Mathematics Colloquium



Department of Mathematics


University of Nebraska at Omaha


WHEN:
Thursday, March 22, 2007 at 2:30 PM

WHERE:
Durham Science Center, Room 256

WHAT:


Steve From

UNO-Mathematics


will give a talk on

NEW BOUNDS ON THE LOCATIONS OF BLOWUP SINGULARITIES OF SOLUTIONS TO CERTAIN NONLINEAR DIFFERENTIAL EQUATIONS


ABSTRACT: The theory of oscillation and nonoscillation of differential equations has been considered in many hundreds of papers. However, the important problem of locating singularities to solutions of differential equations has only been considered in a few cases. I will discuss some of my results giving new bounds for these singularities. Some inequalities and ideas from probability theory shall be utilized to derive some of these bounds. In addition, the problem of obtaining bounds on certain non-monotonic functions of the solution and its derivatives is achieved without the need to find critical points of these functions. These bounds will be compared to the few existing bounds in several cases. Although these new bounds are not uniformly better than previously-proposed bounds, they are the only bounds available in some cases, and can also be used to solve a problem involving distance between asymptotes posed by S. Eliason in 1972. Some possibilities for further research and some open problems will also be discussed.


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