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

Abstract EN

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.