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Article

Cardinali, Tiziana ; Portigiani, Francesco ; Rubbioni, Paola
Nonlocal Cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities. (English). Czechoslovak Mathematical Journal, vol. 61 (2011), issue 1, pp. 225-245
MSC: 34G25, 34H05 | MR 2782771 | Zbl 1224.34195
Keywords:
nonlocal conditions; semilinear differential inclusions; selection theorem; mild solutions; lower Scorza-Dragoni property; controllability
Summary:

References:
[1] Abraham, R., Marsden, J. E., Ratiu, T. S.: Manifolds, Tensor Analysis, and Applications. Second Edition, Springer-Verlag, New York (1988). MR 0960687 | Zbl 0875.58002
[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. MR 2495847
[3] Balachandran, K., Dauer, J. P.: Controllability of nonlinear systems in Banach spaces: a survey. J. Optim. Theory Appl. 115 (2002), 7-28. MR 1937343 | Zbl 1023.93010
[4] Boulite, S., Idrissi, A., Maniar, L.: Controllability of semilinear boundary problems with nonlocal initial conditions. J. Math. Anal. Appl. 316 (2006), 566-578. MR 2206690 | Zbl 1105.34036
[5] Bressan, A., Colombo, G.: Extensions and selections of maps with decomposable values. Studia Math. 90 (1988), 69-85. MR 0947921 | Zbl 0677.54013
[6] Byszewski, L.: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal. Appl. 162 (1991), 494-505. MR 1137634 | Zbl 0748.34040
[7] Cardinali, T., Panfili, S.: Global mild solutions for semilinear differential inclusions and applications to impulsive problems. PU.M.A. 19 (2008), 1-19. MR 2551816 | Zbl 1224.34196
[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. MR 2494057 | Zbl 1193.34123
[9] Chang, Y.-K., Li, W.-T., Nieto, J. J.: Controllability of evolution differential inclusions in Banach spaces. Nonlinear Anal. 67 (2007), 623-632. MR 2317194 | Zbl 1128.93005
[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. MR 2300434 | Zbl 1131.34045
[11] Górniewicz, L., Ntouyas, S. K., O'Regan, D.: Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces. Rep. Math. Phys. 56 (2005), 437-470. MR 2190735 | Zbl 1185.93016
[12] Hernández, E. M., O'Regan, D.: Controllability of Volterra-Fredholm type systems in Banach spaces. J. Franklin Inst. 346 (2009), 95-101. MR 2499965
[13] Hu, S., Papageorgiou, N. S.: Handbook of Multivalued Analysis. Vol. I: Theory. Mathematics and its Applications, 419. Kluwer Academic Publishers, Dordrecht (1997). MR 1485775
[14] Hu, S., Papageorgiou, N. S.: Handbook of Multivalued Analysis. Vol. II: Applications. Mathematics and its Applications, 500 Kluwer Academic Publishers, Dordrecht (2000). MR 1741926
[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). MR 1831201
[16] Krein, S. G.: Linear Differential Equations in Banach Spaces. Amer. Math. Soc., Providence (1971). MR 0342804
[17] Li, G., Xue, X.: Controllability of evolution inclusions with nonlocal conditions. Appl. Math. Comput. 141 (2003), 375-384. MR 1972917 | Zbl 1029.93003
[18] Michael, E.: Continuous selections I. Ann. Math. 63 (1956), 361-382. MR 0077107 | Zbl 0071.15902
[19] Royden, H. L.: Real Analysis. Macmillan Publishing Company, New York (1988). MR 1013117 | Zbl 0704.26006
[20] Sussman, H. J.: Needle variations and almost lower semicontinuous differential inclusions. Set-Valued Analysis 10 (2002), 233-285. MR 1926382
[21] Taylor, A. E., Lay, D. C.: Introduction to Functional Analysis. Robert E. Krieger Publishing Co., Inc., Malabar, FL (1986). MR 0862116 | Zbl 0654.46002
[22] Tolstonogov, A.: Differential Inclusions in a Banach Space. Kluwer Academic Publishers, Dordrecht (2000). MR 1888331 | Zbl 1021.34002
[23] Zhu, L., Li, G.: On a nonlocal problem for semilinear differential equations with upper semicontinuous nonlinearities in general Banach spaces. J. Math. Anal. Appl. 341 (2008), 660-675. MR 2394114 | Zbl 1145.34034
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