We study the existence of solutions for nonlinear boundary value problems , where denotes the boundary conditions on a compact interval , is a homeomorphism such that , and is a continuous function. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree is used.
Dionicio Pastor Dallos Santos. "Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions." Abstr. Appl. Anal. 2016 (SI2) 1 - 10, 2016. https://doi.org/10.1155/2016/5283263