Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (2): 465-471.

• Articles • Previous Articles     Next Articles

Multiple Solutions for a Class of p(x)-Laplacian Problems in RN

FU Yong-Qiang, ZHANG Xia   

  1. Department of Mathematics, Harbin Institute of Technology, Harbin 150001
  • Received:2008-09-25 Revised:2009-12-26 Online:2010-04-25 Published:2010-04-25
  • Supported by:

    哈尔滨工业大学自然科学基金(HITC200702) 和黑龙江省自然科学基金 (A2007-04)资助.

Abstract:

In this paper, the authors study the solutions to the following p(x)-Laplacian problem

-div(|\nablau|p(x)-2nablau)+|u|p(x)-2u=f 1(x, u)+f 2(x, u),       x ∈ RN.
 where 1< p - ≤ p(x) ≤ p+ < N.  Based on the theory of the variable exponent Sobolev space W1, p(x) (RN) it is showed that the above problem possesses a sequence of solutions associated with a sequence of positive energies going toward infinity.

Key words: p(x)-Laplacian equation, Variable exponent Sobolev space, Critical point

CLC Number: 

  • 35J60
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