Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1431-1438.

• Articles • Previous Articles     Next Articles

Multiple Solutions for a p(x)}-Kirchhoff-type Equation with Nonsmooth Potential

 GE Bin1,2, XUE Xiao-Ping2, ZHOU Qing-Mei3   

  1. 1.Department of Applied Mathematics, Harbin Engineering University, Harbin 150001;
    2.Department of Mathematics, Harbin Institute of Technology, Harbin 150001;
    3.Library, Northeast Forestry University, Harbin 150040
  • Received:2009-12-25 Revised:2010-12-17 Online:2011-10-25 Published:2011-10-25

Abstract:

In this paper the authors  consider the differential inclusion problem involving the p(x)-Kirchhoff-type. Using Weierstrass Theorem and Mountain Pass Theorem, they obtain the existence of at least two nontrivial solutions of the problem in W01, p(x)(Ω).

Key words: p(x)-Kirchhoff-type, Variational method, Dirichlet problem, Differential inclusion problem

CLC Number: 

  • 35J20
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