On Oleck-Opial-Beesack-Troy integro-differential inequalities
Date
2004-01-02
Authors
Bravyi, Evgeniy I.
Gusarenko, Sergey S.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We obtain necessary and sufficient conditions for the integro-differential inequality
∫bα ẋ2(t) dt ≥ γ ∫bα q(t) |ẋ(t)x(t) | dt
to be valid with one of the three boundary conditions: x(α) = 0, or x(b) = 0, or x(α) = x(b) = 0. For a power functions q, the best constants γ are found.
Description
Keywords
Integral inequalities, Integro-differential inequalities, Functional differential equations, Variational problems
Citation
Bravyi, E. I., & Gusarenko, S. S. (2004). On Oleck-Opial-Beesack-Troy integro-differential inequalities. <i>Electronic Journal of Differential Equations, 2004</i>(4), pp. 1-24.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.