Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (1): 201-211.

• Articles • Previous Articles     Next Articles

Discussion on the Existence of Solution to Nonlinear Boundary Value Problem with Generalized p-Laplacian Operator

魏利, Ravi P Agarwal   

  1. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061|Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA
  • Received:2010-11-29 Revised:2011-10-18 Online:2012-02-25 Published:2012-02-25
  • Supported by:

    国家自然科学基金(11071053)、河北省自然科学基金(A2010001482)和河北省教育厅科学研究计划项目(2010第二批)资助

Abstract:

Two kinds of nonlinear boundary value problems with generalized p-Laplacian operator are studied in this paper. By using a result on the existence of solutions for variational inequalities, the result on the existence of solution of the nonlinear Dirichlet boundary value problem with generalized p-Laplacian operator is proved. Later, a kind of nonlinear Neumann boundary value problem with generalized p-Laplacian operator is presented. By digging deeply into the relationship between the above two kinds of nonlinear boundary value problems and by using a perturbation resulton the ranges of maximal monotone operators, an abstractresult for the existence of solution of the nonlinear Neumann boundary value problem with generalized p-Laplacianoperatoris obtained. In this paper, somenew prooftechniques areemployed, which extend and complement some of the previous research work.

Key words: Maximal monotone operator, Hemi-continuousmapping, Generalized p-Laplacian operator, Sum of ranges, Nonlinear Dirichlet (Neumann) boundary value problem

CLC Number: 

  • 47H09
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