Differential inclusion obstacle problems with variable exponents and
The elliptic obstacle problems with variable exponents and multivalued
reaction terms, depending on the gradient, are considered in this paper.
Under general assumptions on the convection term, we prove two existence
theorems of a (weak) nontrivial solution by using the surjective theorem
and the Leray-Schauder fixed point theorem for multivalued mappings,
respectively. Our assumptions are suitable and different from those
required in the previous literature.