A boundary value problem on the half-line for superlinear differential equations with changing sign weight

Abstract

The existence of positive solutions x for a superlinear differential equation with p-Laplacian is here studied, satisfying the boundary conditions x(0) = x(∞) = 0. Under the assumption that the weight changes its sign from nonpositive to nonnegative, necessary and sufficient conditions for the existence are derived by combining Kneser-type properties for solutions of an associated boundary value problem on a compact set, a-priori bounds for solutions of suitable boundary value problems on noncompact intervals, and continuity arguments.