Problems with mixed boundary conditions in Banach spaces

Abstract

Using Leray-Schauder degree or degree for $\alpha$-condensing maps we obtain the existence of at least one solution for the boundary value problem of the type \[ \left\{\begin{array}{lll} (φ(u' ))' = f(t,u,u') & & \\ u(T)=0=u'(0), & & \quad \quad \end{array}\right. \] where $\phi :X\to X$ is a homeomorphism with reverse Lipschitz such that $\phi (0)=0$, $f:\left[0,T\right]\times X\times X\to X$ is a continuous function, $T$ a positive real number and $X$ is a real Banach space.

arXiv comment15 pages. arXiv admin note: text overlap with arXiv:1606.00801