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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 • Previous Articles     Next Articles

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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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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