Asymptotic to polynomials solutions for nonlinear differential equations
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Philos, C. G.
Purnaras, I. K.
Tsamatos, P. C.
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Elsevier
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peer reviewed
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Nonlinear Analysis-Theory Methods & Applications
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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 less than or equal to m less than or equal to 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 infinity to this polynomial. Conditions are also given, which are sufficient for every solution to be asymptotic at infinity 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. (C) 2004 Elsevier Ltd. All tights reserved.
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nonlinear differential equation, asymptotic behavior, asymptotic properties, asymptotic expansions, asymptotic to polynomials solutions, integrable coefficients, 2nd order, nonoscillatory solutions, deviating arguments, positive solutions, global existence, behavior, 2nd-order
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<Go to ISI>://000225181100010
http://ac.els-cdn.com/S0362546X04003232/1-s2.0-S0362546X04003232-main.pdf?_tid=3849cb80-cf38-11e2-a2a0-00000aacb35d&acdnat=1370585294_2a8dbf1496dc29d00367943ea56f017f
http://ac.els-cdn.com/S0362546X04003232/1-s2.0-S0362546X04003232-main.pdf?_tid=3849cb80-cf38-11e2-a2a0-00000aacb35d&acdnat=1370585294_2a8dbf1496dc29d00367943ea56f017f
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en
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Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών