Guiding functions for generalized periodic problems and applications (Q388573)

By using the method of guiding functions, the authors obtain the existence of solutions for the class of differential inclusions in \(\mathbb R^n\) NEWLINE\[NEWLINE u'(t)\in F(t,u(t))\text{ for a.e. } t\in [0,T] NEWLINE\]NEWLINE with generalized periodic condition NEWLINE\[NEWLINE u(T)\in M(u(0)),NEWLINE\]NEWLINE where \(F\) is an upper Carathéodory type multimap with compact convex values and \(M\) is a multimap in \(\mathbb R^n\) which can be represented as the finite composition of upper semicontinuous multimaps with \(R_\delta\)-values. The classical periodic and anti-periodic problems are contained as particular cases. Further, examples from the theory of differential games are presented.