# 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)
Existence of solutions for integral inclusions. (English) Zbl 1125.45006

This paper presents sufficient conditions for the existence of positive solutions to a class of nonlinear integral inclusion of the form

$x\left(t\right)=f\left(t,x\right){\int }_{0}^{t}{u}_{x}\left(t,s\right)\phantom{\rule{0.166667em}{0ex}}ds,$

where $f:{R}_{+}×{R}^{n}\to {R}^{n}$ is a single valued map, ${u}_{x}\in {S}_{U,x},\phantom{\rule{4pt}{0ex}}{S}_{U,x}$ is the set of selections of the multivalued map $U:H×{R}^{n}\to {2}^{{R}^{n}},$ and $H=\left\{\left(t,s\right)\in {R}_{+}×{R}_{+}:s\le t\right\}$. These results are obtained via a fixed point theorem due to M. Martelli [Boll. Unione Mat. Ital., IV. Ser. 11, Suppl. Fasc. 3, 70–76 (1975; Zbl 0314.47035)] or the author [S. Hong, Electron. J. Differ. Equ. 2003, Paper No. 32 (2003; 1023.34056)] for condensing multivalued maps on ordered Banach spaces.

##### MSC:
 45G10 Nonsingular nonlinear integral equations 47H09 Mappings defined by “shrinking” properties