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

Abstract

Abstract 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 ) $\lambda \in (0,\Lambda )$ , one positive solution for λ = Λ $\lambda =\Lambda $ , and no positive solution for λ > Λ $\lambda >\Lambda $ , where Λ > 0 $\Lambda >0$ is a constant.

Keywords

• Impulsive differential equation
• Sturm
• Liouville boundary value problem
• Positive solution
• Critical point