Communications on Applied Nonlinear Analysis
In this paper, the compression contraction fixed point theorem is applied to a right focal boundary value problem for a second order ordinary differential equation to provide sufficient conditions for existence of solutions in a cone. The nonlinear term is a function of three variables and singularities are allowed. A cone is defined in the Banach space C1[0, 1] and concavity of derivatives of solutions plays a key role. A family of examples is provided in which explicit sufficient conditions are exhibited.
Abid, Ahlam and Eloe, Paul, "Positive solutions of boundary value problems for ordinary differential equations with dependence on higher order derivatives" (2017). Mathematics Faculty Publications. 129.