Uniqueness implies uniqueness and existence for nonlocal boundary value problems for fourth order differential equations.

In this dissertation, we are concerned with uniqueness and existence of solutions of certain types of boundary value problems for fourth order differential equations. In particular, we deal with uniqueness implies uniqueness and uniqueness implies existence questions for solutions of the fourth order ordinary differential equation, y⁴ = f (x, y, y¹, yⁿ, yᵐ) , satisfying nonlocal 5-point boundary conditions given by y(x₁) = y₁, y(x₂) = y₂, y(x₃) = y₃, y(x) - y(x₅) = y₄ , where a < x₁ < x₂ < x₃ < x₄ < x₅ < b, and y₁, y₂, y₃, y₄ ∈ R. We also consider solutions of this fourth order differential equation satisfying nonlocal 4-point and 3-point boundary conditions given by y(x₁) = y₁, y'(x₁) = y₂, y(x₂) = y₃, y(x₃) - y(x₄) = y₄ , y(x₁) = y₁, y'(x₁) = y₂, y''(x₁) = y₃, y(x₂) - y(x₃) =y₄.