Twin Solutions of Even Order Boundary Value Problems for Ordinary Differential Equations and Finite Difference Equations

Author

Xun Sun

Date of Award

2009

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Dr. Bonita Lawrence, Ph.D., Committee Chairperson

Second Advisor

Dr. Basant Karna, Ph.D., Committee Co-Chairperson

Third Advisor

Dr. Anna Mummert, Ph.D., Committee Member

Abstract

The Avery-Henderson fixed-point theorem is first applied to obtain the existence of at least two positive solutions for the boundary value problem

(-1)ⁿy⁽²ⁿ⁾ = f(y); n = 1; 2; 3 ... and t 2 [0; 1];

with boundary conditions

y(2k)(0) = 0

y^(2k+1)(1) = 0 for k = 0; 1; 2 ... n - 1:

This theorem is subsequently used to obtain the existence of at least two positive solutions for the dynamic boundary value problem

(-1)^{n (2n)}u(k)g(u(k)); n = 1; 2; 3 .... and k (0; ... N);

with boundary conditions

(2k)u(0) = 0

(2k+1)u(N + 1) = 0 for k = 0; 1; 2 ... n 1:

Subject(s)

Fixed point theory.

Boundary value problems.

Green's function.

Recommended Citation

Sun, Xun, "Twin Solutions of Even Order Boundary Value Problems for Ordinary Differential Equations and Finite Difference Equations" (2009). Theses, Dissertations and Capstones. 1274.
https://mds.marshall.edu/etd/1274