Existence of solutions for a nonlocal (P_1(x), P_2(x))-Laplace equation with dependence on the gradient

Abstract

The object of this work is to study the existence of solutions for a nonlocal (p1(x), p2(x)) Laplace equation with dependence on the gradient. We establish our results by using the degree theory for operators of (S+) type in the framework of variable exponent Sobolev spaces.

Existence and uniqueness of renormalized solution to multivalued homogeneous Neumann problem with L1-data

“…Equations with non-standard growth and L 1 -data in Lebesgue and Sobolev space with variable exponent are investigated by several authors. For more details, one can refer to [3,6,8,12,15] and references therein.The need to work in these spaces is motivated by its use in modeling electrorheological and thermorheological fluids (cf. [12]), as well as for image restoration [3].…”