On the principle eigencurve of a coupled system

Abstract:

We prove that for any λ ∈ IR, there is a sequence of eigencurves (µ_k(λ))_k for the nonlinear coupled elliptic system

by using min-max methods. We prove also via an homogeneity type condition that the eigenvector corresponding to the principal µ₁(λ) is bounded, positive and smooth. We end this work by proving that µ₁(λ) is simple.