Article
| Title: | Periodic boundary value problem of a fourth order differential inclusion (English) |
| Author: | Švec, Marko |
| Language: | English |
| Journal: | Archivum Mathematicum |
| ISSN: | 0044-8753 (print) |
| ISSN: | 1212-5059 (online) |
| Volume: | 33 |
| Issue: | 1 |
| Year: | 1997 |
| Pages: | 167-171 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The paper deals with the periodic boundary value problem (1) $L_4 x(t) + a(t)x(t) \in F(t,x(t))$, $t\in J= [a,b]$, (2) $L_i x(a)= L_i x(b)$, $i=0,1,2,3$, where $L_0x(t)= a_0x(t)$, $L_ix(t)=a_i(t)L_{i-1}x(t)$, $i=1,2,3,4$, $a_0(t)= a_4(t)=1$, $a_i(t)$, $i=1,2,3$ and $a(t)$ are continuous on $J$, $a(t)\geq 0$, $a_i(t)>0$, $i=1,2$, $a_1(t)= a_3(t)\cdot F(t,x): J \times R \to$\{nonempty convex compact subsets of $R$\}, $R= (-\infty , \infty )$. The existence of such periodic solution is proven via Ky Fan's fixed point theorem. (English) |
| Keyword: | nonlinear boundary value problem |
| Keyword: | differential inclusion |
| Keyword: | measurable selector |
| Keyword: | Ky Fan’s fixed point theorem |
| MSC: | 34A60 |
| MSC: | 34B15 |
| MSC: | 34C25 |
| MSC: | 47J05 |
| MSC: | 47N20 |
| idZBL: | Zbl 0914.34015 |
| idMR: | MR1464311 |
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| Date available: | 2008-06-06T21:33:05Z |
| Last updated: | 2012-05-10 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/107607 |
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| Reference: | [1] Y. Kitamura: On nonoscillatory solutions of functional differential equations with a general deviating argument.Hiroshima Math. J. 8 (1978), 49-62. Zbl 0387.34048, MR 0466865 |
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| Files | Size | Format | View |
|---|---|---|---|
| ArchMathRetro_033-1997-1_18.pdf | 214.5Kb | application/pdf |
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