Multiplicity and nonexistence of positive solutions to impulsive Sturm–Liouville boundary value problems

In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we prove that the problem has at least two positive solutions for the parameter λ ∈ (0,Λ ) λ ∈ ( 0 , Λ ) , one positive solution for λ =Λ λ = Λ , and no positive solution for λ >Λ λ > Λ , where Λ >0 Λ > 0 is a constant.