| Title:
|
On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions (English) |
| Author:
|
Cernea, Aurelian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
215-224 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set. (English) |
| Keyword:
|
hyperbolic differential inclusions |
| Keyword:
|
fixed point |
| Keyword:
|
solution set |
| MSC:
|
34A60 |
| MSC:
|
35B30 |
| MSC:
|
35L20 |
| MSC:
|
35L70 |
| MSC:
|
35R70 |
| idZBL:
|
Zbl 1010.34002 |
| idMR:
|
MR1885466 |
| . |
| Date available:
|
2009-09-24T10:50:19Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127711 |
| . |
| Reference:
|
[1] F. S. De Blasi and J. Myjak: On the set of solutions of a differential inclusion.Bull. Inst. Math. Acad. Sinica 14 (1986), 271–275. MR 0866561 |
| Reference:
|
[2] F. S. De Blasi and J. Myjak: On the structure of the set of solutions of the Darboux problem of hyperbolic equations.Proc. Edinburgh Math. Soc. 29 (1986), 7–14. MR 0829175 |
| Reference:
|
[3] F. S. De Blasi, G. Pianigiani and V. Staicu: On the solution sets of some nonconvex hyperbolic differential inclusions.Czechoslovak Math. J. 45 (1995), 107–116. MR 1314533 |
| Reference:
|
[4] L. Gorniewicz and T. Pruszko: On the set of solutions of the Darboux problem for some hyperbolic equations.Bull. Acad. Polon. Sci. Math. Astronom. Phys. 38 (1980), 279–285. MR 0620202 |
| Reference:
|
[5] S. Marano: Generalized solutions of partial differential inclusions depending on a parameter.Rend. Accad. Naz. Sci. Mem. Mat. 107 (1989), 281–295. Zbl 0702.35168, MR 1041756 |
| Reference:
|
[6] S. Marano: Fixed points of multivalued contractions with nonclosed, nonconvex values.Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 5 (1994), 203–212. Zbl 0862.54040, MR 1298263 |
| Reference:
|
[7] S. Marano and V. Staicu: On the set of solutions to a class of nonconvex nonclosed differential inclusions.Acta Math. Hungar. 76 (1997), 287–301. MR 1459237, 10.1023/A:1006533606338 |
| Reference:
|
[8] S. Marano and V. Staicu: Correction to the paper On the set of solutions to a class of nonconvex nonclosed differential inclusions.Acta Math. Hungar. 78 (1998), 267–268. MR 1604707, 10.1023/A:1006539007972 |
| Reference:
|
[9] V. Staicu: On a non-convex hyperbolic differential inclusion.Proc. Edinburgh Math. Soc. 35 (1992), 375–382. Zbl 0769.34018, MR 1187000 |
| Reference:
|
[10] G. Teodoru: A characterization of the solutions of the Darboux problem for the equation $u_{xy}\in F(x,y,u)$.An. Stiint. Univ. Al. I. Cuza Iasi Mat. 33 (1987), 33–38. MR 0925687 |
| . |
