Nontrivial solutions of a fully fourth-order periodic boundary value problem (Q2336816)

Summary: 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 \(f : [0, T] \times \mathbb{R}^4 \to \mathbb{R}\) 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.