Philos, Christos G.Tsamatos, P. Ch.2021-05-282021-05-282005-07-11Philos, C. G., & Tsamatos, P. C. (2005). Solutions approaching polynomials at infinity to nonlinear ordinary differential equations. <i>Electronic Journal of Differential Equations, 2005</i>(79), pp. 1-25.1072-6691https://hdl.handle.net/10877/13680This paper concerns the solutions approaching polynomials at ∞ to n-th order (n > 1) nonlinear ordinary differential equations, in which the nonlinear term depends on time t and on x, x', ..., x(N), where x is the unknown function and N is an integer with 0 ≤ N ≤ n - 1. For each given integer m with max{1, N} ≤ m ≤ n - 1, conditions are given which guarantee that, for any real polynomial of degree at most m, there exists a solution that is asymptotic at ∞ to this polynomial. Sufficient conditions are also presented for every solution to be asymptotic at ∞ to a real polynomial of degree at most n - 1. The results obtained extend those by the authors and by Purnaras [25] concerning the particular case N = 0.Text25 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear differential equationsAsymptotic propertiesAsymptotic expansionsAsymptotic to polynomials solutionsArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.