Asymptotic to polynomials solutions for nonlinear differential equations

✍ Scribed by Ch.G. Philos; I.K. Purnaras; P.Ch. Tsamatos

• Book ID: 104062310
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 253 KB
• Volume: 59
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2004.08.011

✦ Synopsis

This article is concerned with solutions that behave asymptotically like polynomials for nth order (n > 1) nonlinear ordinary differential equations. For each given integer m with 1 m n -1, sufficient conditions are presented in order that, for any real polynomial of degree at most m, there exists a solution which is asymptotic at ∞ to this polynomial. Conditions are also given, which are sufficient for every solution to be asymptotic at ∞ to a real polynomial of degree at most n -1. The application of the results obtained to the special case of second order nonlinear differential equations leads to improved versions of the ones contained in the recent paper by Lipovan [Glasg. Math. J. 45 (2003) 179] and of other related results existing in the literature.