Superlinear Singular Problems on the Half Line. (15th December 2010)

• Record Type: Journal Article
• Authors: Rachůnková Rachůnková, Irena Irena; Tomeček Tomeček, Jan Jan
• Other Names: Zhang Zhang Zhitao Zhitao Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-12-15
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/429813
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : The paper studies the singular differential equation ( p ( t ) u ′ ) ′ = p ( t ) f ( u ), which has a singularity at t = 0 . Here the existence of strictly increasing solutions satisfying sup { | u ( t ) | : t ∈ [ 0, ∞ ) } ≥ L > 0 is proved under the assumption that f has two zeros 0 and L and a superlinear behaviour near - ∞ . The problem generalizes some models arising in hydrodynamics or in the nonlinear field theory.