Existence and Multiplicity of Solutions for p(x)-LaplacianEquations in $${\mathbb {R}}^N$$ R N

Li, Ying; Liu, Lin

doi:10.1007/s40840-015-0142-0

Cited by 9 publications

(8 citation statements)

References 15 publications

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“…By a simple transformation, they found that the solutions of autonomous Kirchhoff-type equation or system could be obtained by using the known solutions of the corresponding local equation or system, which is very interesting. In [3], Ying Li and Lin Li considered the existence and multiplicity of solutions to a class of p(x)-Laplacian-like equations. They introduced a revised Ambrosetti-Rabinowitz condition and obtained that the problem had a nontrivial solution and infinitely many solutions, respectively.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity

Yao

Han

2019

Discrete Dynamics in Nature and Society

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In this paper, we firstly discuss the existence of the least energy sign-changing solutions for a class of p-Kirchhoff-type problems with a (2p-1)-linear growth nonlinearity. The quantitative deformation lemma and Non-Nehari manifold method are used in the paper to prove the main results. Remarkably, we use a new method to verify that Mb≠∅. The main results of our paper are the existence of the least energy sign-changing solution and its corresponding energy doubling property. Moreover, we also give the convergence property of the least energy sign-changing solution as the parameter b↘0.

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Section: Introduction and The Main Resultsmentioning

confidence: 99%

The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity

Yao

Han

2019

Discrete Dynamics in Nature and Society

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“…The main role of AR-condition is to ensure the compactness required by minimax arguments, and without the AR-condition the situation is more complicated. However, there are many functions which are superlinear at infinity, but do not satisfy the AR-condition, and these functions have attracted much interest in recent years, for example; see [29][30][31][32][33]. In this paper, under no AR-condition, we study the existence of nontrivial periodic solutions for problem (1.3) with p + -superlinear nonlinear terms at infinity.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Periodic solutions for nonlocal $p(t)$-Laplacian systems

Shengui

2019

Bound Value Probl

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The purpose of this paper is to investigate the existence of periodic solutions for a class of nonlocal p(t)-Laplacian systems. When the nonlinear term is p +-superlinear at infinity, some new solvability conditions of nontrivial periodic solutions are obtained by using a version of the local linking theorem. A major point is that we ensure compactness without the well-known Ambrosetti-Rabinowitz type superlinearity condition. In addition, by applying the saddle point theorem, we established the existence of at least one periodic solution for such problems with a p-subquadratic potential.

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“…The results were extended by G. Bin in [3], where the Ambrosetti-Rabinowitz type condition did not hold. Some further results on this type of problems can be found in the papers [17,22].…”

Section: Introductionmentioning

confidence: 90%

EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR SOME p(x)-LAPLACIAN-LIKE PROBLEMS VIA VARIATIONAL METHODS

Afrouzi¹,

Shokooh²,

Chung³

2017

Journal of applied mathematics & informatics

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Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti-Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F .

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Existence and Multiplicity of Solutions for p(x)-LaplacianEquations in $${\mathbb {R}}^N$$ R N

Abstract: This article concerns the existence and multiplicity of solutions to a class of p(x)-Laplacian-like equations. We introduce a revised Ambrosetti-Rabinowitz condition, and show that the problem has a nontrivial solution and infinitely many solutions, respectively.

Cited by 9 publications

References 15 publications

The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity

The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity

Periodic solutions for nonlocal $p(t)$-Laplacian systems

EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR SOME p(x)-LAPLACIAN-LIKE PROBLEMS VIA VARIATIONAL METHODS

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