Existence of positive solution for a nonlinear problem with mixed conditions

In this work, we prove the existence of a positive solution to the second-order nonlinear problem $u^{\mathrm{\prime }\mathrm{\prime }}+f(t,u,u^{\mathrm{\prime }})=0$ 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.