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Lyapunov-type inequalities for fractional partial differential equations
Journal article   Open access  Peer reviewed

Lyapunov-type inequalities for fractional partial differential equations

Mohamed Jleli, Mokhtar Kirane and Bessem Samet
Applied mathematics letters, Vol.66, pp.30-39
04/2017
DOI: https://doi.org/10.1016/j.aml.2016.10.013

Abstract

Eigenvalues Fractional p-Laplacian Fractional Sobolev spaces Lyapunov inequality
We present Lyapunov inequalities for the fractional p-Laplacian (−Δp)s, 1<p<∞, s∈(0,1), in an open bounded set Ω⊂RN, under homogeneous Dirichlet boundary conditions. We discuss two cases, the case sp>N and the case sp<N. We use the obtained inequalities to provide lower bounds for the first eigenvalue of the fractional p-Laplacian. To the best of our knowledge, this is the first work dealing with Lyapunov-type inequalities for fractional partial differential equations.
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https://doi.org/10.1016/j.aml.2016.10.013View
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