Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations. (13th October 2009) - Rachůnková, Irena; Tomeček, Jan
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− ∞ .