Nontrivial Solutions of a Fully Fourth-Order Periodic Boundary Value Problem

Abstract

We investigate the solvability of a fully fourth-order periodic boundary value problem of the form x(4)=f(t,x,x′,x′′,x′′′), x(i)(0)=x(i)(T), i=0,1,2,3, where f:[0,T]×R4→R satisfies Carathéodory conditions. By using the coincidence degree theory, the existence of nontrivial solutions is obtained. Meanwhile, as applications, some examples are given to illustrate our results.