p-Laplacian with nonlinearities on the gradient with natural growth

Prof. Djairo Guedes de Figueiredo

Abstract:This talk is concerned with existence of solutions for the problem

 
Here −∆_pu:=div(|∇u|p∇u) is the p−Laplacian operator with 1 <p< ∞ and Ω⊂R^N is a smooth bounded domain. This kind of problem is known as ”...gradient term with natural growth” to contrast with problems where the power on the gradient is strictly smaller than p. In this last case there is a very extensive literature.In the case of natural growth there are several works using topological techniques. Here we use variational methods.