MR2351214 Ch. G. PHILOS, I. K. PURNARAS and P. Ch. TSAMATOS Ch. G. PHILOS, I. K. PURNARAS and P. Ch. TSAMATOS Global Solutions Approaching Lines at Infinity to Second Order Nonlinear Delay Differential Equations Funkcialaj Ekvacioj. Serio Internacia 50 2007 213--259 http://fe.math.kobe-u.ac.jp/FE/FullPapers/50-2/50_213.pdf http://www.ams.org/mathscinet-getitem?mr=MR2351214 This article is concerned with second order nonlinear delay, and especially ordinary, differential equations. By the use of the fixed point technique based on the classical Schauder's theorem, for any given line, sufficient conditions are established in order that there exists at least one global solution which is asymptotic at $\infty$ to this line. In the special case of ordinary differential equations, via the Banach's Contraction Principle, for any given line, conditions are presented which guarantee that there exists a unique global solution that is asymptotic at $\infty$ to this line. The application of the results obtained to second order delay, and ordinary, differential equations of Emden-Fowler type is presented, and some examples demonstrating the applicability of the results are given. Finally, some supplementary results are obtained, which provide sufficient conditions for all global solutions belonging to a suitable class to be asymptotic at $\infty$ to lines. Nonlinear differential equation, Delay differential equation, Ordinary differential equation, Asymptotic behavior, Asymptotic properties, Asymptotic expansions, Global solutions, Asymptotic to lines solutions, Fixed point theory. Primary 34K25, 34E05, 34E10; Secondary 34D05, 47H10. 50-213 2007 Global Solutions Approaching Lines at Infinity to Second Order Nonlinear Delay Differential Equations Ch. G. PHILOS, I. K. PURNARAS and P. Ch. TSAMATOS Ch. G. PHILOS, I. K. PURNARAS and P. Ch. TSAMATOS
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