Lyapunov-Type Inequalities for Fractional $(p, q)$-Laplacian Systems (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we establish some new Lyapunov type inequalitiesfor fractional $(p, q)$-Laplacian operators in an open bounded set $Ω⊂\mathbb{R}^N$,under homogeneous Dirichlet boundary conditions. Next, we use the obtainedinequalities to derive some geometric properties of the generalized spectrumassociated to the considered problem.
Keywords: Fractional Sobolev spaces; fractional $(p; q)$-Laplacian operators; Lyapunov inequality; generalized eigenvalues.