Solvability of functional third-order problems of Ambrosetti-Prodi-type

This work presents an Ambrosetti-Prodi alternative for functional problems composed of a fully third-order differential equation with two types of functional boundary conditions. The discussion of existence and non-existence of solution is obtained in a more general case, and the multiplicity of solution is done with restrictive boundary conditions- The main arguments are based on the lower and upper solutions method, together with the Leray-Schauder topological degree theory. We stress that the multiplicity situation requires different speed growths on the variables. An example illustrates the results' applicability and shows a technique to estimate the bifurcation values of the parameter.