On the global stability of an autonomous system on the plane

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Abstract

In this chapter we consider an old problem of Olech (which is equivalent to a global univalent problem in R2) on the global stability of an autonomous system on the plane and extend a result of Olech using some of the recent global univalent theorems (see [52]). We present also a variety of examples to show the sharpness of the results. In the second half of this chapter we present the results obtained by Vidossich [71] in this direction.