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On the asymptotic behavior of solutions of nonlinear ordinary differential equations. (English) Zbl 0698.34049
The authors study the asymptotic behavior for \(t\to \infty\) of solutions to the equation \(y^{(n)}+f(t,y)=0,\) \(n\geq 2\), where f: [0,\(\infty)\times {\mathbb{R}}\to (0,\infty)\) is continuous and nondecreasing in y. The set S of solutions existing on [a,\(\infty)\) is classified according to the order of increase (decrease) of its members. The behavior of solutions is then described in 19 theorems where various additional conditions on f are used (often as necessary and sufficient). Some applications to radially symmetric solutions of a class of elliptic partial differential equation is also given.
Reviewer: V.Maric

MSC:
34E05 Asymptotic expansions of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C11 Growth and boundedness of solutions to ordinary differential equations
34E99 Asymptotic theory for ordinary differential equations
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References:
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