A weighted eigenvalue problem for the p-Laplacian plus a potential |
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Authors: | Mabel Cuesta Humberto Ramos Quoirin |
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Affiliation: | 1. LMPA, Université du Littoral C?te d’Opale (ULCO), 50 rue F. Buisson, 62228, Calais, France 2. Université Libre de Bruxelles, CP 214, 1050, Bruxelles, Belgium
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Abstract: | Let Δ p denote the p-Laplacian operator and Ω be a bounded domain in . We consider the eigenvalue problemfor a potential V and a weight function m that may change sign and be unbounded. Therefore the functional to be minimized is indefinite and may be unbounded from below. The main feature here is the introduction of a value α(V, m) that guarantees the boundedness of the energy over the weighted sphere . We show that the above equation has a principal eigenvalue if and only if either m ≥ 0 and α(V, m) > 0 or m changes sign and α(V, m) ≥ 0. The existence of further eigenvalues is also treated here, mainly a second eigenvalue (to the right) and their dependence with respect to V and m. |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000) 35J20 35J70 35P05 35P30 |
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