AN INDEFINITE SUPERLINEAR ELLIPTIC EQUATION WITH A NONLINEAR BOUNDARY CONDITION OF SUBLINEAR TYPE (Shapes and other properties of solutions of PDEs)

Abstract

We investigate an indefinite superlinear elliptic equation coupled with a sublinear Neumann boundary condition depending on a positive parameter $lambda$. We establish a global multiplicity result for positive solutions of this concave-convex problem in the spirit of Ambrosetti-Brezis-Cerami and obtain their asymptotic profiles as $lambda$rightarrow 0^{+}. Furthermore, we discuss the existence of a global subcontinuum of positive solutions bifurcating from the trivial solutions. Our arguments are based on a bifurcation analysis, a comparison principle, variational techniques, and a topological method.