Existence results for degenerate $p(x)$-Laplace equations with   Leray-Lions type operators
  We show the various existence results for degenerate $p(x)$-Laplace equations with Leray-Lions type operators. A suitable condition on degeneracy is discussed and proofs are mainly based on direct methods and critical point theories in Calculus of Variations. In particular, we investigate the various situations of the growth rates between principal operators and nonlinearities. 
Ky Ho, Inbo Sim
math.AP