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Fredholm Alternative for the p-Laplacian in Higher Dimensions

✍ Scribed by Pavel Drábek; Gabriela Holubová

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
115 KB
Volume
263
Category
Article
ISSN
0022-247X

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

On the Number and Structure of Solutions
On the Number and Structure of Solutions for a Fredholm Alternative with the p-Laplacian
✍ Peter Takác 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 401 KB

We investigate the existence and multiplicity of weak solutions u 2 W 1;p 0 ðOÞ to the degenerate quasilinear Dirichlet boundary value problem where z 2 R is a parameter. It is assumed that 1opo1; p=2; and O is a bounded domain in R N : The number l 1 stands for the first (smallest) eigenvalue of t