Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Quadratic functionals of second order

Author: Walter Leighton
Journal: Trans. Amer. Math. Soc. 151 (1970), 309-322
MSC: Primary 49.00; Secondary 34.00
MathSciNet review: 0264485
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study the minimizing of the general second-order quadratic functional (1.3) in a class of admissible functions $ y(x)$ with fixed endpoint conditions on $ y(x)$ and its derivative at $ x = a$ and at $ 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 49.00, 34.00

Retrieve articles in all journals with MSC: 49.00, 34.00

Additional Information

Keywords: Quadratic functional of second order, selfadjoint fourth-order differential equation, second variation, minimum of a functional, Euler equation, conjugate point, admissible variation, comparison theorem, Wirtinger inequality
Article copyright: © Copyright 1970 American Mathematical Society