Multiple solutions for ${\bm p}({\bm x})$-Laplacian problems in ${\bf R}^{\bm N}$

CHEN Zi-gao

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Sep. 2012

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CHEN Zi-gao. Multiple solutions for ${\bm p}({\bm x})$-Laplacian problems in ${\bf R}^{\bm N}$[J]. Journal of East China Normal University (Natural Sciences), 2012, (5): 109-119.

Citation:

CHEN Zi-gao. Multiple solutions for ${\bm p}({\bm x})$-Laplacian problems in ${\bf R}^{\bm N}$[J]. Journal of East China Normal University (Natural Sciences), 2012, (5): 109-119.

CHEN Zi-gao. Multiple solutions for ${\bm p}({\bm x})$-Laplacian problems in ${\bf R}^{\bm N}$[J]. Journal of East China Normal University (Natural Sciences), 2012, (5): 109-119.

Citation:

CHEN Zi-gao. Multiple solutions for ${\bm p}({\bm x})$-Laplacian problems in ${\bf R}^{\bm N}$[J]. Journal of East China Normal University (Natural Sciences), 2012, (5): 109-119.

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Multiple solutions for ${\bm p}({\bm x})$-Laplacian problems in ${\bf R}^{\bm N}$

CHEN Zi-gao

1.
Department of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou Henan} 450011, China

Received Date: 2011-12-01
Rev Recd Date: 2012-03-01
Publish Date: 2012-09-25

Abstract

Abstract

By using the fountain theorem and the dual fountain theorem, respectively, the existence and multiplicity of solutions for $p(x$)-Laplacian equations in $\mathbf{R}^{N}$ were studied, assumed that one of the perturbation terms $f_1(x,u),\, f_2(x,u)$ is superlinear and satisfies the Ambrosetti-Rabinowitz type condition and the other one is sublinear. The discussion was based on variable exponent Lebesgue and Sobolev spaces.
- variable exponent Sobolev spaces,
- $p(x)$-Laplacian,
- (PS)$_c^\ast$ condition,
- fountain theorem,
- dual fountain theorem

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References(1)

References

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