Henderson, Johnny.Ma, Ding.Baylor University. Dept. of Mathematics.2006-07-072006-07-0720052006-07-07http://hdl.handle.net/2104/3577Includes bibliographical references (p. 54-58).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.iv, 58 p.62450210 bytesapplication/pdfen-USBaylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission.Boundary value problems -- Research.Differential equations -- Research.ThesisWorldwide access