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, an
β¦ LIBER β¦
On Eigenvalue Problems of the p-Laplacian with Neumann Boundary Conditions
β Scribed by Yin Xi Huang
- Book ID
- 118118077
- Publisher
- American Mathematical Society
- Year
- 1990
- Tongue
- English
- Weight
- 173 KB
- Volume
- 109
- Category
- Article
- ISSN
- 0002-9939
- DOI
- 10.2307/2048377
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We term the conditions (2) and (3), respectively, Neumann-type and Dirichlet-type boundary conditions, since they reduce to the standard Neumann and Dirichlet boundary conditions when Ξ± Β± = 0. Given a suitable pair of boundary conditions, a number Ξ» is an eigenvalue of the corresponding boundary val