THE POINT AT INFINITY AND PERIODIC SOLUTIONS,
POLYTECHNIC INST OF BROOKLYN N Y
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Some practical criteria for stability of certain nonelementary critical points are obtained. The criteria are practical in the sense that elementary computations can be used to determine if a particular critical point of a given two-dimensional system satisfies the criteria. These criteria are obtained by reformulating certain results from the analysis of general critical points and adding certain topological and analytical considerations. The fact that the criteria obtained are really practical is then illustrated with some examples. The results are applied to the theory and limit cycles and periodic solutions are obtained and the existence of unbounded solutions of a particular kind is established. Periodic solutions for certain two-dimensional systems are obtained by using the concept of the line at infinity.