Lyapunov-Type Inequalities for Higher-Dimensional Hamiltonian Systems on Time Scales: Anew Generalized Vector Zero Approach

Abstract

By defining a generalized zero for a vector-valued function and making use of it, we obtain new Lyapunov-type inequalities for a general linear 2n x2n Hamiltonian system z(Delta) = JH(t) z of dynamic equations on time scales. The new definition is an extension from scalar functions to valued functions with respect to a matrix. Our approach in the proofs is different in the sense that several tools such as matrix measure, exponential bound function, and Dini derivatives on time scales are employed. As a classical application, we also show how the new inequalities are useful for related boundary value problems. (C) 2022 Elsevier Inc. All rights reserved.