| Title:
|
Boundary value problems for semilinear evolution inclusions: Carathéodory selections approach (English) |
| Author:
|
Cardinali, Tiziana |
| Author:
|
Santori, Lucia |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
115-125 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove two existence theorems for abstract boundary value problems controlled by semilinear evolution inclusions in which the nonlinear part is a lower Scorza-Dragoni multifunction. Then, by using these results, we obtain the existence of periodic mild solutions. (English) |
| Keyword:
|
semilinear differential inclusion |
| Keyword:
|
selection theorem |
| Keyword:
|
mild solution |
| Keyword:
|
lower Scorza Dragoni multifunction |
| Keyword:
|
mild periodic solution. |
| MSC:
|
34A60 |
| MSC:
|
34G20 |
| idZBL:
|
Zbl 1240.34288 |
| idMR:
|
MR2828367 |
| . |
| Date available:
|
2011-03-08T17:41:23Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141431 |
| . |
| Reference:
|
[1] Andres J., Malaguti L., Taddei V.: On Boundary value problems in Banach spaces.Dynam. Systems Appl. 18 (2009), 275–302. Zbl 1195.34091, MR 2543232 |
| Reference:
|
[2] Anichini G., Zecca P.: Problemi ai limiti per equazioni differenziali multivoche su intervalli non compatti.Riv. Mat. Univ. Parma 1 (1975), 199–212. Zbl 0359.34057, MR 0447728 |
| Reference:
|
[3] Artstein Z., Prikry K.: Carathéodory selections and the Scorza Dragoni property.J. Math. Anal. Appl. 127 (1987), no. 2, 540–547. Zbl 0649.28011, MR 0915076, 10.1016/0022-247X(87)90128-4 |
| Reference:
|
[4] Brezis H.: Analisi Funzionale-Teoria e Applicazioni.Liguori, Napoli, 1986. |
| Reference:
|
[5] Chang K.C.: The obstacle problem and partial differential equations with discontinuous nonlinearities.Comm. Pure Appl. Math. 33 (1980), 117–146. Zbl 0405.35074, MR 0562547, 10.1002/cpa.3160330203 |
| Reference:
|
[6] Conti R.: Recent trends in the theory of boundary value problems for ordinary differential equations.Boll. Univ. Mat. Ital. 22 (1967), 135–178. Zbl 0154.09101, MR 0218650 |
| Reference:
|
[7] Himmelberg C.J.: Measurable relations.Fund. Math. 87 (1975), 53–71. Zbl 0465.28002, MR 0367142 |
| Reference:
|
[8] Hu S., Papageorgiou N.S.: Handbook of Multivalued Analysis.1, Kluwer Academic Publishers, Dordrecht, 1997. Zbl 0943.47037, MR 1485775 |
| Reference:
|
[9] Kamenskii M.I., Obukhovskii V.V., Zecca P.: Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces.De Gruyter Ser. Nonlinear Anal. Appl. 7, De Gruyter, Berlin-New York, 2001. Zbl 0988.34001, MR 1831201 |
| Reference:
|
[10] Kolmogorov A.N., Fomin S.V.: Introductory Real Analysis.Prentice-Hall, Inc. Englewood Cliffs, N.J., 1970. Zbl 0213.07305, MR 0267052 |
| Reference:
|
[11] Krein S.G.: Linear Differential Equations in Banach Spaces.American Mathematical Society, Providence, R.I., 1971. MR 0342804 |
| Reference:
|
[12] Martin R.: Nonlinear Operators and Differential Equations in Banach Spaces.Wiley, New York, 1976. Zbl 0333.47023, MR 0492671 |
| Reference:
|
[13] Michael E.: Continuous selections I.Ann. of Math. (2) 63 (1956), 361–382. Zbl 0071.15902, MR 0077107, 10.2307/1969615 |
| Reference:
|
[14] Naito K.: Approximation and controllability for solution of semilinear control systems.Control Theory Adv. Tech. 1 (1985), 165–173. MR 0927841 |
| Reference:
|
[15] Obukhovskii V.V., Zecca P.: On Boudary value problems for degenerate differential inclusions in Banach spaces.Abstr. Appl. Anal. 13 (2003), 769–784. MR 1996923, 10.1155/S108533750330301X |
| Reference:
|
[16] Papageorgiou N.S.: Boundary value problems for evolution inclusions.Ann. Polon. Math. 50 (1990), 251–259. Zbl 0715.35090, MR 1064999 |
| Reference:
|
[17] Papageorgiou N.S.: Boundary value problems and periodic solutions for semilinear evolution inclusions.Comment. Math. Univ. Carolin. 35 (1994), no. 2, 325–336. Zbl 0807.34077, MR 1286579 |
| Reference:
|
[18] Papageorgiou N.S.: Existence of solutions for boundary problems of semilinear evolution inclusions.Indian J. Pure Appl. Math. 23 (1992), no. 7, 477–488. MR 1174609 |
| Reference:
|
[19] Pazy A.: Semigroups of Linear Operators and Applications to Partial Differential Equations.Springer, Berlin, 1983. Zbl 0516.47023, MR 0710486 |
| Reference:
|
[20] Zecca P., Zezza P.: Nonlinear boundary value problems in Banach spaces for multivalue differential equations on a non-compact interval.Nonlinear Anal. T.M.A. 3 (1979), 347–352. Zbl 0443.34060, MR 0532895 |
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