On the Solvability of Nonlinear Discrete Multipoint Boundary Value Problems

Brouwer Fixed Point Theorem;boundary value problems;projection;Implicit Function Theorem;Lyapunov-Schmidt Procedure

Taylor, Padraic Whittingham ; Dr. Jesus Rodriguez, Committee Chair,Dr. James Selgrade, Committee Member,Dr. Tom Lada, Committee Member,Dr. Kailash Misra, Committee Member,Taylor, Padraic Whittingham ; Dr. Jesus Rodriguez ; Committee Chair ; Dr. James Selgrade ; Committee Member ; Dr. Tom Lada ; Committee Member ; Dr. Kailash Misra ; Committee Member

University:North Carolina State University

关键词: Brouwer Fixed Point Theorem;    boundary value problems;    projection;    Implicit Function Theorem;    Lyapunov-Schmidt Procedure;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/5605/etd.pdf?sequence=1&isAllowed=y

美国|英语

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【 摘 要 】

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.