A result on the bifurcation from the principal eigenvalue of the A p -Laplacian

P. Drábek, A. Elkhalil and A. Touzani

Abstract and Applied Analysis, 1997, vol. 2, 1-11

Abstract:

We study the following bifurcation problem in any bounded domain Ω in ℝ N : { A p u : = − ∑ i , j = 1 N ∂ ∂ x i [ ( ∑ m , k = 1 N a m k ( x ) ∂ u ∂ x m ∂ u ∂ x k ) p − 2 2 a i j ( x ) ∂ u ∂ x j ] = λ g ( x ) | u | p − 2 u + f ( x , u , λ ) , u ∈ W 0 1 , p ( Ω ) . . We prove that the principal eigenvalue λ 1 of the eigenvalue problem { A p u = λ g ( x ) | u | p − 2 u , u ∈ W 0 1 , p ( Ω ) , is a bifurcation point of the problem mentioned above.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:468501

DOI: 10.1155/S108533759700033X

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