Boundary Value Problems
Volume 2009 (2009), Article ID 959636, 21 pages
doi:10.1155/2009/959636
Research Article

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

Irena Rachůnková and Jan Tomeček

Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17 listopadu 12, 771 46 Olomouc, Czech Republic

Received 27 April 2009; Revised 1 September 2009; Accepted 15 September 2009

Academic Editor: Donal O'Regan

Copyright © 2009 Irena Rachůnková and Jan Tomeček. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the singular differential equation (p(t)u′)′=p(t)f(u), having a singularity at t=0. The existence of a strictly increasing solution (a homoclinic solution) satisfying u′(0)=0, u(∞)=L>0 is proved provided that f has two zeros and a linear behaviour near −∞.