nagumo type existence results of sturm–liouville bvp for impulsive differential equations

in this paper, the method of upper and lower solutions and the schauder degree theory are employed in the study of sturm–liouville boundary value problems for second order impulsive differential equations. we obtain the existence of at least three solutions to the problem under the assumption that the nonlinear term f satisfies a nagumo condition with respect to the first order derivative.