Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0714.35029
Lindqvist, Peter
On the equation $div(\vert \nabla u\vert \sp{p-2}\nabla u)+\lambda \vert u\vert \sp{p-2}u=0$. (English)
[J] Proc. Am. Math. Soc. 109, No.1, 157-164 (1990). ISSN 0002-9939; ISSN 1088-6826/e

The paper deals with the multiplicity of solutions of the equation $$ div(\vert \nabla u\vert\sp{p-2}\nabla u)+\lambda \vert u\vert\sp{p- 2}u=0\text{ in } W\sb 0\sp{1,p}(\Omega), $$ where $\Omega$ is any bounded domain, $1<p<+\infty$, and $\lambda$ is the minimum of the Rayleigh quotient $\int\sb{\Omega}\vert \nabla u\vert\sp p dx/\int\sb{\Omega}\vert u\vert\sp p dx$ as u varies in $W\sb 0\sp{1,p}(\Omega)$. It is shown that any two solutions are proportional. This result was known in the linear case $(p=2)$ and, for general p, under special assumptions on $\partial \Omega$. By improving the method of {\it A. Anane} [C. R. Acad. Sci., Paris, Sér. I 305, 725-728 (1987; Zbl 0633.35061)] the author obtains the optimal result.
[L.Ambrosio]

MSC 2000:: *35J60 Nonlinear elliptic equations
35J70 Elliptic equations of degenerate type
35P30 Nonlinear eigenvalue problems for PD operators
35J20 Second order elliptic equations, variational methods

Keywords: p-Laplacian; multiplicity of solutions

Citations: Zbl 0633.35061

Cited in: Zbl 1185.35017 Zbl 1152.35046 Zbl 0787.35027

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]