Electronic Journal of Differential Equations, Vol. 2010(2010), No. 45, pp. 1-10. Title: Existence of solutions for an eigenvalue problem with weight Authors: Abdel Rachid El Amrouss (Univ. Mohamed I, Oujda, Morocco) Siham El Habib (Univ. Mohamed I, Oujda, Morocco) Najib Tsouli (Univ. Mohamed I, Oujda, Morocco) Abstract: In this work we study the existence of solutions for the nonlinear eigenvalue problem with p-biharmonic $ \Delta_p^2 u =\lambda m(x)|u|^{p-2}u$ in a smooth bounded domain under Neumann boundary conditions. Submitted December 11, 2009. Published March 26, 2010. Math Subject Classifications: 35J66, 35P30, 58E05. Key Words: p-Biharmonic operator; Existence of solutions; Neumann problem