A result on the bifurcation from the principal eigenvalue of the Ap‐Laplacian

P. Drábek, A. Elkhalil and A. Touzani

Abstract and Applied Analysis, 1997, vol. 2, issue 3-4, 185-195

Abstract: We study the following bifurcation problem in any bounded domain Ω in ℝN: {Apu:=−∑i,j=1N∂∂xi[(∑m,k=1Namk(x)∂u∂xm∂u∂xk)p−22aij(x)∂u∂xj]= λg(x)|u|p−2u+f(x,u,λ),u∈W01,p(Ω). . We prove that the principal eigenvalue λ1 of the eigenvalue problem {Apu=λg(x)|u|p−2u,u∈W01,p(Ω), is a bifurcation point of the problem mentioned above.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2:y:1997:i:3-4:p:185-195

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