Exact multiplicity and numerical computation of solutions for two classes of non-autonomous problems with concave–convex nonlinearities

Abstract

We establish the exact multiplicity of positive solutions, and the global solution structure for two classes of problems on circular domains. The first class involves non-autonomous concave–convex problems on a ball in Rn, and the second one deals with concave–convex problems on a “thin” annulus in Rn. We illustrate our results by numerical computations, using a novel algorithm, which involves continuation in a global parameter.