International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 10, Pages 625-634
doi:10.1155/S0161171201004628
On a nonresonance condition between the first and the second eigenvalues for the p-Laplacian
A. Anane
and N. Tsouli
Department of Mathematics, Faculty of Sciences, University Mohammed I, Oujda, Morocco
Abstract
We are concerned with the existence of solution for the Dirichlet problem −Δpu=f(x,u)+h(x) in Ω, u=0 on ∂Ω, when f(x,u) lies in some sense between the first and the second eigenvalues of the p-Laplacian Δp. Extensions to more general operators which are (p−1)-homogeneous at infinity are also considered.