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

Lyapunov-Type Inequalities for Second-Order Boundary Value Problems with a Parameter

“…We find that in [36], the authors studied the case 0 < c < 1 < α < 2 of equation (10). It will be interesting to prove Lyapunov-type inequalities for equation (10) or other equation when α and c have other relation.…”

“…Theorem 4 (see [36]). Suppose that a, b, a < b, are consecutive zeros of a nontrivial solution of the first part of equation (10), then the inequality…”

“…where q + (t): � max q(t), 0 . Following Lyapunov's landmark work, there have been plenty of references focused on the Lyapunov-type inequality and its generalizations which are widely used in various problems such as asymptotic theory, disconjugacy, and eigenvalue problems of differential equations and difference equations (see [29][30][31][32][33][34][35][36][37][38][39][40][41] and the references therein).…”

“…Agarwal andÖzbekler [36] also established a Lyapunovtype inequality for the second-order forced boundary value problem with mixed nonlinearities:…”

Lyapunov-type inequalities for higher-order half-linear difference equations

“…For some recent work, the reader is referred to [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] and the references therein. In particular, Liu and Tang [37] studied the following m-order p-Laplace difference equation: m u(n) p-2 m u(n) + r(n) u(n) p-2 u(n) = 0,…”