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Polynomially-divided solutions of bipartite self-differential functional equations
Dimitrov, Youri

2006, Doctor of Philosophy, Ohio State University, Mathematics.
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.
Gerald Edgar (Advisor)

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Dimitrov, Y. (2006). Polynomially-divided solutions of bipartite self-differential functional equations. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Dimitrov, Youri. "Polynomially-divided solutions of bipartite self-differential functional equations." Electronic Thesis or Dissertation. Ohio State University, 2006. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Dimitrov, Youri "Polynomially-divided solutions of bipartite self-differential functional equations." Electronic Thesis or Dissertation. Ohio State University, 2006. https://etd.ohiolink.edu/

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