Singular Solutions of Differential Equations of the Second Order

Limit Properties of Solutions of Singular Second-Order Differential Equations

We discuss the properties of the differential equation u′′ t a/t u′ t f t, u t , u′ t , a.e. on 0, T , where a ∈ R\{0}, and f satisfies the Lp-Carathéodory conditions on 0, T × R2 for some p > 1. A full description of the asymptotic behavior for t → 0 of functions u satisfying the equation a.e. on 0, T is given. We also describe the structure of boundary conditions which are necessary and suffi...

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

C-approximate Solutions of Second-order Singular Ordinary Differential Equations

In this work a new method is developed to obtain C1-approximate solutions of initial and boundary-value problems generated from a one parameter second order singular ordinary differential equation. Information about the order of approximation is also given by introducing the so called growth index of a function. Conditions are given for the existence of such approximations for initial and bound...

On Singular Solutions for Second Order Delayed Differential Equations

Asymptotic properties and estimate of singular solutions (either defined on a finite interval only or trivial in a neighbourhood of ∞) of the second order delay differential equation with p-Laplacian are investigated.

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty