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

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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.

Keywords

p(x)-Laplacian-like operator Variational method Radial solution Ambrosetti–Rabinowitz condition 

Mathematics Subject Classification

35J60 35J20 47J30 58E30 

Notes

Acknowledgments

The authors are very grateful to the anonymous referees for their knowledgeable reports, which helped us to improve our manuscript.

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  1. 1.Department of Mathematics and System Science, College of ScienceNational University of Defense TechnologyChangshaChina
  2. 2.School of Mathematics and StatisticsChongqing Technology and Business UniversityChongqingChina

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