Uniqueness of solutions of linear nonlocal boundary value problems

Abstract

For n ≥ 3 and 1 ≤ k ≤ n − 1 , conditions are established for which the nonlocal boundary value problem, y ( n ) + ∑ i = 0 n − 1 a i ( x ) y ( i ) = 0 , y ( i − 1 ) ( x j ) = 0 , 1 ≤ i ≤ m j , 1 ≤ j ≤ k , y ( x k + 1 ) − y ( x k + 2 ) = 0 , has only the trivial solution, for all positive integers m 1 , … , m k such that m 1 + ⋯ + m k = n − 1 , and all a < x 1 < ⋯ < x k + 2 < b .