Eigenvalues for a nonlocal pseudo p-Laplacian
In this paper we study the eigenvalue problems for a nonlocal operator of order s that is analogous to the local pseudo p-Laplacian. We show that there is a sequence of eigenvalues λn→ ∞and that the first one is positive, simple, isolated and has a positive and bounded associated eigenfunction. For...
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10780947_v36_n12_p6737_DelPezzo |
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| Sumario: | In this paper we study the eigenvalue problems for a nonlocal operator of order s that is analogous to the local pseudo p-Laplacian. We show that there is a sequence of eigenvalues λn→ ∞and that the first one is positive, simple, isolated and has a positive and bounded associated eigenfunction. For the first eigenvalue we also analyze the limits as p → ∞ (obtaining a limit nonlocal eigenvalue problem analogous to the pseudo infinity Laplacian) and as s → 1- (obtaining the first eigenvalue for a local operator of p-Laplacian type). To perform this study we have to introduce anisotropic fractional Sobolev spaces and prove some of their properties. |
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