Abstract and Applied Analysis

A result on the bifurcation from the principal eigenvalue of the $A_p$-Laplacian

P. Drábek, A. Elkhalil, and A. Touzani

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Abstract

We study the following bifurcation problem in any bounded domain Ω in N: {Apu:=i,j=1Nxi[(m,k=1Namk(x)uxmuxk)p22aij(x)uxj]=λg(x)|u|p2u+f(x,u,λ),uW01,p(Ω).. We prove that the principal eigenvalue λ1 of the eigenvalue problem {Apu=λg(x)|u|p2u,uW01,p(Ω), is a bifurcation point of the problem mentioned above.

Article information

Source
Abstr. Appl. Anal., Volume 2, Number 3-4 (1997), 185-195.

Dates
First available in Project Euclid: 14 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050355232

Digital Object Identifier
doi:10.1155/S108533759700033X

Mathematical Reviews number (MathSciNet)
MR1704867

Zentralblatt MATH identifier
0933.35151

Subjects
Primary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35J70
Secondary: 35P30

Keywords
$A_p$-Laplacian indefinite weight the first eigenvalue bifurcation problem

Citation

Drábek, P.; Elkhalil, A.; Touzani, A. A result on the bifurcation from the principal eigenvalue of the $A_p$-Laplacian. Abstr. Appl. Anal. 2 (1997), no. 3-4, 185--195. doi:10.1155/S108533759700033X. https://projecteuclid.org/euclid.aaa/1050355232


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