A note on the persistence of an s-shaped bifurcation curve

Abstract

We study the non-negative solutions of the Dirichlet problem

where λ≤0, α>2 are constants and Ω is a smooth bounded region in R^N, which arises in the Theroy of Combustion. We Study the persistence of an S-Shaped curve for the bifurcation diagram λ=ρ(λ) where , as α is increased. Our methods are based on sub and super solution techniques.

AMS (MOS):

• 35B30