Open Access Research Article

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

Irena Rachůnková* and Jan Tomeček

Author Affiliations

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

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Boundary Value Problems 2009, 2009:959636 doi:10.1155/2009/959636

Published: 13 October 2009

Abstract

This paper investigates the singular differential equation , having a singularity at . The existence of a strictly increasing solution (a homoclinic solution) satisfying , is proved provided that has two zeros and a linear behaviour near .