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)
A necessary and sufficient condition for to existence of solutions the differential inclusions. (English) Zbl 0910.34029
The author gives necessary and sufficient conditions for the existence of a solution to scalar differential inclusions $x'\in F(x)$, $x\in\bbfR$. The proof is based on a selection of a single-valued function $f(x)\in F(x)$ which satisfies a necessary and sufficient condition for the existence of a solution to the differential equation $x'=f(x)$ given by {\it P. Binding} [J. Differ. Equations, 31, 183-199 (1979; Zbl 0363.34001)].

MSC:
34A60Differential inclusions
WorldCat.org
Full Text: DOI
References:
[1] Bressan, A.: Directionally continuous selections and differential inclusions. Funkcialaj ekvacioj 31, 459-470 (1988) · Zbl 0676.34014
[2] Bressan, A.: On the qualitative theory of lower semicontinuous differential inclusions. Journal of differential equations 77, 379-391 (1989) · Zbl 0675.34011
[3] Bressan, A.: Upper and lower semicontinuous differential inclusions. A unified approach. Controllability and optimal control (1990) · Zbl 0704.49011
[4] Bressan, A.: Selections of Lipschitz multifunctions generating a continuous flow. Differential and integral equations 4, No. 3, 483-490 (1991) · Zbl 0722.34009
[5] Bressan, A.; Cortesi, A.: Directionally continuous selections in Banach spaces. Nonlinear analysis, theory, methods and applications 13, No. 8, 987-992 (1989) · Zbl 0687.34013
[6] Cambini, A.; Querci, S.: Equazioni differenziali del primo ordine con secondo membro discontinuo rispetto all’incognita. Rend. ist. Mat. univ. Trieste 1, 89-97 (1969) · Zbl 0193.04203
[7] Colombo, G.: Weak flow-invariance for nonconvex differential inclusions. Differential and integral equations 5, No. 1, 173-180 (1992) · Zbl 0757.34017
[8] Pucci, A.: Sistemi di equazioni differenziali con secondo membro discontinuo rispetto all’incognita. Rend. ist. Mat. univ. Trieste 3, 75-80 (1971) · Zbl 0238.34008
[9] Binding, P.: The differential equation x \dot{} = f $\circ $x. Journal of differential equations 31, 183-199 (1979) · Zbl 0363.34001
[10] Coddington, E. A.; Levinson, N.: Theory of ordinary differential equations. (1955) · Zbl 0064.33002
[11] Aubin, J. P.; Cellina, A.: Differential inclusions. (1984) · Zbl 0538.34007
[12] Jarnik, J.: Multivalued mappings and Filippov’s operation. Czechoslovak math. J. 31, 275-288 (1981) · Zbl 0473.34018