Lyapunov's Type Inequalities for Fourth-Order Differential Equations
For a fourth-order differential equation, we will establish some new Lyapunov-type inequalities, which give lower bounds of the distance between zeros of a nontrivial solution and also lower bounds of the distance between zeros of a solution and/or its derivatives. The main results will be proved by...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/795825 |
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| _version_ | 1832566943241994240 |
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| author | Samir H. Saker |
| author_facet | Samir H. Saker |
| author_sort | Samir H. Saker |
| collection | DOAJ |
| description | For a fourth-order differential equation, we will establish some new Lyapunov-type inequalities, which give lower bounds of the distance between zeros of a nontrivial solution and also lower bounds of the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardy’s inequality and some generalizations of Opial-Wirtinger-type inequalities involving higher-order derivatives. Some examples are considered to illustrate the main results. |
| format | Article |
| id | doaj-art-56691e18b90c4a0abc4a722406fc59be |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-56691e18b90c4a0abc4a722406fc59be2025-02-03T01:02:45ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/795825795825Lyapunov's Type Inequalities for Fourth-Order Differential EquationsSamir H. Saker0College of Science Research Centre, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaFor a fourth-order differential equation, we will establish some new Lyapunov-type inequalities, which give lower bounds of the distance between zeros of a nontrivial solution and also lower bounds of the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardy’s inequality and some generalizations of Opial-Wirtinger-type inequalities involving higher-order derivatives. Some examples are considered to illustrate the main results.http://dx.doi.org/10.1155/2012/795825 |
| spellingShingle | Samir H. Saker Lyapunov's Type Inequalities for Fourth-Order Differential Equations Abstract and Applied Analysis |
| title | Lyapunov's Type Inequalities for Fourth-Order Differential Equations |
| title_full | Lyapunov's Type Inequalities for Fourth-Order Differential Equations |
| title_fullStr | Lyapunov's Type Inequalities for Fourth-Order Differential Equations |
| title_full_unstemmed | Lyapunov's Type Inequalities for Fourth-Order Differential Equations |
| title_short | Lyapunov's Type Inequalities for Fourth-Order Differential Equations |
| title_sort | lyapunov s type inequalities for fourth order differential equations |
| url | http://dx.doi.org/10.1155/2012/795825 |
| work_keys_str_mv | AT samirhsaker lyapunovstypeinequalitiesforfourthorderdifferentialequations |