Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 99, pp. 1-8.

Title: Solvability of a second-order singular boundary-value problem

Author: Petio S. Kelevedjiev (Technical Univ. of Sliven, Bulgaria)

Abstract:
 Using the barrier strips technique, we study the  existence of
 solutions to the boundary-value problem
 $$\displaylines{
 x''=f(t,x,x'),\quad t\in(0,1),\cr
 x'(0)=A,\quad x(1)=Bx'(1)+C,
 }$$
 where the scalar function f may be singular at t=0.

Submitted February 21, 2012. Published June 12, 2012.
Math Subject Classifications: 34B15, 34B16.
Key Words: Boundary value problem;  second order differential equation;
           singularity; sign conditions.