Uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for nth order differential equations

Abstract

For the nth order differential equation, y ( n ) = f ( x , y , y ′ , … , y ( n − 1 ) ) , we consider uniqueness implies existence results for solutions satisfying certain nonlocal ( k + 2 ) -point boundary conditions, 1 ⩽ k ⩽ n − 1 . Uniqueness of solutions when k = n − 1 is intimately related to uniqueness of solutions when 1 ⩽ k ⩽ n − 2 . These relationships are investigated as well.