Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 13, pp. 1-16.

Title: Existence of solutions for  quasilinear parabolic equations at resonance
        
Authors: Gao Jia         (Univ. of Shanghai for Science and Tech., China)
         Xiao-Juan Zhang (Univ. of Shanghai for Science and Tech., China)
         Li-Na Huang     (Univ. of Shanghai for Science and Tech., China)
        
Abstract:
 In this article, we show the existence of nontrivial solutions
 for a class of quasilinear parabolic differential equations.
 To obtain the  solution in a weighted Sobolev space,
 we use the  Galerkin method, Brouwer's theorem, and a
 compact Sobolev-type embedding theorem  proved by Shapiro.

Submitted  March 29, 2012. Published January 14, 2013.
Math Subject Classifications: 35H30,  35K58,  65L60.
Key Words: Weighted Sobolev space; quasilinear parabolic equation; resonance.