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.

In this paper, we construct an integer-valued degree function in a suitable classes of mappings of monotone type, using a complementary system formed of Generalized Sobolev Spaces in which the variable exponent p ∈ P log (Ω) satisfy 1 < p − ≤ p + ≤ ∞, where Ω ⊂ R N is open and bounded. This kind of spaces are not reflexives.

No abstract

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.

The aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form\left\{ {\matrix{{A\left( u \right) = f} \hfill & {in} \hfill & \Omega \hfill \cr {u = 0} \hfill & {on} \hfill & {\partial \Omega } \hfill \cr } } \right.where A(u) = −diva(x, u, ∇u) is a Leray-Lions operator and f ∈ W−1,p′(.)(Ω) with p(x) ∈ (1, ∞). Our technical approach is based on topological degree method and the theory of variable exponent Sobolev spaces.