Nonnegative solution curves of semipositone problems with Dirichlet boundary conditions

We consider the boundary value problem-u′′(x)=λf(u(x)),x∈(-1,1),u(-1)=0=u(1),where λ>0 is a parameter and f∈C2(0,∞) is monotonically increasing and concave up such that f(0)<0 (i.e. is the semipositone). In this paper we study the case p=θ and p∈(θ,+∞). (p is the supremum of the nonnegative solution and θ is such that F(θ)=∫0θf(s)ds=0.) We discuss existence and multiplicity results for nonnegative solutions.