Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation

Singular differential equation (p(t)u′)′=p(t)f(u) is investigated. Here f is Lipschitz continuous on ℝ and has at least two zeros 0 and L>0 . The function p is continuous on [0,∞) and has a positive continuous derivative on (0,∞) and p(0)=0. An asymptotic formula for oscillatory solutions is de...

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Main Authors: Irena Rachůnková, Lukáš Rachůnek
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/981401
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author Irena Rachůnková
Lukáš Rachůnek
author_facet Irena Rachůnková
Lukáš Rachůnek
author_sort Irena Rachůnková
collection DOAJ
description Singular differential equation (p(t)u′)′=p(t)f(u) is investigated. Here f is Lipschitz continuous on ℝ and has at least two zeros 0 and L>0 . The function p is continuous on [0,∞) and has a positive continuous derivative on (0,∞) and p(0)=0. An asymptotic formula for oscillatory solutions is derived.
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institution Kabale University
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publishDate 2011-01-01
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series Abstract and Applied Analysis
spelling doaj-art-90d8c85d37e242a7a312a016769e92ef2025-02-03T01:21:50ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/981401981401Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential EquationIrena Rachůnková0Lukáš Rachůnek1Department of Mathematics, Faculty of Science, Palacký University, 17. Listopadu 12, 771 46 Olomouc, Czech RepublicDepartment of Mathematics, Faculty of Science, Palacký University, 17. Listopadu 12, 771 46 Olomouc, Czech RepublicSingular differential equation (p(t)u′)′=p(t)f(u) is investigated. Here f is Lipschitz continuous on ℝ and has at least two zeros 0 and L>0 . The function p is continuous on [0,∞) and has a positive continuous derivative on (0,∞) and p(0)=0. An asymptotic formula for oscillatory solutions is derived.http://dx.doi.org/10.1155/2011/981401
spellingShingle Irena Rachůnková
Lukáš Rachůnek
Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation
Abstract and Applied Analysis
title Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation
title_full Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation
title_fullStr Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation
title_full_unstemmed Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation
title_short Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation
title_sort asymptotic formula for oscillatory solutions of some singular nonlinear differential equation
url http://dx.doi.org/10.1155/2011/981401
work_keys_str_mv AT irenarachunkova asymptoticformulaforoscillatorysolutionsofsomesingularnonlineardifferentialequation
AT lukasrachunek asymptoticformulaforoscillatorysolutionsofsomesingularnonlineardifferentialequation