## On continuous selections and properties of solutions of differential inclusions with $$m$$-accretive operators.(English. Russian original)Zbl 0815.54013

Sov. Math., Dokl. 42, No. 3, 861-865 (1991); translation from Dokl. Akad. Nauk SSSR 315, No. 5, 1035-1039 (1990).
A theorem is announced on the existence of a common continuous selection for finitely many multivalued mappings with nonconvex values in the space of inhibited functions, in the Bochner sense; the theorem is applied to the study of properties of solutions of differential inclusions with $$m$$- accretive operators. This note is related to the papers [H. A. Antosiewicz and A. Cellina, J. Differ. Equations 19, 386-398 (1975; Zbl 0279.54007); A. Fryszkowski, Stud. Math. 76, 163-174 (1983; Zbl 0534.28003); A. Bressan and G. Colombo, ibid. 90, No. 1, 69-86 (1988; Zbl 0677.54013); A. I. Bulgakov, Math. USSR, Sb. 64, No. 1, 295-303 (1989); translation from Mat. Sb., Nov. Ser. 136(178), No. 2(6), 292-300 (1988; Zbl 0664.46025); A. Cellina, G. Colombo and A. Fonda, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 5, No. 1, 23-36 (1988; Zbl 0647.28002); A. Cellina and M. V. Marchi, Isr. J. Math. 46, 1-11 (1983; Zbl 0542.47036); D. Kravvaritis and N. S. Papageorgiou, J. Differ. Equations 76, No. 2, 238-255 (1988; Zbl 0667.34078); G. Pianigiani, ibid. 25, 30- 38 (1977; Zbl 0398.34017); A. F. Filippov, SIAM J. Control 5, 609- 621 (1967); translation from Vestn. Mosk. Univ., Ser. I 22, No. 3, 16-26 (1967; Zbl 0238.34010); A. Bressan, Boll. Unione Mat. Ital., Suppl. 1, 53-59 (1980; Zbl 0445.49012) and others].

### MSC:

 54C65 Selections in general topology 47H06 Nonlinear accretive operators, dissipative operators, etc. 34A60 Ordinary differential inclusions 28B05 Vector-valued set functions, measures and integrals