Multiple solutions for a class of p(x)-Laplacian equations in RN involving the critical exponent

Yongqiang Fu; Xia Zhang

doi:10.1098/rspa.2009.0463

Multiple solutions for a class of p(x)-Laplacian equations in R^N involving the critical exponent

Yongqiang Fu
, Xia Zhang^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

65 Scopus citations

Abstract

In this paper, we first establish a principle of concentration compactness in W1,p(x)(RN). Then, based on this concentration compactness principle, we study the existence of solutions for a class of p(x)-Laplacian equations in RN involving the critical exponent. Under suitable assumptions, we obtain a sequence of radially symmetric solutions associated with a sequence of positive energies going towards infinity.

Original language	English
Pages (from-to)	1667-1686
Number of pages	20
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	466
Issue number	2118
DOIs	https://doi.org/10.1098/rspa.2009.0463
State	Published - 8 Jun 2010

Keywords

Multiple solution
P(x)-Laplacian equation
Variable exponent sobolev space

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10.1098/rspa.2009.0463

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abstract = "In this paper, we first establish a principle of concentration compactness in W1,p(x)(RN). Then, based on this concentration compactness principle, we study the existence of solutions for a class of p(x)-Laplacian equations in RN involving the critical exponent. Under suitable assumptions, we obtain a sequence of radially symmetric solutions associated with a sequence of positive energies going towards infinity.",

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AU - Fu, Yongqiang

AU - Zhang, Xia

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Y1 - 2010/6/8

N2 - In this paper, we first establish a principle of concentration compactness in W1,p(x)(RN). Then, based on this concentration compactness principle, we study the existence of solutions for a class of p(x)-Laplacian equations in RN involving the critical exponent. Under suitable assumptions, we obtain a sequence of radially symmetric solutions associated with a sequence of positive energies going towards infinity.

AB - In this paper, we first establish a principle of concentration compactness in W1,p(x)(RN). Then, based on this concentration compactness principle, we study the existence of solutions for a class of p(x)-Laplacian equations in RN involving the critical exponent. Under suitable assumptions, we obtain a sequence of radially symmetric solutions associated with a sequence of positive energies going towards infinity.

KW - Multiple solution

KW - P(x)-Laplacian equation

KW - Variable exponent sobolev space

UR - https://www.scopus.com/pages/publications/77953436511

U2 - 10.1098/rspa.2009.0463

DO - 10.1098/rspa.2009.0463

M3 - 文章

AN - SCOPUS:77953436511

SN - 1364-5021

VL - 466

SP - 1667

EP - 1686

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2118

ER -

Multiple solutions for a class of p(x)-Laplacian equations in R^N involving the critical exponent

Abstract

Keywords

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