There are studied two classes of differential inclusions with right-hand side admitting noncompact values in a Banach space. Co-density, lower semicontinuity in initial point and relaxation property of the solution set have been obtained.
@article{bwmeta1.element.bwnjournal-article-div16i2n1bwm, author = {Vladimir V. Goncharov}, title = {Co-density and other properties of the solution set of differential inclusions with noncompact right-hand side}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {16}, year = {1996}, pages = {103-120}, zbl = {0906.34012}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div16i2n1bwm} }
Vladimir V. Goncharov. Co-density and other properties of the solution set of differential inclusions with noncompact right-hand side. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996) pp. 103-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div16i2n1bwm/
[000] [1] A.A. Tolstonogov, Differential inclusions in a Banach space, Nauka (Sib. otd.), Novosibirsk 1986 (in Russian). | Zbl 0689.34014
[001] [2] A.A. Tolstonogov, On density and co-density of a set of solutions of a differential inclusion in a Banach space, Dokl. AN SSSR 261 (1981), 293-296. | Zbl 0504.34006
[002] [3] G. Colombo, Weak flow-invariance for non-convex differential inclusions, Differential and Integral Equations 5 (1992), 173-180. | Zbl 0757.34017
[003] [4] Z. Kánnai, Viability theorems on strongly sleek tubes, Annales Univ. Sci. Budapest, Sect. Comp. 13 (1992), 63-75. | Zbl 0881.34030
[004] [5] A.A. Tolstonogov and V.V Goncharov, On solutions of differential inclusion with noncompact-valued right-hand side in a Banach space. Manuscript deposited in All-Union Research Institute of Thechnical Information, Moscow 1986 (in Russian).
[005] [6] F. Riesz and B.SZ.-Nagy, Functional Analysis, Frederick Ungar Publishing CO., Budapest 1978. | Zbl 0070.10902
[006] [7] J.-P. Aubin and A. Cellina, Differential Inclusions, Set-valued Maps and Viability Theory, Springer-Verlag, Berlin 1984.
[007] [8] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin 1977.
[008] [9] C.J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 53-72. | Zbl 0296.28003
[009] [10] A. Fryszkowski, Continuous selections for a class of nonconvex multivalued maps, Studia Math. 76 (1983), 163-174. | Zbl 0534.28003
[010] [11] Phan van Chuong, A density theorem with an application in relaxation of nonconvex-valued differential equations, Seminare d'Analyse Convexe 15 (1985) 2.1-2.22.