Uniqueness of solutions of linear nonlocal boundary value problems

For n≥3n≥3 and 1≤k≤n−11≤k≤n−1, conditions are established for which the nonlocal boundary value problem, y(n)+∑i=0n−1ai(x)y(i)=0,y(i−1)(xj)=0,1≤i≤mj,1≤j≤k,y(xk+1)−y(xk+2)=0,y(xk+1)−y(xk+2)=0, has only the trivial solution, for all positive integers m1,…,mkm1,…,mk such that m1+⋯+mk=n−1m1+⋯+mk=n−1, and all a