Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


White FINAL 5 5 2021 with cert.pdf (298.65 KB)

ETD Abstract Container

Abstract Header

On the Existence of Solutions to Discrete, Nonlinear, Multipoint, Boundary Value Problems

White, Dylan
http://rave.ohiolink.edu/etdc/view?acc_num=ysu1620309402550166

Abstract Details

2021, Master of Science in Mathematics, Youngstown State University, Department of Mathematics and Statistics.
In this manuscript we study a general family of discrete nonlinear boundary value problems of the form x(t + 1) = A(t)x(t) + f(x(t)) where t ∈ {0, 1, ...,N – 1} subject to B0x(0) + B1x(1) + ... + BNx(N) = 0. We concern ourselves with establishing conditions that are sufficient to guarantee the existence of solutions to these boundary value problems in two distinct cases. First, we will examine this problem as a scalar, discrete, nonlinear, mulitpoint boundary value problem. We then tackle this problem in the setting of a full n×n system. In both of these cases, if the associated linear homogeneous boundary value problem only has trivial solutions we are able to show the existence of solutions when the nonlinear term exhibits sublinear growth. We then allow for the solution space of the associated linear problem to be of dimension one. In this instance, we introduce a projection scheme in order to relate the solution space of the linear problem to the nonlinearity. We then leverage this relationship to establish a framework that is sufficient to guarantee the existence of a solution.
Padraic Taylor, PhD (Advisor)
Richard Goldthwait, PhD (Committee Member)
Jozsi Jalics, PhD (Committee Member)
58 p.
Mathematics
Boundary value problems; Multipoint; Degree theory; Lyapunov-Schmidt

Recommended Citations

Citations

  • White, D. (2021). On the Existence of Solutions to Discrete, Nonlinear, Multipoint, Boundary Value Problems [Master's thesis, Youngstown State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1620309402550166

    APA Style (7th edition)

  • White, Dylan. On the Existence of Solutions to Discrete, Nonlinear, Multipoint, Boundary Value Problems. 2021. Youngstown State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ysu1620309402550166.

    MLA Style (8th edition)

  • White, Dylan. "On the Existence of Solutions to Discrete, Nonlinear, Multipoint, Boundary Value Problems." Master's thesis, Youngstown State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1620309402550166

    Chicago Manual of Style (17th edition)

ysu1620309402550166
110
© 2021, all rights reserved.
This open access ETD is published by Youngstown State University and OhioLINK.