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On the Fredholm alternative for the -Laplacian at higher eigenvalues (in one dimension)

✍ Scribed by Jiří Benedikt; Petr Girg; Peter Takáč


Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
1020 KB
Volume
72
Category
Article
ISSN
0362-546X

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Fredholm Alternative for the p-Laplacian
✍ Pavel Drábek; Gabriela Holubová 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 115 KB

In this paper we characterize the set of all right-hand sides h ∈ C for which the boundary value problem . Here 1 < p < 2, and λ 1 > 0 is the first eigenvalue of the p-Laplacian. In particular, we prove that for hϕ 1 = 0 this problem is solvable and the energy functional is unbounded from below.