Existence results for impulsive second-order periodic problems Original Research Article

This paper provides existence results for the nonlinear impulsive periodic boundary value problem View the MathML sourceu″=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), Turn MathJax on where f∈Car([0,T]×R2)f∈Car([0,T]×R2) and Ji,Ji,Mi∈C(R)Mi∈C(R). The basic assumption is the existence of lower/upper functions σ1/σ2σ1/σ2 associated with the problem. Here, we generalize and extend the existence results of our previous papers.