Multiple solutions of nonlinear functional boundary value problems

Abstract

A class of nonlinear functional boundary conditions for the system of functional differential equations \(x''(t)=(F(x,y))(t)\), \(y''(t)=(H(x,y))(t)\) is introduced. Here \(F,\,H:C^1([a,b]) \times C^1([a,b]) \rightarrow L_1([a,b])\) are nonlinear continuous operators. Sufficient conditions for the existence of at least four solutions are given. Results are proved by the Bihari lemma, the Leray-Schauder degree theory and the Borsuk theorem.