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A minimax formula for the principal eigenvalue of a nonselfadjoint elliptic problem was established in [17]. In this paper we extend this formula to the case where an indefinite weight is present. An application is given to the study of the uniformity of the antimaximum principle. (2000): 35J20, 35P15 Mathematics Subject Classification

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This paper is concerned with nonself-adjoint elliptic problems involving indefinite weights and boundary conditions of the Dirichlet, Neumann or Robin type. We study the asymptotic behavior of the principal eigenvalues, when the first order term (drift term) becomes larger and larger. The basic results of Berestycki et al. (Commun. Math. Phys., 253:451-480, 2005) are extended to the present context. Moreover, answers are provided to some open problems raised in Berestycki et al. (Commun. Math. Phys., 253:451-480, 2005).

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