Author
Dimitrov, Youri

Year
2006

Advisor
Edgar, Gerald

Abstract

A real valued function Fon the interval [ a,b] is self-differentialif [ a,b] can be subdivided into a finite number of subintervals, and on each subinterval the derivative of Fis equal to Fwith the graph transformed by an affine map. In the four bipartite self-differential equations studied here, the interval [ 0,1] is decomposed into [ 0,1/2] and [ 1/2,1], and the affine transformed images of Fare aF(2x),F(2-2x),aF(1-2x),aF(2x-1).The bipartite self-differential equations have a solution for every value of the parameter aand initial value f(0)=c. The boundary value f(1)=dis determined from the values of aand c. When ais an odd power of 2there exist infinitely many continuously differentiable solutions. The solution is unique for all other values of a.

 

Thesis
Dimitrov, Youri .pdf