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Classification of initial data for the Riccati equation

N. Chernyavskaya, L. Shuster (2002)

Bollettino dell'Unione Matematica Italiana

We consider a Cauchy problem y x + y 2 x = q x , y x x = x 0 = y 0 where x 0 , y 0 R and q x L 1 loc R is a non-negative function satisfying the condition: - x q t d t > 0 , x q t d t > 0  for  x R . We obtain the conditions under which y x can be continued to all of R . This depends on x 0 , y 0 and the properties of q x .

Generalized iterated function systems, multifunctions and Cantor sets

Maciej Klimek, Marta Kosek (2009)

Annales Polonici Mathematici

Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.

The multi-morphisms and their properties and applications

Mirosław Ślosarski (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

In this paper a new class of multi-valued mappings (multi-morphisms) is defined as a version of a strongly admissible mapping, and its properties and applications are presented.

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