Periodic Solutions for Second Order Systems with Not Uniformly Coercive Potential

✍ Scribed by Chun-Lei Tang; Xing-Ping Wu

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 87 KB
• Volume: 259
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7401

✦ Synopsis

The existence and multiplicity of periodic solutions are obtained for the nonau-Ž . tonomous second order systems with locally coercive potential; that is, F t, x ª < < w x qϱ as x ª ϱ for a.e. t in some positive-measure subset of 0, T , by using an analogy of Egorov's Theorem, the properties of subadditive functions, the least action principle, and a three-critical-point theorem proposed by Brezis and Nirenberg.