Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations
Asymptotic properties of solutions of the singular differential equation (p(t)u′(t))′=p(t)f(u(t)) are described. 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. Further...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/408525 |
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| author | Irena Rachůnková Lukáš Rachůnek Jan Tomeček |
| author_facet | Irena Rachůnková Lukáš Rachůnek Jan Tomeček |
| author_sort | Irena Rachůnková |
| collection | DOAJ |
| description | Asymptotic properties of solutions of the singular differential equation (p(t)u′(t))′=p(t)f(u(t)) are described. 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. Further conditions for f and p under which the equation has oscillatory solutions converging to 0 are given. |
| format | Article |
| id | doaj-art-67d215a10e3041c6b81d792f2f3566af |
| 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-67d215a10e3041c6b81d792f2f3566af2025-08-20T03:34:02ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/408525408525Existence of Oscillatory Solutions of Singular Nonlinear Differential EquationsIrena Rachůnková0Lukáš Rachůnek1Jan Tomeček2Department 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 RepublicDepartment of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech RepublicAsymptotic properties of solutions of the singular differential equation (p(t)u′(t))′=p(t)f(u(t)) are described. 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. Further conditions for f and p under which the equation has oscillatory solutions converging to 0 are given.http://dx.doi.org/10.1155/2011/408525 |
| spellingShingle | Irena Rachůnková Lukáš Rachůnek Jan Tomeček Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations Abstract and Applied Analysis |
| title | Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations |
| title_full | Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations |
| title_fullStr | Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations |
| title_full_unstemmed | Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations |
| title_short | Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations |
| title_sort | existence of oscillatory solutions of singular nonlinear differential equations |
| url | http://dx.doi.org/10.1155/2011/408525 |
| work_keys_str_mv | AT irenarachunkova existenceofoscillatorysolutionsofsingularnonlineardifferentialequations AT lukasrachunek existenceofoscillatorysolutionsofsingularnonlineardifferentialequations AT jantomecek existenceofoscillatorysolutionsofsingularnonlineardifferentialequations |