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.
Hailong Zhu. Shengjun Li. "Existence and Multiplicity Results for Nonlinear Differential Equations Depending on a Parameter in Semipositone Case." Abstr. Appl. Anal. 2012 (SI07) 1 - 10, 2012. https://doi.org/10.1155/2012/215617