A result on the bifurcation from the principal eigenvalue of the Ap-Laplacian. (1997) - Drábek, P.; Elkhalil, A.; Touzani, A.
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.