摘要：This paper shows conditions for the existence of weak solutions of the problem { −∆u = λ 1 u + f(x,u) − h(x) in Ω, ∂u ∂n = g(x,u) on ∂Ω, where Ω is a bounded domain in R N (N ≥ 1) with smooth boundary, ∂u ∂n denotes the derivative of u with respect to the outer normal n, f : Ω × R → R and g : ∂Ω × R → R are bounded Carath´ eodory functions, h ∈ L 2 (Ω) and λ 1 > 0 is the principal eigenvalue of −∆ on Ω with zero Dirichlet boundary conditions. Our method is based on the minimum principle.
