# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Criteria for viability of trajectories of nonautonomous differential inclusions and their applications. (English) Zbl 0798.34019
The author gives a necessary and sufficient condition for the existence of (viable) solutions of the problem $\left[\stackrel{˙}{x}\left(t\right)\in F\left(t,x\left(t\right)\right)$, $x\left(\tau \right)=x$, $x\left(t\right)\in W\left(t\right)$, $t\ge \tau \right]$, where the map $F\left(t,·\right)$ is upper semicontinuous, $F\left(·,x\right)$ is measurable, $\parallel F\left(t,x\right)\parallel \le r$ for some $r>0$, and the graph of $W$ is closed. This condition is expressed in terms of the contingent derivative of the map ${G}_{\tau ,x}\left(t\right)=W\left(t\right)-X\left(t,\tau ,x\right)$, where $X\left(t,\tau ,x\right)$ is the reachable set of the differential inclusion. It is used for comparison of solutions to differential equations and generalized differential inequalities. Under some additional assumptions a differential inclusion whose trajectories coincide with viable trajectories of the original problem is constructed.
##### MSC:
 34A60 Differential inclusions