Problems with Mixed Boundary Conditions in Banach Spaces

Abstract

Using Leray-Schauder degree or degree for α-condensing maps we obtain the existence of at least one solution for the boundary value problem of the following type: φu′′=ft,u,u′,  u(T)=0=u′(0), where φ:X→X is a homeomorphism with reverse Lipschitz constant such that φ(0)=0, f:0,T×X×X→X is a continuous function, T is a positive real number, and X is a real Banach space.