Non-ordered lower and upper solutions and solvability of the periodic problem for the Liénard and the Rayleigh equations

Abstract

In questo lavoro si studia l’esistenza di soluzioni periodiche per le equazioni di Liénard e di Rayleigh in presenza di sotto e sopra soluzioni non necessariamente ordinate. In questo modo si completano ed estendono vari risultati precedentemente apparsi in letteratura.

In this paper we study the existence of periodic solutions for the Liénard and the Rayleigh equations in presence of lower and upper solutions which are not necessarily ordered. In this way several previous results in the literature are completed and extended.