Nonmonotone impulse effects in second-order periodic boundary value problems

Abstract

We deal with the nonlinear impulsive periodic boundary value problem u″=f(t,u,u′), u(ti+)=Ji(u(ti)), u′(ti+)=Mi(u′(ti)), i=1,2,…,m, u(0)=u(T), u′(0)=u′(T). We establish the existence results which rely on the presence of a well-ordered pair (σ1,σ2) of lower/upper functions (σ1≤σ2 on [0,T]) associated with the problem. In contrast to previous papers investigating such problems, the monotonicity of the impulse functions Ji, Mi is not required here.