Boundedness of solutions for a class of second-order differential equations

✍ Scribed by Chunrui Cheng; Junxiang Xu

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 254 KB
• Volume: 68
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.01.026

✦ Synopsis

In this paper we study the boundedness of solutions for the second-order differential equation

where F p (s) = |s| p-2 s, p > 1 and α, β are strictly positive constants satisfying a resonant relation

n with n being a positive integer, and ϕ(t, x) is a 2π -periodic function in t. There exists a function W (θ) such that if it is of constant sign, under some increasing restrictions on ψ(x ) and ϕ(t, x), by a small twist theorem we prove that all the solutions of the above equation are bounded in the sense of Lagrangian stability.