Superlinear Singular Problems on the Half Line. (15th December 2010) - Rachůnková Rachůnková, Irena Irena; Tomeček Tomeček, Jan Jan
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.