Abstract
In this chapter we consider the differential equation
where
and
is a nonlinear function of x 1,...,x n . Unfortunately, there are no known methods of solving Equation (1). This, of course, is very disappointing. However, it is not necessary, in most applications, to find the solutions of (1) explicitly. For example, let x 1(t) and x 2(t) denote the populations, at time t, of two species competing amongst themselves for the limited food and living space in their microcosm. Suppose, moreover, that the rates of growth of x 1(t) and x 2(t) are governed by the differential equation (1). In this case, we are not really interested in the values of x 1(t) and x 2(t) at every time r. Rather, we are interested in the qualitative properties of x 1(t) and x 2(t). Specically, we wish to answer the following questions.
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© 1983 Springer-Verlag New York, Inc.
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Braun, M. (1983). Qualitative theory of differential equations. In: Differential Equations and Their Applications. Applied Mathematical Sciences, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9229-3_4
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DOI: https://doi.org/10.1007/978-1-4684-9229-3_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97938-0
Online ISBN: 978-1-4684-9229-3
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