On periodic Ambrosetti-Prodi-type problems

Abstract

This work presents a discussion of Ambrosetti-Prodi-type second-order periodic problems. In short, the existence, non-existence, and multiplicity of solutions will be discussed on the parameter $ \lambda $. The arguments rely on a Nagumo condition, to guarantee an apriori bound on the first derivative, lower and upper-solutions method, and the Leray-Schauder's topological degree theory. There are two types of new results based on the parameter's variation: An existence and non-existence theorem and a multiplicity theorem, proving the existence of a bifurcation point. An application to a damped and forced pendulum is studied, suggesting a method to estimate the critical values of the parameter.

Keywords

• nagumo-type condition
• lower and upper solutions
• leray-schauder degree
• ambrosetti-prodi problems