Existence of infinitely many weak solutions for the -Laplacian with nonlinear boundary conditions

Abstract. We analyze a class of quasilinear elliptic problems involving a p(·)-Laplace-type operator on a bounded domain Ω ⊂ R N , N ≥ 2, and we deal with nonlinear conditions on the boundary. Working on the variable exponent Lebesgue-Sobolev spaces, we follow the steps described by the "fountain theorem" and we establish the existence of a sequence of weak solutions. Mathematics Subject Classification (2010

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“…Another remark is that the first example enables us to connect (1) to the problem presented in [29],…”

Section: A(x −η) = A(x η)mentioning

confidence: 99%

Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions

Boureanu

Preda

2011

Nonlinear Differ. Equ. Appl.

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“…Regarding existence and multiplicity of solutions to (1.2) we point out (without guarantee of completeness) the papers in [20], [21], [22], [30], [32], [37], [46], [48], and the references therein. Referring to homogeneous Neumann problems, the existence of at least three solutions in case p > N was shown with different methods for example in [1], [5] and [6] (see also [7] for infinitely many solutions) while the more complicated case p ≤ N was recently studied in [19].…”

Section: Introductionmentioning

confidence: 99%

Multiplicity results to a class of variational-hemivariational inequalities

Bonanno¹,

Winkert²

2016

TMNA

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Abstract. This paper deals with variational-hemivariational inequalities involving the p-Laplace operator and a nonlinear Neumann boundary condition. Based on an abstract critical point result, which is developed at the beginning of the paper, it is shown the existence of at least three solutions to such inequalities whereby the cases p > N and p ≤ N are treated separately. The applicability of these results is emphasized with suitable examples.

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“…The existence of nontrivial solutions to nonlinear elliptic boundary value problems has been extensively studied by many researchers; see [7,8,13,26,27,28,31] and references therein. Motivated by the pioneer work of A. Ambrosetti and P. Rabinowitz in [1], J. Yao [28] showed the existence of nontrivial solutions for the inhomogeneous and nonlinear Neumann boundary value problems involving the p(x)-Laplacian; see [7] for p(x)-Laplace type operator.…”

Section: Introductionmentioning

confidence: 99%

MULTIPLE SOLUTIONS FOR EQUATIONS OF p(x)-LAPLACE TYPE WITH NONLINEAR NEUMANN BOUNDARY CONDITION

Ki¹,

Park²

2016

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace typewhich is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type |v| p(x)−2 v with continuous function p : Ω → (1, ∞) and the functions f, g satisfy a Carathéodory condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.

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Existence of infinitely many weak solutions for the -Laplacian with nonlinear boundary conditions

Cited by 31 publications

References 14 publications

Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions

Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions

Multiplicity results to a class of variational-hemivariational inequalities

MULTIPLE SOLUTIONS FOR EQUATIONS OF p(x)-LAPLACE TYPE WITH NONLINEAR NEUMANN BOUNDARY CONDITION

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