On periodic Ambrosetti-Prodi-type problems

Abstract

<abstract><p>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.</p></abstract>

Ambrosetti–Prodi Alternative for Coupled and Independent Systems of Second-Order Differential Equations

“…[4,5] for Neumann boundary conditions; ref. [6][7][8][9][10] for periodic problems; ref. [11] for parametric problems with (p, q)-Laplacian equations; ref.…”