| Description |
This report constitutes a compilation of the research literature with respect to the problem of determining the uniqueness of solution to the initial value problem for ordinary differential equations. The basic problem consists of the following. Suppose that f(x,y) is a continuous vector-valued function for x in an interval I and y in a domain CR^n. Then for any x0 E I, yo E delta, the initial value problem y'=f(x.y), y(x0)=y0 has at least one local solution y(x) E C^1(J), that is , E a nontrivial subinterval J of I about x0. In general, there may be more than one solution. Under what additional assumptions on f, will there be exactly on solution locally at x0? The next section lists a number of the research papers written on this problem over the past century. The papers are listed alphabetically by the author's last name. Following the bibliographical entry of each paper is a short review of the contributions (hopefully, the main contributions) of that paper, when that paper or a review was done for the most part by Mr. Steven W. Andreasen, a student at the University of Utah during the winter quarter 1969-1970. The work constituted partial fulfillment of his requirements for a Bachelor of Science Honors degree in mathematics. In section 3, Mr. Andreasen compares some of the results from different papers. |
