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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (10): 1283-1292.doi: https://doi.org/10.1007/s10483-010-1361-9

• Articles • 上一篇    下一篇

Three solutions to inequalities of Dirichlet problem driven by p(x)-Laplacian

葛斌1 薛小平2 郭梦舒2   

  1. 1. Department of Mathematics, Harbin Engineering University, Harbin 150001, P. R. China;
    2. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China
  • 收稿日期:2009-12-03 修回日期:2010-08-24 出版日期:2010-10-01 发布日期:2010-10-01

Three solutions to inequalities of Dirichlet problem driven by p(x)-Laplacian

GE Bin1, XUE Xiao-Ping2, GUO Meng-Shu2   

  1. 1. Department of Mathematics, Harbin Engineering University, Harbin 150001, P. R. China;
    2. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China
  • Received:2009-12-03 Revised:2010-08-24 Online:2010-10-01 Published:2010-10-01

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摘要： A class of nonlinear elliptic problems driven by p(x)-Laplacian with a non-smooth locally Lipschitz potential is considered. By applying the version of the non-smooth three-critical-point theorem, the existence of three solutions to the problems is proved.

Abstract: A class of nonlinear elliptic problems driven by p(x)-Laplacian with a non-smooth locally Lipschitz potential is considered. By applying the version of the non-smooth three-critical-point theorem, the existence of three solutions to the problems is proved.

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