Acta mathematica scientia,Series A

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Existence of Multiple Solutions for the One-dimensional Singular p-Laplacian Equations

Zhang Xiaoyan;Sun Jingxian   

  1. School of Mathematics and System Science, Shandong University;Department of Mathematics, Xuzhou Normal University
  • Received:2003-12-03 Revised:2004-11-25 Online:2006-02-25 Published:2006-02-25
  • Contact: Zhang Xiaoyan

Abstract: This paper deals with the existence of multiple solutions for the singularp-Laplacian nonlinear BVP (\varphi(u'))'+a(t)f(u)=0,\ u'(0)=u(1)=0 (or u(0)=u'(1)=0), where \varphi(s)=|s|^{p-2}s,\ p>1. Sufficient conditions are established for the multiplicity of solutions of this problem by using Leggett-Williams theorem.The results presented here generalize many known results

Key words: p-Laplacian operator, Leggett-Williams theorem, Cone

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