On the Existence of Solutions With Prescribed Asymptotic Behaviour for Perturbed Nonlinear Differential Equations of Second Order

Abstract

Abstract. A global existence result for solutions u(t) of the differential equation

On a Local Theory of Asymptotic Integration for Nonlinear Differential Equations

“…The distance between the elements v 1 and v 2 of the set D has the formula d(v 1 , v 2 ) = sup t≥t 0 {t c |v 1 (t) − v 2 (t)|} and the metric space S = (G, d) is complete. We define the operator T : G → C([t 0 , +∞), R) taking into account the comments in [35,Theorem 8]. Precisely,…”

“…According to [32, p. 183], and taking into account (35), the double inequality (32) follows from the next estimates…”

“…and the metric space S = (G, d) is complete. We define the operator T : G → C([t 0 , +∞), R) taking into account the comments in [35,Theorem 8]. Precisely,…”

On t 2-like solutions of certain second order differential equations

“…Several investigations of interest have been done in this direction in the last years (see, e.g., [5][6][7][8] and their references). As mentioned before, many papers, see [9,10] or the recent [11][12][13][14][15]28,17,18], deal with the existence and asymptotic behavior of nonoscillatory/positive solutions to large classes of ordinary differential equations that have power-like nonlinearities, usually associated with the names Emden-Fowler, Thomas-Fermi or Lane, that is…”

On oscillatory solutions of certain first order ordinary differential equations

“…The papers [2,3,20,22,23] present various properties of the functional quantity W, which shall be called pseudo-wronskian in the sequel. Our aim in this note is to complete their conclusions by giving some sufficient conditions upon a and w which lead to the existence of a solution x to (2) that verifies (3) while having an oscillatory pseudo-wronskian (this means that there exist the unbounded from above sequences (t…”