Singular Dirichlet problem for ordinary differential equation with impulses

The paper deals with the impulsive Dirichlet problemu″(t)=f(t,u(t),u′(t)),u″(t)=f(t,u(t),u′(t)),u(0)=A,u(T)=B,u(tj+)=Ij(u(tj)),u′(tj+)=Mj(u′(tj)),j=1,…,p,where f∈Car((0,T)×R2)f∈Car((0,T)×R2), f   has time singularities at t=0t=0 and t=Tt=T, IjIj, Mj∈C0(R)Mj∈C0(R), A  , B∈RB∈R. We prove the existence of a solution to this problem under the assumption that there exist lower and upper functions associated with the problem. Our proofs are based on the Schauder fixed point theorem and on the method of a priori estimates.