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)
Extremal solutions of a discontinuous scalar differential equation. (English) Zbl 0949.34005
The authors prove the existence of minimal and maximal absolutely continuous solutions x:[0,1] to the initial value problem x ' (t)=f(t,x(t)), x(0)=0. Here, f:[0,1]× ¯ satisfies standard “measurability” assumptions and a nonstandard “continuity” assumption: for every x, the function tf(t,x) is Lebesgue measurable; there exists a Lebesgue integrable function M:[0,1] ¯ such that |f(t,x)|M(t) for almost all t[0,1] and for all x; lim sup yx f(t,y)f(t,x)lim inf yx f(t,y) for almost all t[0,1] and for all x. Applications concern the scalar equation x ' (t)=q(x(t))f(t,x(t)) where q is Lebesgue measurable as well as the vector equation x ' (t)=f(t,x(t)) where x k f i (t,,x k-1 ,x k ,x k+1 ,) is nondecreasing for each ik [cf. J. Szarski, Differential inequalities, Warszawa: PWN-Polish Scientific Publishers (1967; Zbl 0171.01502)].

MSC:
34A36Discontinuous equations