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Inequalities Associated with Regular and Singular Problems in the Calculus of Variations
| Content Provider | Scilit |
|---|---|
| Author | Bradley, J. S. Everitt, W. N. |
| Copyright Year | 1973 |
| Description | An inequality of the form is established, where p and q are real-valued coefficient functions and f is a complex-valued function in a set D so chosen that both sides of the inequality are finite. The interval of integration is of the form . The inequality is first established for functions in the domain of an operator in the Hilbert function space that is associated with the differential equation , and the number in the inequality is the smallest number in the spectrum of this operator. An approximation theorem is given that allows the inequality to be established for the larger set of functions D. An extension of some classical results from the calculus of variations and some spectral theory is then used to give necessary and sufficient conditions for equality and to show that the constant is best possible. Certain consequences of these conclusions are also discussed. |
| Related Links | http://www.ams.org/tran/1973-182-00/S0002-9947-1973-0330606-8/S0002-9947-1973-0330606-8.pdf |
| Ending Page | 321 |
| Page Count | 19 |
| Starting Page | 303 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/1996536 |
| Journal | Transactions of the American Mathematical Society |
| Volume Number | 182 |
| Language | English |
| Publisher | Duke University Press |
| Access Restriction | Open |
| Subject Keyword | Logic Calculus of Variations Singular Problems Inequalities Associated Associated with Regular |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
