Differential inclusion obstacle problems with variable exponents and convection terms

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.