Asymptotic behavior of functions and solutions of some nonlinear differential equations (Q1120051)

The author develops a theory of behaviour of functions for \(t\to \infty\). The functions are assumed to take their values in a Banach space. Three classes of functions are defined with respect to their nature at infinity and several important properties are proved. After that the author derives other properties valid only for real-valued functions. In the last section he applies his theory to the nth-order ordinary differential equation \((*)\quad y^{(n)}=\Phi (t)| y|^{\lambda} sgn y\) and obtains some results dealing with the asymptotic and oscillatory behvaiour of the solutions of (*).