International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 10, Pages 625-634

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

Received 24 February 2000

Copyright © 2001 A. Anane and N. Tsouli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 (p1)-homogeneous at infinity are also considered.