Superlinear Singular Problems on the Half Line

• Main Authors: Rachůnková Irena, Tomeček Jan
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Boundary Value Problems
• Online Access: http://www.boundaryvalueproblems.com/content/2010/429813

<p/> <p>The paper studies the singular differential equation <inline-formula> <graphic file="1687-2770-2010-429813-i1.gif"/></inline-formula>, which has a singularity at <inline-formula> <graphic file="1687-2770-2010-429813-i2.gif"/></inline-formula>. Here the existence of strictly increasing solutions satisfying <inline-formula> <graphic file="1687-2770-2010-429813-i3.gif"/></inline-formula> is proved under the assumption that <inline-formula> <graphic file="1687-2770-2010-429813-i4.gif"/></inline-formula> has two zeros 0 and <inline-formula> <graphic file="1687-2770-2010-429813-i5.gif"/></inline-formula> and a superlinear behaviour near <inline-formula> <graphic file="1687-2770-2010-429813-i6.gif"/></inline-formula>. The problem generalizes some models arising in hydrodynamics or in the nonlinear field theory.</p>