Lyapunov-Type Inequalities for Fractional $(p, q)$-Laplacian Systems

Abstract

In this paper, we establish some new Lyapunov type inequalities for fractional $(p, q)$-Laplacian operators in an open bounded set $Ω⊂\mathbb{R}^N$, under homogeneous Dirichlet boundary conditions. Next, we use the obtained inequalities to derive some geometric properties of the generalized spectrum associated to the considered problem.