Asymptotic Integration of Second Order Systems
Copyright policy )Asymptotic Integration of Second Order Systems
Nonlinear systems of the form (1) \((P(t,u,u') A(t,u,u'))' + Q(t,u,u') = 0\) and (2) \((A(t,u,u'))' + D(t,u,u') A(t,u,u') + Q(t,u,u') = 0\) are considered. It is proved that under appropriate conditions generalizing the ones of \textit{A. Witner} [Duke Math. J. 15, 55-67 (1948; Zbl 0034.355)] the set of attainable limits as \(t \to \infty\) of solutions of (1) and of (2) is exactly \(\mathbb{R}^ N\), as in the linear case, and that all bounded solutions approach a finite limit. Moreover, if \(Q\) satisfies additional growth conditions, then all solutions are bounded.
asymptotic behaviour, Asymptotic expansions of solutions to ordinary differential equations, Asymptotic properties of solutions to ordinary differential equations, second order systems
asymptotic behaviour, Asymptotic expansions of solutions to ordinary differential equations, Asymptotic properties of solutions to ordinary differential equations, second order systems
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