Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE EXISTENCE AND MULTIPLICITY OF SOLUTIONS TO p-LAPLACE EQUATION WITH PERIODIC BOUNDARY CONDITIONS

  • Chen, Taiyong (College of Sciences, China University of Mining and Technology) ;
  • Liu, Wenbin (College of Sciences, China University of Mining and Technology) ;
  • Zhang, Jianjun (College of Sciences, China University of Mining and Technology) ;
  • Zhang, Huixing (College of Sciences, China University of Mining and Technology)
  • Published : 2009.05.31
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Abstract

In this paper, we consider p-Laplace equation which models the turbulent flow in a porous medium. Using a continuation principle (cf. [R. $Man{\acute{a}}sevich$ and J. Mawhin, Periodic solutions for nonlinear systems with p-Lplacian-like operators, J. Diff. Equa. 145(1998), 367-393]), we prove the existence of solutions for p-Laplace equation subject to periodic boundary conditions, under some sign and growth conditions for f. With the help of Leray-Schauder degree theory, the multiplicity of periodic solutions for p-Laplace equation is obtained under the similar conditions above and some known results are improved.

Keywords

References

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