Multiplicity of positive solutions to second order Neumann boundary value problems with impulse actions

This paper deals with existence theorems for single and multiple positive solutions to a kind of Neumann boundary value problems with impulse actions. The proof of the main results relies on a nonlinear alternative principle of Leray–Schauder type and a well-known fixed point theorem in cones. The impulses are not restricted to be monotonous in the results obtained by us.