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

Abstract

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.

Keywords

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