Lyapunov-type inequalities for fractional partial differential equations

Mohamed Jleli, Mokhtar Kirane, Bessem Samet

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

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.

Original languageBritish English
Pages (from-to)30-39
Number of pages10
JournalApplied Mathematics Letters
Volume66
DOIs
StatePublished - 1 Apr 2017

Keywords

  • Eigenvalues
  • Fractional p-Laplacian
  • Fractional Sobolev spaces
  • Lyapunov inequality

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