On a Hamiltonian elliptic system with concave-convex nonlinearities

Abstract: In this talk we discuss a Hamiltonian elliptic system of equations with Dirichlet boundary condition and with non-linearities that are concave near the origin and convex and superlinear at infinity. The concavity of the non-linearities depends on non-negative parameters λ and μ and we provide regions for the pairs (λ, μ) guaranteeing existence and non-existence of non-negative solutions. This work is inspired by the seminal work for the single equation done by Ambrosetti, Brezis and Cerami.

This is a joint work with Berhand Ruf and Carlos Velez.