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On the Existence of Oscillatory Solutions of the Second Order Nonlinear ODE

Martin Rohleder (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The paper investigates the singular initial problem[4pt] ( p ( t ) u ' ( t ) ) ' + q ( t ) f ( u ( t ) ) = 0 , u ( 0 ) = u 0 , u ' ( 0 ) = 0 [4pt] on the half-line [ 0 , ∞ ) . Here u 0 ∈ [ L 0 , L ] , where L 0 , 0 and L are zeros of f , which is locally Lipschitz continuous on ℝ . Function p is continuous on [ 0 , ∞ ) , has a positive continuous derivative on ( 0 , ∞ ) and p ( 0 ) = 0 . Function q is continuous on [ 0 , ∞ ) and positive on ( 0 , ∞ ) . For specific values u 0 we prove the existence and uniqueness of damped solutions of this problem. With additional conditions for f , p and q it is shown that the problem has for each specified u 0 a unique...

On the existence of periodic solutions for nonconvex differential inclusions

Dimitrios Kravvaritis, Nikolaos S. Papageorgiou (1996)

Archivum Mathematicum

Using a Nagumo type tangential condition and a recent theorem on the existence of directionally continuous selector for a lower semicontinuous multifunctions, we establish the existence of periodic trajectories for nonconvex differential inclusions.

On the existence of solutions for nonlinear impulsive periodic viable problems

Tiziana Cardinali, Raffaella Servadei (2004)

Open Mathematics

In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].

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