Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping
Some new oscillation criteria for a general class of second-order differential equations with nonlinear damping are shown. Except some general structural assumptions on the coefficients and nonlinear terms, we additionally assume only one sufficient condition (of Fite-Wintner-Leighton type). It is d...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/852180 |
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| _version_ | 1832567068650635264 |
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| author | Mervan Pašić |
| author_facet | Mervan Pašić |
| author_sort | Mervan Pašić |
| collection | DOAJ |
| description | Some new oscillation criteria for a general class of second-order differential equations with nonlinear damping are shown. Except some general structural assumptions on the coefficients and nonlinear terms, we additionally assume only one sufficient condition (of Fite-Wintner-Leighton type). It is different compared to many early published papers which use rather complex sufficient conditions. Our method contains three items: classic Riccati transformations, a pointwise comparison principle, and a blow-up principle for sub- and supersolutions of a class of the generalized Riccati differential equations associated to any nonoscillatory solution of the main equation. |
| format | Article |
| id | doaj-art-ea1d32ebf08c4ed4b59968298f4a20e6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ea1d32ebf08c4ed4b59968298f4a20e62025-02-03T01:02:32ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/852180852180Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear DampingMervan Pašić0Department of Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, 10000 Zagreb, CroatiaSome new oscillation criteria for a general class of second-order differential equations with nonlinear damping are shown. Except some general structural assumptions on the coefficients and nonlinear terms, we additionally assume only one sufficient condition (of Fite-Wintner-Leighton type). It is different compared to many early published papers which use rather complex sufficient conditions. Our method contains three items: classic Riccati transformations, a pointwise comparison principle, and a blow-up principle for sub- and supersolutions of a class of the generalized Riccati differential equations associated to any nonoscillatory solution of the main equation.http://dx.doi.org/10.1155/2013/852180 |
| spellingShingle | Mervan Pašić Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping Abstract and Applied Analysis |
| title | Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping |
| title_full | Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping |
| title_fullStr | Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping |
| title_full_unstemmed | Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping |
| title_short | Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order Differential Equations with Nonlinear Damping |
| title_sort | fite wintner leighton type oscillation criteria for second order differential equations with nonlinear damping |
| url | http://dx.doi.org/10.1155/2013/852180 |
| work_keys_str_mv | AT mervanpasic fitewintnerleightontypeoscillationcriteriaforsecondorderdifferentialequationswithnonlineardamping |