Existence and Multiplicity Results for Nonlinear Differential Equations Depending on a Parameter in Semipositone Case

Abstract

The existence and multiplicity of solutions for second-order differential equations with a parameter are discussed in this paper. We are mainly concerned with the semipositone case. The analysis relies on the nonlinear alternative principle of Leray-Schauder and Krasnosel'skii's fixed point theorem in cones.