Three-point boundary value problems in Banach spaces

Abstract

Using degree for α-condensing maps, we obtain the existence of at least one solution for nonlinear boundary value problems {(φ(u′))′=f(t,u,u′)u(0)=u(1)=u′(0),where φ: X→ X is a linear homeomorphism, f: [0 , 1] × X× X→ X is a continuous function and X is a real Banach space.