Existence of Nonnegative Solutions for Semilinear Elliptic Equations with Subcritical Exponents

where Ω is a bounded domain in R , N ≥ 3, with a smooth boundary ∂Ω and f : Ω× R× R → R. The existence of positive solutions to (1.1) in the case where f depends only on u and grows subcritically has been studied extensively in recent years (see the review article by Lions [3] and the references therein). In this paper, we establish the existence of nonnegative solutions to (1.1) where f has a subcritical growth in u and at most linear growth in ∇u. Aside from the above we do not make any other assumptions on the domain Ω. Our results imply, for instance, the existence of nonnegative solutions to { ∆u = −λu− ∑m j=1 cju pj − b|∇u| − h(x), x ∈ Ω, u = 0, x ∈ ∂Ω,