Nonlocal Cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities

Tiziana Cardinali; Francesco Portigiani; Paola Rubbioni

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 225-245
  • ISSN: 0011-4642

Abstract

top
In this paper we prove the existence of mild solutions and the controllability for semilinear differential inclusions with nonlocal conditions. Our results extend some recent theorems.

How to cite

top

Cardinali, Tiziana, Portigiani, Francesco, and Rubbioni, Paola. "Nonlocal Cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities." Czechoslovak Mathematical Journal 61.1 (2011): 225-245. <http://eudml.org/doc/196746>.

@article{Cardinali2011,
abstract = {In this paper we prove the existence of mild solutions and the controllability for semilinear differential inclusions with nonlocal conditions. Our results extend some recent theorems.},
author = {Cardinali, Tiziana, Portigiani, Francesco, Rubbioni, Paola},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlocal conditions; semilinear differential inclusions; selection theorem; mild solutions; lower Scorza-Dragoni property; controllability; nonlocal condition; semilinear differential inclusion; selection theorem; mild solution; lower Scorza-Dragoni property; controllability},
language = {eng},
number = {1},
pages = {225-245},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonlocal Cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities},
url = {http://eudml.org/doc/196746},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Cardinali, Tiziana
AU - Portigiani, Francesco
AU - Rubbioni, Paola
TI - Nonlocal Cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 225
EP - 245
AB - In this paper we prove the existence of mild solutions and the controllability for semilinear differential inclusions with nonlocal conditions. Our results extend some recent theorems.
LA - eng
KW - nonlocal conditions; semilinear differential inclusions; selection theorem; mild solutions; lower Scorza-Dragoni property; controllability; nonlocal condition; semilinear differential inclusion; selection theorem; mild solution; lower Scorza-Dragoni property; controllability
UR - http://eudml.org/doc/196746
ER -

References

top
  1. Abraham, R., Marsden, J. E., Ratiu, T. S., Manifolds, Tensor Analysis, and Applications, Second Edition, Springer-Verlag, New York (1988). (1988) Zbl0875.58002MR0960687
  2. Al-Omair, R. A., Ibrahim, A. G., Existence of mild solutions of a semilinear evolution differential inclusion with nonlocal conditions, Electron. J. Differential Equations 42 (2009), 11 pp. (2009) MR2495847
  3. Balachandran, K., Dauer, J. P., 10.1023/A:1019668728098, J. Optim. Theory Appl. 115 (2002), 7-28. (2002) Zbl1023.93010MR1937343DOI10.1023/A:1019668728098
  4. Boulite, S., Idrissi, A., Maniar, L., 10.1016/j.jmaa.2005.05.006, J. Math. Anal. Appl. 316 (2006), 566-578. (2006) Zbl1105.34036MR2206690DOI10.1016/j.jmaa.2005.05.006
  5. Bressan, A., Colombo, G., 10.4064/sm-90-1-69-86, Studia Math. 90 (1988), 69-85. (1988) Zbl0677.54013MR0947921DOI10.4064/sm-90-1-69-86
  6. Byszewski, L., 10.1016/0022-247X(91)90164-U, J. Math. Anal. Appl. 162 (1991), 494-505. (1991) Zbl0748.34040MR1137634DOI10.1016/0022-247X(91)90164-U
  7. Cardinali, T., Panfili, S., Global mild solutions for semilinear differential inclusions and applications to impulsive problems, PU.M.A. 19 (2008), 1-19. (2008) MR2551816
  8. Cardinali, T., Portigiani, F., Rubbioni, P., Local mild solutions and impulsive mild solutions for semilinear Cauchy problems involving lower Scorza-Dragoni multifunctions, Topol. Methods Nonlinear Anal. 32 (2008), 247-259. (2008) Zbl1193.34123MR2494057
  9. Chang, Y.-K., Li, W.-T., Nieto, J. J., 10.1016/j.na.2006.06.018, Nonlinear Anal. 67 (2007), 623-632. (2007) Zbl1128.93005MR2317194DOI10.1016/j.na.2006.06.018
  10. Górniewicz, L., Ntouyas, S. K., O'Regan, D., Existence results for first and second order semilinear differential inclusions with nonlocal conditions, J. Comput. Anal. Appl. 9 (2007), 287-310. (2007) MR2300434
  11. Górniewicz, L., Ntouyas, S. K., O'Regan, D., 10.1016/S0034-4877(05)80096-5, Rep. Math. Phys. 56 (2005), 437-470. (2005) MR2190735DOI10.1016/S0034-4877(05)80096-5
  12. Hernández, E. M., O'Regan, D., 10.1016/j.jfranklin.2008.08.001, J. Franklin Inst. 346 (2009), 95-101. (2009) MR2499965DOI10.1016/j.jfranklin.2008.08.001
  13. Hu, S., Papageorgiou, N. S., Handbook of Multivalued Analysis. Vol. I: Theory. Mathematics and its Applications, 419, Kluwer Academic Publishers, Dordrecht (1997). (1997) MR1485775
  14. Hu, S., Papageorgiou, N. S., Handbook of Multivalued Analysis. Vol. II: Applications, Mathematics and its Applications, 500 Kluwer Academic Publishers, Dordrecht (2000). (2000) MR1741926
  15. Kamenskii, M., Obukhovskii, V. V., Zecca, P., Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, de Gruyter Series in Nonlinear Analysis and Applications, 7, Berlin: de Gruyter (2001). (2001) MR1831201
  16. Krein, S. G., Linear Differential Equations in Banach Spaces, Amer. Math. Soc., Providence (1971). (1971) MR0342804
  17. Li, G., Xue, X., 10.1016/S0096-3003(02)00262-X, Appl. Math. Comput. 141 (2003), 375-384. (2003) Zbl1029.93003MR1972917DOI10.1016/S0096-3003(02)00262-X
  18. Michael, E., 10.2307/1969615, Ann. Math. 63 (1956), 361-382. (1956) Zbl0071.15902MR0077107DOI10.2307/1969615
  19. Royden, H. L., Real Analysis, Macmillan Publishing Company, New York (1988). (1988) Zbl0704.26006MR1013117
  20. Sussman, H. J., 10.1023/A:1016540217523, Set-Valued Analysis 10 (2002), 233-285. (2002) MR1926382DOI10.1023/A:1016540217523
  21. Taylor, A. E., Lay, D. C., Introduction to Functional Analysis, Robert E. Krieger Publishing Co., Inc., Malabar, FL (1986). (1986) Zbl0654.46002MR0862116
  22. Tolstonogov, A., Differential Inclusions in a Banach Space, Kluwer Academic Publishers, Dordrecht (2000). (2000) Zbl1021.34002MR1888331
  23. Zhu, L., Li, G., 10.1016/j.jmaa.2007.10.041, J. Math. Anal. Appl. 341 (2008), 660-675. (2008) Zbl1145.34034MR2394114DOI10.1016/j.jmaa.2007.10.041

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.