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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/981401 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562748391686144 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-90d8c85d37e242a7a312a016769e92ef |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |