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Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations
Authors:Stephen Clark  Johnny Henderson
Institution:Department of Mathematics, Baylor University, Waco, Texas 76798-7328 ; Department of Mathematics, Baylor University Waco, Texas 76798-7328
Abstract: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.

Keywords:Boundary value problem  uniqueness  existence  nonlocal
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