Topological degree methods for partial differential operators in generalized Sobolev spaces

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.

Topological degree methods for a Neumann problem governed by nonlinear elliptic equation

In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation- div\,\,a\left( {x,u,\nabla u} \right) = b\left( x \right){\left| u \right|^{p - 2}}u + \lambda H\left( {x,u,\nabla u} \right),where Ω is a bounded smooth domain of 𝕉N.

Topological degree methods for a Strongly nonlinear p(x)-elliptic problem

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

Periodic Solutions of Systems with Singularities of Repulsive Type

Motivated by the classical Coulomb central motion model, we study the existence of T-periodic solutions for the nonlinear second order system of singular ordinary differential equations u′′ + g(u) = p(t). Using topological degree methods, we prove that when the nonlinearity g : ℝ