Quadratic functionals of second order
| Autor: | Walter Leighton |
|---|---|
| Rok vydání: | 1970 |
| Předmět: | |
| Zdroj: | Transactions of the American Mathematical Society. 151:309-322 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/s0002-9947-1970-0264485-1 |
| Popis: | In this paper we study the minimizing of the general second-order quadratic functional (1.3) in a class of admissible functions y ( x ) y(x) with fixed endpoint conditions on y ( x ) y(x) and its derivative at x = a x = a and at x = b x = b . Necessary conditions and sufficient conditions are obtained. These lead, in turn, to natural extensions of the Sturm comparison theorem to fourth-order selfadjoint equations. These extensions include and are more general than previously stated comparison theorems. Finally, it is found that the present variational theory provides an orderly approach to second-order Wirtinger-like inequalities, and the results include as special cases many published results of this type. |
| Databáze: | OpenAIRE |
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