A continuation approach to fourth order superlinear periodic boundary value problems
The purpose of this paper is to prove existence of \(T\)-periodic solutions of \(u''''= g(u)+e(t)\) in case \(g\) is a continuous function satisfying \(\lim_{| x|\to +\infty} g(x)/x =+\infty\) and \(e\) is continuous and \(T\)-periodic. The method of proof is based on degree theory and uses a continuation theorem developed in \textit{A. Capietto}, \textit{J. Mawhin} and \textit{F. Zanolin} [J. Differ. Equations 88, 347-395 (1990; Zbl 0718.34053)] in order to deal with problems in which there is no a priori bounds for the solutions.
scientific article; zbMATH DE number 591505