Existence of Positive Solutions of a Second Order Right Focal Boundary Value Problem

摘要

This paper deals with the existence of a positive solution of a second order right focal boundary value problem. In particular, this paper profiles an application of a recent generalization of the Leggett-Williams fixed point theorem, which is void of any invariance like conditions, by utilizing operators and functionals. The sets in the fixed point theorem are defined using operators by an ordering generated by a border symmetric set, which leads to functional type boundaries of positive solutions of the boundary value problem over some parts of the domain. An example is provided to demonstrate the advantages of the flexibility of the results and the fixed point theorems.