Multiplicity of solutions for a singular $p$-laplacian elliptic equation

Volume 99 / 2010

Wen-shu Zhou, Xiao-dan Wei Annales Polonici Mathematici 99 (2010), 157-180 MSC: Primary 35J25; Secondary 35J75. DOI: 10.4064/ap99-2-4

Abstract

The existence of two continuous solutions for a nonlinear singular elliptic equation with natural growth in the gradient is proved for the Dirichlet problem in the unit ball centered at the origin. The first continuous solution is positive and maximal; it is obtained via the regularization method. The second continuous solution is zero at the origin, and follows by considering the corresponding radial ODE and by sub-sup solutions method.

Authors

  • Wen-shu ZhouDepartment of Mathematics
    Dalian Nationalities University
    116600 Dalian, P.R. China
  • Xiao-dan WeiDepartment of Mathematics
    Dalian Nationalities University
    116600 Dalian, P.R. China
    e-mail

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