Geodesic
An integro-differential inequality related to the smallest positive eigenvalue of<i>p</i>(<i>x</i>)-Laplacian Dirichlet problem
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 15 (2016).

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We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
Keywords: p(x)-Laplacian, eigenvalue, variable exponent Sobolev space, Dirichlet problem, unbounded domain 
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     author = {Wi\'sniewski, Damian and Bodzioch, Mariusz},
     title = {An integro-differential inequality related to the smallest positive eigenvalue {of&lt;i&gt;p&lt;/i&gt;(&lt;i&gt;x&lt;/i&gt;)-Laplacian} {Dirichlet} problem},
     journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
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Wiśniewski, Damian; Bodzioch, Mariusz. An integro-differential inequality related to the smallest positive eigenvalue of<i>p</i>(<i>x</i>)-Laplacian Dirichlet problem. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 15 (2016). http://geodesic.mathdoc.fr/item/AUPCM_2016_15_a2/