Periodic solutions of some second-order differential equations with desultorily sublinear nonlinearities

✍ Scribed by Tiantian Ma; Zaihong Wang

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 223 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2010.08.011

✦ Synopsis

In this paper, we study the existence of periodic solutions of the Rayleigh equations

The nonlinear term g satisfies the following conditions:

x ⩽ 0, and lim inf

where a is a non-negative constant, S a = {x ∈ R + : g(x) > a} with sup S a = +∞ and f satisfies the sublinear condition. Using the Leray-Schauder continuation theorem, we give sufficient conditions for the existence of periodic solutions of the given equations.