Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

Periodic Solutions of Second-order Nonautonomous Impulsive Differential Equations

The main purpose of this paper is to study the existence of periodic solutions of second order impulsive differential equations with superlinear nonlinear terms. Our result generalizes one of Paul H. Rabinowitz’s existence results of periodic solutions of second order ordinary differential equations to impulsive cases. Mountain Pass Lemma is applied in order to prove our main results. AMS Subje...

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...

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.