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

where a, b Î R with a <b, and the constant 4 cannot be replaced by a larger number, where and in the sequel q(t) = max{q(t), 0}. Since then, there are many improvements and generalizations of (1.2) in some literatures. Especially, Lyapunov inequality has been generalized extensively to the higher-order linear equations and the linear Hamiltonian systems. A thorough literature review of continuous and discrete Lyapunov-type inequalities and their applications can be found in the survey article by Cheng [3]. Some other recent related results can be found in the articles [4-14]. We consider the even-order equation x(t) + (−1)n−1q(t)x(t) = 0, (1:4)