Christos G. Philos

Periodic first order linear neutral delay differential equations

Some new asymptotic and stability results are given for a first order linear neutral delay differential equation with periodic coefficients and constant delays. The asymptotic behavior of the solutions and the stability of the trivial solution are described by the use of an appropriate real root of an equation, which is in a sense the corresponding characteristic equation.

Global solutions of a singular initial value problem to second order nonlinear delay differential equations

The paper is concerned with an initial value problem to second order nonlinear singular delay differential equations. By the use of the Schauder fixed point theorem, a result for the existence of global solutions is derived. Also, via the Banach contraction principle, another result concerning the existence and uniqueness of global solutions is established. Moreover, applications of these results to a particular case of second order nonlinear singular delay differential equations as well as to the special case of second order nonlinear singular ordinary differential equations are presented. Finally, some specific applications to certain equations and two examples are given to demonstrate the applicability of the results of the paper.

A boundary value problem on the whole line to second order nonlinear differential equations

Abstract Second order nonlinear ordinary differential equations are considered, and a certain boundary value problem on the whole line is studied. Two theorems are obtained as main results. The first theorem is established by the use of the Schauder theorem and concerns the existence of solutions, while the second theorem is concerned with the existence and uniqueness of solutions and is derived by the Banach contraction principle. These two theorems are applied, in particular, to the specific class of second order nonlinear ordinary differential equations of Emden–Fowler type and to the special case of second order linear ordinary differential equations, respectively.

An asymptotic property of the solutions to second order linear nonautonomous delay differential equations

Second order linear nonautonomous delay differential equations are considered, and a fundamental asymptotic criterion for the solutions is established, by the use of the concept of generalized characteristic equation.

Asymptotic behavior of the oscillatory solutions to first order non-autonomous linear neutral delay differential equations of unstable type

This article is concerned with the asymptotic behavior of the oscillatory solutions to a class of first order unstable type linear neutral delay differential equations with variable coefficients and constant delays. A sufficient condition for all oscillatory solutions to tend to zero at ~ is established. This condition considerably improves a previous one given by Ladas and the third author [G. Ladas, Y.G. Sficas, Asymptotic behavior of oscillatory solutions, Hiroshima Math. J. 18 (1988) 351-359].