An integro-differential inequality related to the smallest positive eigenvalue of p(x)-Laplacian Dirichlet problem

Damian Wiśniewski, Mariusz Bodzioch


We consider the eigenvalue problem for the p(x)-Laplace - Beltrami operator on the unit sphere. We prove an integro - differential inequality related to the smallest positive eigenvalue of this problem.


p(x)-Laplacian; eigenvalue; variable exponent Sobolev space; Dirichlet problem; unbounded domain

Mathematics Subject Classification (2010)

26D10; 35J60; 35J70


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