This article is devoted to study the existence of weak solutions for the strongly nonlinear p(x)-elliptic problemOur technical approach is based on the recent Berkovits topological degree.

The main aim of this paper is to prove, by using the topological degree methods, the existence of solutions for nonlinear elliptic equation Au = f where Au  is partial dierential operators of general divergence form.

No abstract

No abstract

We prove the existence of a solution for the strongly nonlinear parabolic initial boundary value problem associated to the equation ut − div a(x, t, ∇u) + g(x, t, u, ∇u) = f, where the vector field a(x, t, ξ) exhibits non-standard growth conditions.