On nonlocal existence results for elliptic equations with convex–concave nonlinearities

Abstract

In this paper we study the family of nonlinear elliptic Dirichlet boundary value problems with p-Laplacian and with concave–convex nonlinearity which depend on real parameter λ . We introduce nonlocal intervals ( λ i , λ i + 1 ) such that the characteristic points λ i , λ i + 1 (a priori bifurcation values) expressed in terms of exact variational principles. In these intervals, new results on the existence of positive solutions, multiple positive solutions and existence of multiple disjoint sets with infinitely many solutions are proved.