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On the Fu c ˘ ik spectrum for the -Laplacian with Robin boundary condition

✍ Scribed by Dumitru Motreanu; Patrick Winkert

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
283 KB
Volume
74
Category
Article
ISSN
0362-546X

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✦ Synopsis

The aim of this paper is to study the Fucik spectrum of the p-Laplacian with Robin boundary condition given by

where β ≥ 0. If β = 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 properties of this curve, e.g., C is Lipschitz continuous, decreasing and has a certain asymptotic behavior. A variational characterization of the second eigenvalue λ 2 of the Robin eigenvalue problem involving the p-Laplacian is also obtained.

📜 SIMILAR VOLUMES

Positive solutions for the -Laplacian wi
Positive solutions for the -Laplacian with Robin boundary conditions on irregular domains
✍ P. Drábek; I. Schindler 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 214 KB

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.

On the Lp–Lq maximal regularity for Stok
On the Lp–Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain
✍ Rieko Shimada 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 328 KB

## Abstract We obtain the __L__~__p__~–__L__~__q__~ maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ℝ^__n__^ (__n__⩾2). The Robin condition consists of two conditions: __v__ ⋅ __u__=0 and α__u__+β(__T__(__u__, __p__)__v__ – 〈__T__(__u__, __p__)__v__,