Lyapunov-type inequalities for fractional partial differential equations

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• 作者：Mohamed Jleli^a ; ^{jleli@ksu.edu.sa} ; Mokhtar Kirane^b ; ^c ; ^{mokhtar.kirane@univ-lr.fr} ; Bessem Samet^a ; ^{bsamet@ksu.edu.sa}
• 关键词：Fractional Sobolev spaces ; Fractional p-Laplacian ; Lyapunov inequality ; Eigenvalues
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：66
• 期：Complete
• 页码：30-39
• 全文大小：809 K
• 卷排序：66

文摘

We present Lyapunov inequalities for the fractional p-Laplacian (−Δp)s(−Δp)s, 1<p<∞1<p<∞, s∈(0,1)s∈(0,1), in an open bounded set Ω⊂RNΩ⊂RN, under homogeneous Dirichlet boundary conditions. We discuss two cases, the case sp>Nsp>N and the case sp<Nsp<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.