Periodic solution | Liénard equation | EXISTENCE | MATHEMATICS, APPLIED | MOTION | MULTIPLICITY | Lienard equation | 2ND-ORDER DIFFERENTIAL-EQUATIONS | ATOM

Singularity | Continuation theorem | Periodic solution | Liénard equation | EXISTENCE | MATHEMATICS, APPLIED | MOTION | MULTIPLICITY | Lienard equation | 2ND-ORDER DIFFERENTIAL-EQUATIONS | ATOM

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2017, Volume 455, Issue 2, pp. 1152 - 1177

In this paper, we consider the critical Klein–Gordon–Maxwell system with external potential. When the potential well is steep, by using the penalization...

Klein–Gordon–Maxwell system | Variational method | Critical growth | EXISTENCE | MATHEMATICS, APPLIED | EXPONENTS | MULTIPLICITY | NONEXISTENCE | POSITIVE SOLUTIONS | WELL |

Klein–Gordon–Maxwell system | Variational method | Critical growth | EXISTENCE | MATHEMATICS, APPLIED | EXPONENTS | MULTIPLICITY | NONEXISTENCE | POSITIVE SOLUTIONS | WELL |