Existence Results for a Fully Fourth-Order Boundary Value Problem - Yongxiang Li; Qiuyan Liang (Journal of Function Spaces and Applications)
We discuss the existence of solution for the fully fourth-order boundary value problem u(4)=f(t,u,u′,u′′,u′′′), 0≤t≤1, u(0)=u(1)=u′′(0)=u′′(1)=0. A growth condition on f guaranteeing the existence of solution is presented. The discussion is based on the Fourier analysis method and Leray-Schauder fixed point theorem.