On inequalities of Lyapunov type

Lyapunov-type inequalities for a class of even-order differential equations

“…In this article, motivated by the references [15][16][17][18], we attempt to establish some sharper Lyapunov-type inequalities for (1.4) under the same boundary value conditions of Theorem 1.1.…”

Lyapunov-type inequalities for Laplacian systems and applications to boundary value problems

“…In 2003, Yang [11] considered the following second order half linear differential equation r(t) x (t) γ−2 x (t) + q(t) x(t) γ−2 x(t) = 0, (1.2) and obtained the following inequality provided that Eq. (1.2) has a nontrivial solution x(t) which satisfies x(a) = x(b) = 0 and x(t) = 0, t ∈ (a, b).…”

Disconjugacy via Lyapunov and Vallée-Poussin type inequalities for forced differential equations

“…(1.8) Various extensions of Theorem 1.1 are available in the survey paper [44], see also references therein. For Lyapunov type inequalities, Yang [45] showed that there is a striking similarity between linear and half-linear equations (r(t) γ (x (t))) + q(t ) γ (x(t)) = 0, γ > 0 (1.9) where * (s) = |s| * −1 s. He obtained the following interesting result. …”