Lyapunov and Wirtinger inequalities
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Abstract
In this paper, we prove the Lyapunov inequality for the second-order linear differential equation where
- (i)
φ(s) = |s|αt-2s, α > 1 is a fixed real number
- (ii)
r(t) and p(t) are integrable on [a, b] with r(t) > 0 on [a, b].
On the other hand, a generalized Wirtinger inequality is also given.
Lyapunov's inequality
Hö
lder's inequality
Wirtinger's inequality
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