Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problem via variational techniques

Donal O'Regan

doi:10.5817/AM2015-3-163

Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problem via variational techniques

Donal O'Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

6 Citations (Scopus)

Abstract

This paper discusses the existence and multiplicity of solutions for a class of p(x)-Kirchhoff type problems with Dirichlet boundary data of the following form (Formula presented), where Ω is a smooth open subset of ℝ^N and pϵ C(formula presented) with N < p^- = inf_x_ϵΩ p(x) ≤ p⁺ = sup inf_x_ϵΩ p(x) <+∞, a, b are positive constants and f : (formula presented) × ℝ → ℝ is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.

Original language	English (Ireland)
Pages (from-to)	163-173
Number of pages	10
Journal	Arch. Math. (Brno)
Volume	51
Issue number	3
DOIs	https://doi.org/10.5817/AM2015-3-163
Publication status	Published - 1 Jan 2015

Keywords

Critical point theory
Existence results
Genus theory
Nonlocal problems kirchhoff equation

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Mokhtari, A. and Moussaoui, T. and O'Regan, D.

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10.5817/AM2015-3-163

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abstract = "This paper discusses the existence and multiplicity of solutions for a class of p(x)-Kirchhoff type problems with Dirichlet boundary data of the following form (Formula presented), where Ω is a smooth open subset of ℝN and pϵ C(formula presented) with N < p- = infxϵΩ p(x) ≤ p+ = sup infxϵΩ p(x) <+∞, a, b are positive constants and f : (formula presented) × ℝ → ℝ is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.",

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AU - O'Regan, Donal

PY - 2015/1/1

Y1 - 2015/1/1

N2 - This paper discusses the existence and multiplicity of solutions for a class of p(x)-Kirchhoff type problems with Dirichlet boundary data of the following form (Formula presented), where Ω is a smooth open subset of ℝN and pϵ C(formula presented) with N < p- = infxϵΩ p(x) ≤ p+ = sup infxϵΩ p(x) <+∞, a, b are positive constants and f : (formula presented) × ℝ → ℝ is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.

AB - This paper discusses the existence and multiplicity of solutions for a class of p(x)-Kirchhoff type problems with Dirichlet boundary data of the following form (Formula presented), where Ω is a smooth open subset of ℝN and pϵ C(formula presented) with N < p- = infxϵΩ p(x) ≤ p+ = sup infxϵΩ p(x) <+∞, a, b are positive constants and f : (formula presented) × ℝ → ℝ is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.

KW - Critical point theory

KW - Existence results

KW - Genus theory

KW - Nonlocal problems kirchhoff equation

UR - https://www.scopus.com/pages/publications/84942106799

U2 - 10.5817/AM2015-3-163

DO - 10.5817/AM2015-3-163

M3 - Article

VL - 51

SP - 163

EP - 173

JO - Arch. Math. (Brno)

JF - Arch. Math. (Brno)

IS - 3

ER -

Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problem via variational techniques

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

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