A multiplicity result for a quasilinear gradient elliptic system

The aim of this work is to establish the existence of infinitely many solutions to gradient elliptic system problem, placing only conditions on a potential function H, associated to the problem, which is assumed to have an oscillatory behaviour at infinity. The method used in this paper is a shooting technique combined with an elementary variational argument. We are concerned with the existence of upper and lower solutions in the sense of Hernández

Existence and nonexistence of radial positive solutions of superlinear elliptic systems

The main goal in this paper is to prove the existence of radial positive solutions of the quasilinear elliptic system [formula], where [omega] is a ball in RN and f, g are positive continuous functions satisfying f(x, 0, 0) = g(x, 0, 0) = 0 and some growth conditions which correspond, roughly speaking, to superlinear problems. Two different sets of conditions, called strongly and weakly coupled, are given in order to obtain existence. We use the topological degree theory combined with the blow up method of Gidas and Spruck. When [omega] = RN, we give some sufficient conditions of nonexistence of radial positive solutions for Liouville systems

Existence and nonexistence of radial positive solutions of superlinear elliptic systems

The main goal in this paper is to prove the existence of radial positive solutions of the quasilinear elliptic system [formula], where [omega] is a ball in RN and f, g are positive continuous functions satisfying f(x, 0, 0) = g(x, 0, 0) = 0 and some growth conditions which correspond, roughly speaking, to superlinear problems. Two different sets of conditions, called strongly and weakly coupled, are given in order to obtain existence. We use the topological degree theory combined with the blow up method of Gidas and Spruck. When [omega] = RN, we give some sufficient conditions of nonexistence of radial positive solutions for Liouville systems

Quelques applications des groupes nilpotents aux equations aux derivees partielles

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

On the existence of bounded solutions of nonlinear elliptic systems

We study the existence of bounded solutions to the elliptic system −Δpu=f(u,v)+h1 in Ω, −Δqv=g(u,v)+h2 in Ω, u=v=0 on ∂Ω, non-necessarily potential systems. The method used is a shooting technique. We are concerned with the existence of a negative subsolution and a nonnegative supersolution in the sense of Hernandez; then we construct some compact operator T and some invariant set K where we can use the Leray Schauder's theorem