Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
evolution inclusions; mild solutions; Lusin measurable multifunctions; Banach spaces; relaxation
evolution inclusions; mild solutions; Lusin measurable multifunctions; Banach spaces; relaxation
Summary:
We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.
References:
[1] Bressan A., Colombo G.: Extensions and selections of maps with decomposable values. Studia Math. 90 (1988), 69-86. MR 0947921 | Zbl 0677.54013
[2] Castaing C., Valadier M.: Convex analysis and measurable multifunctions. Lecture Notes in Mathematics, vol. 580, Springer-Verlag, Berlin, 1977. MR 0467310 | Zbl 0346.46038
[3] De Blasi F.S., Pianigiani G.: Hausdorff measurable multifunctions. J. Math. Anal. Appl. 228 (1998), 1-15. MR 1659936 | Zbl 0921.54013
[4] Filippov A.F.: Classical solutions of differential equations with multivalued right hand side. SIAM J. Control Optim. 5 (1967), 609-621. MR 0220995
[5] Frankowska H.: A priori estimates for operational differential inclusions. J. Differential Equations 84 (1990), 100-128. MR 1042661 | Zbl 0715.49010
[6] Hermes H.: The generalized differential equation $x'\in R(t,x)$. Advances in Math. 4 (1970), 149-169. MR 0252722
[7] Hille E., Phillips R.S.: Functional analysis and semi-groups. Amer. Math. Soc. Colloq. Publ., Vol. 31, Providence R.I., 1957. MR 0089373 | Zbl 0392.46001
[8] Himmelberg C.J.: Measurable relations. Fund. Math. 87 (1975), 53-72. MR 0367142 | Zbl 0296.28003
[9] Himmelberg C.J., Van Vleck F.S.: Lipschitzian generalized differential equations. Rend. Sem. Mat. Univ. Padova 48 (1973), 159-169. MR 0340692 | Zbl 0289.49009
[10] Hu S., Lakshmikantham V., Papageorgiou N.S.: On the solutions set of nonlinear differential inclusions. Dynamic Systems and Appl. 1 (1992), 71-82. MR 1154650
[11] Klein E., Thompson A.C.: Theory of correspondences. J. Wiley, New York, 1984. MR 0752692 | Zbl 0556.28012
[12] Kuratowski K., Ryll-Nardzewski C.: A general theorem on selectors. Bull. Acad. Pol. Sci. Sér. Soc. Math. Astron. Phys. 13 (1965), 397-403. MR 0188994 | Zbl 0152.21403
[13] Papageorgiou N.S.: Convexity of the orientor field and the solution set of a class of evolution inclusions. Math. Slovaca 43 (1993), 593-615. MR 1273713 | Zbl 0799.34018
[14] Papageorgiou N.S.: A continuous version of the relaxation theorem for nonlinear evolution inclusions. Houston J. Math. 20 (1994), 685-704. MR 1305938 | Zbl 0864.34057
[15] Pazy A.: Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, Berlin, 1983. MR 0710486 | Zbl 0516.47023
[16] Tolstonogov A.A.: On the properties of integral solutions of differential inclusions with $m$-accretive operators. Soviet Math. Notes 49 (1991), 119-131. MR 1135523
Search
Partner of
