Relaxation of nonlocal m-dissipative differential inclusions

[1] R. P. Agarwal, Asma, V. Lupulescu, D. O’Regan, Fractional semilinear equations with causal operators. RASCAM 111 (2017), 257–269.10.1007/s13398-016-0292-4Search in Google Scholar

[2] R. Ahmed, T. Donchev, A. I. Lazu, Nonlocal m-dissipative evolution inclusions in general Banach spaces. Mediterr. J. Math. 14:215 (2017), doi:10-1007/s00009-017-1016-5.10.1007/s00009-017-1016-5Search in Google Scholar

[3] S. Aizicovici, V. Staicu, Multivalued evolution equations with nonlocal initial conditions in Banach spaces. NoDEA Nonlinear Differential Equations Appl. 14 (2007), 361–376.10.1007/s00030-007-5049-5Search in Google Scholar

[4] V. Barbu, Nonlinear differential equations of monotone types in Banach spaces. Springer, New York, 2010.10.1007/978-1-4419-5542-5Search in Google Scholar

[5] P. Benilan, Solutions intégrales d’équations d’évolution dans un espace de Banach. C. R. Acad. Sci. Paris Sér. A-B 274 (1972), 47–50.Search in Google Scholar

[6] D. Bothe, Nonlinear Evolutions in Banach Spaces. Habilitationsschritt, Paderborn, 1999.Search in Google Scholar

[7] M. Burlică, M. Necula, D. Roşu, I. I. Vrabie, Delay Differential Evolutions Subjected to Nonlocal Initial Conditions. Monographs and Research Notes in Mathematics. CRC Press, New York, 2016.Search in Google Scholar

[8] L. Byszewski, Theorem about the existence and uniqueness of a semilinear nonlocal Cauchy problem. J. Math. Anal. Appl. 162 (1991), 494–505.10.1016/0022-247X(91)90164-USearch in Google Scholar

[9] T. Cardinali, N. Papageorgiou, F. Papalini, On nonconvex functional evolution inclusions involving m-dissipative operators. Czech. Math. J. 47 (1997), 135–148.10.1023/A:1022452507677Search in Google Scholar

[10] O. Cârjă, T. Donchev, V. Postolache, Relaxation results for nonlinear evolution inclusions with one-sided Perron right-hand side. Set-Valued Var. Anal. 22 (4), (2014), 657–671.10.1007/s11228-014-0284-5Search in Google Scholar

[11] T. Donchev, Multi-valued perturbations of m-dissipative differential inclusions in uniformly convex spaces. New Zealand Journal of Mathematics 31 (2002), 19–32.Search in Google Scholar

[12] T. Donchev, E. Farkhi, On the theorem of Filippov-Plis and some applications. Control Cybern 38 (2009), 1–21.Search in Google Scholar

[13] Y. Dong, Relaxation theorem for evolution differential inclusions. J. Math. Anal. Appl. 237 (1999), 188–200.10.1006/jmaa.1999.6473Search in Google Scholar

[14] S. Hu, N. Papageorgiou, Handbook of Multivalued Analysis. Volume II: Applications. Kluwer, Dordrecht, 2000.10.1007/978-1-4615-4665-8Search in Google Scholar

[15] T. Ke, Cauchy problems for functional evolution inclusions involving accretive operators. EJQTDE 75 (2013), 1–13.10.14232/ejqtde.2013.1.75Search in Google Scholar

[16] V. Lakshmikantham, S. Leela, Nonlinear differential equations in abstract spaces. Pergamon Press, Oxford, 1981.Search in Google Scholar

[17] M. Necula, M. Popescu, I. I. Vrabie, Viability for delay evolution equations with nonlocal initial conditions. Nonlinear Anal. 121 (2015), 164–172.10.1016/j.na.2014.11.014Search in Google Scholar

[18] A. Paicu, I. I. Vrabie, A class of nonlinear evolution equations subjected to nonlocal initial conditions. Nonlinear Anal. 72 (11) (2010), 4091–4100.10.1016/j.na.2010.01.041Search in Google Scholar

[19] R. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. Math. Surv. Monographs 49, AMS, 1997.Search in Google Scholar

[20] A. Tolstonogov, Properties of integral solutions of differential inclusions with m-accretive operators. Mat. Zametki 49 (1991), 119–131.10.1007/BF01156590Search in Google Scholar

[21] A. Tolstonogov, Differential inclusions in a Banach space. Kluwer Academic Publishers, Dordrecht, 2000.10.1007/978-94-015-9490-5Search in Google Scholar

[22] X. Xue, Semilinear nonlocal differential equations with measure of non-compactness in Banach spaces. J. Nanjing. Univ. Math. Big. 24 (2007), 264-276.Search in Google Scholar

[23] L. Zhu, Q. Huang, G. Li, Existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions. J. Math. Anal. Appl. 390 (2012), 523–534.10.1016/j.jmaa.2012.01.055Search in Google Scholar