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|Title: ||On the Solvability of Nonlinear Discrete Multipoint Boundary Value Problems|
|Authors: ||Taylor, Padraic Whittingham|
|Advisors: ||Dr. Jesus Rodriguez, Committee Chair|
Dr. James Selgrade, Committee Member
Dr. Tom Lada, Committee Member
Dr. Kailash Misra, Committee Member
|Keywords: ||Brouwer Fixed Point Theorem|
boundary value problems
Implicit Function Theorem
|Issue Date: ||17-Apr-2007|
|Abstract: ||In this manuscript we study nonlinear, discrete, multipoint boundary value problems. We investigate two types of problems.
We first consider scalar, nonlinear, multipoint boundary value problems. We provide sufficient conditions for the existence of solutions. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems. [8,9].
We also study weakly nonlinear, discrete systems. We provide sufficient conditions for the existence of solutions and we present a qualitative analysis of the way the solutions depend on the parameter.|
|Appears in Collections:||Dissertations|
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