Existence of saddle-type solutions for a class of quasilinear problems in R²

Prof. Claudianor Alves
Universidade Federal de Campina Grande

Abstract: The main goal of the present paper is to prove the existence of saddle-type solutions for the following class of quasilinear problems

−∆_Φu+V'(u) = 0 in R²,

where

∆_Φu = div(φ(|∇u|)∇u),

Φ : R → [0,+∞) is a N-function and the potential V satisfies some technical condition and we have as an example V(t)=Φ(|t² − 1|). This is joint work with Renan Isneri and Piero Montecchiari