Lyapunov and Wirtinger inequalities Original Research Article

In this paper, we prove the Lyapunov inequality for the second-order linear differential equation (r(t)φ(y′(t)))′+p(t)φ(y(t))=0,(r(t)φ(y′(t)))′+p(t)φ(y(t))=0, Turn MathJax on 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.