Lyapunov-type inequalities for linear hyperbolic and elliptic equations on a rectangular domain

Abstract

In the case of oscillatory potential, we present some new Lyapunov-type inequalities for linear hyperbolic and elliptic equations on a rectangular domain in ${\mathbb R}^2$. No sign restriction is imposed on the potential function. As applications of the Lyapunov-type inequalities obtained, we give some estimations for disconjugacy of hyperbolic and elliptic Dirichlet boundary value problems.