Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations. (13th October 2009)

• Record Type: Journal Article
• Authors: Rachůnková, Irena; Tomeček, Jan
• Other Names: O'Regan Donal Academic Editor.
• Is Part Of: Boundary value problems. Volume 2009(2009)
• Publication Date: 2009-10-13
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2009/959636
• Languages: English
• ISSNs: 1687-2762

Abstract

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