Multiplicity of solutions to two-point boundary value problems for second-order impulsive differential equations

In this paper, we obtain some sufficient condition for the existence of at least three solutions to two-point boundary value problems for second-order impulsive differential equations by using Leray–Schauder degree theory. We assume the existence of two pairs of strict lower and upper solutions and the nonlinear term f satisfies a Nagumo’s growth condition with respect to the first order derivative.