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The Laplacian with Robin Boundary Conditions on Arbitrary Domains

โœ Scribed by Wolfgang Arendt; Mahamadi Warma

Book ID
111539887
Publisher
Springer Netherlands
Year
2003
Tongue
English
Weight
190 KB
Volume
19
Category
Article
ISSN
0926-2601

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๐Ÿ“œ SIMILAR VOLUMES

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We consider the Robin boundary conditions on irregular domains where the usual Sobolev embeddings fail. We present a functional framework permitting superhomogeneous growth of the nonlinearity and prove the existence of positive, bounded, and smooth solutions of the p-Laplacian equation.

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The aim of this paper is to study the Fucik spectrum of the p-Laplacian with Robin boundary condition given by where ฮฒ โ‰ฅ 0. If ฮฒ = 0, it reduces to the Fucik spectrum of the negative Neumann p-Laplacian. The existence of a first nontrivial curve C of this spectrum is shown and we prove some propert