A Singular Initial-Value Problem for Second-Order Differential Equations

Afgan Aslanov

doi:10.1155/2014/526549

Abstract

We are interested in the existence of solutions to initial-value problems for second-order nonlinear singular differential equations. We show that the existence of a solution can be explained in terms of a more simple initial-value problem. Local existence and uniqueness of solutions are proven under conditions which are considerably weaker than previously known conditions.

Highlights

In recent years, the studies of singular initial-value problems (IVPs) of the type x󸀠󸀠 + 2t−1x󸀠 + xn (t) = 0, x (0) = 1, x󸀠 (0) = 0, (1)have attracted the attention of many mathematicians and physicists
We extended the class of solvable second-order singular IVPs
The conditions we obtained are weaker than the previously known ones and can be reduced to several special cases

Summary

A Singular Initial-Value Problem for Second-Order Differential Equations

Mathematics and Computing Department, Beykent University, Ayazaga, Sisli, 34396 Istanbul, Turkey. We are interested in the existence of solutions to initial-value problems for second-order nonlinear singular differential equations. We show that the existence of a solution can be explained in terms of a more simple initial-value problem. Local existence and uniqueness of solutions are proven under conditions which are considerably weaker than previously known conditions

Introduction

Existence Theorems

Applications

Concluding Remarks