Eigenvalues of the p(x)-Laplacian Neumann problems☆

By Xianling Fan. 2007

63 citations recorded by the source corpus.

Abstract 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 variable exponent p ( x ) , the first eigenvalue is not isolated, that is, the infimum of all positive eigenvalues of the problem is 0. We also study some properties of the set of functions having p ( x ) -average value zero.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ce082488fb27628020f13d6c83e388d7d7d7dd92