Existence of positive solution for a nonlinear problem with mixed conditions

Abstract

In this work, we prove the existence of a positive solution to the second-order nonlinear problem $u^{\prime \prime }+f(t,u,u^{\prime })=0$ with mixed boundary conditions, where $f$ is an $L^p$-Carathéodory function satisfying certain properties. Three boundary conditions are analyzed. The proofs of the results are based on the Mawhin's. coincidence degree.

arXiv comment19 pages. arXiv admin note: text overlap with arXiv:1503.04954 by other authors