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We study the eigenvalues of the p(x)-Laplacian operator with zero Neumann boundary condition on a bounded domain, where p(x) is a continuous function defined on the domain with p(x)>1. We show that, similarly to the p-Laplacian case, the smallest eigenvalue of the problem is 0 and it is simple, and the supremum of all the eigenvalues is infinity, however, unlike the p-Laplacian case, for very general...
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