A result on the bifurcation from the principal eigenvalue of the Ap-Laplacian. (1997)

• Record Type: Journal Article
• Authors: Drábek, P.; Elkhalil, A.; Touzani, A.
• Is Part Of: Abstract and applied analysis. Volume 2:Number 3/4(1997)
• Page Start: 185
• Page End: 195
• Publication Date: 1997
• Subjects: Ap-Laplacian -- indefinite weight -- the first eigenvalue -- bifurcation problem; Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S108533759700033X
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We study the following bifurcation problem in any bounded domainΩ inℝ 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 eigenvalueλ 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.