Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations

摘要

For the third order differential equation, y''' = f(x, y, y', y''), we consider uniqueness implies existence results for solutions satisfying the nonlocal 4-point boundary conditions, y(x(1)) = y(1), y(x(2)) = y(2), y(x(3)) - y(x(4)) = y(3). Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal 3-point boundary conditions. These relationships are investigated as well.