2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco. Electronic Journal of Differential Equations, Conference 14 (2006), pp. 207-222. Title: Asymmetric elliptic problems in $R^N$ Authors: Jean-Pierre Gossez (Univ. Libre de Bruxelles, Belgium) Liamidi Leadi (Univ. d'Abomey Calavi, Benin Republic) Abstract: We work on the whole $R^N$ and prove the existence of a first nonprincipal eigenvalue for an asymmetric problem with weights involving the p-Laplacian. As an application we obtain a first nontrivial curve in the corresponding Fucik spectrum. Published September 20, 2006. Math Subject Classifications: 35P30, 35J20, 35J60. Key Words: Principal eigenvalue; indefinite weight; unbounded domain; p-Laplacian; Fucik spectrum.