On Oleck-Opial-Beesack-Troy integro-differential inequalities
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.
Citation
Bravyi, E. I., & Gusarenko, S. S. (2004). On Oleck-Opial-Beesack-Troy integro-differential inequalities. Electronic Journal of Differential Equations, 2004(4), pp. 1-24.Rights License

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