Three solutions for a differential inclusion problem involving the p(x)-Kirchhoff-type

Abstract

In this article we consider differential inclusion problem involving the p(x)-Kirchhoff-type. Applying a version of the nonsmooth three critical points theorem we obtain the existence of three solutions of the problem in .

Keywords:

• p(x)-Kirchhoff-type
• differential inclusion problem
• three critical point theorem
• Dirichlet problem

AMS Subject Classifications:

• 35R70
• 35J20
• 35J70

Acknowledgements

Supported by the National Science Fund (grant nos. 10971043, 11001063), the Fundamental Research Funds for the Central Universities (no. HEUCF20111134), Heilongjiang Province Foundation for Distinguished Young Scholars (no. JC200810), Program of Excellent Team in Harbin Institute of Technology and the Natural Science Foundation of Heilongjiang Province (no. A200803).