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 formx(4)=f(t,x,x′,x′′,x′′′),  x(i)(0)=x(i)(T),      i=0,1,2,3,wheref:[0,T]×R4→Rsatisfies 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.