Solutions approaching polynomials at infinity to nonlinear ordinary differential equations
Abstract
This 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.
Citation
Philos, C. G., & Tsamatos, P. C. (2005). Solutions approaching polynomials at infinity to nonlinear ordinary differential equations. Electronic Journal of Differential Equations, 2005(79), pp. 1-25.Rights License

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