Asymptotic properties of solutions of the $n$th order differential equation with delayed argument

Marián Rusnák; Vincent Šoltés

Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations

Luisa Malaguti, Valentina Taddei (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The paper deals with the quasi-linear ordinary differential equation ${(r (t) ϕ (u^{'}))}^{'} + g (t, u) = 0$ with $t \in [0, \infty)$ . We treat the case when $g$ is not necessarily monotone in its second argument and assume usual conditions on $r (t)$ and $ϕ (u)$ . We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. The results generalize previous ones due to Elbert–Kusano,...

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