Previous |  Up |  Next

Article

Keywords:
nonconvex sweeping process; functional differential inclusion; uniformly $\rho$-prox-regular sets
Summary:
We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation.
References:
[1] Aubin J.P., Cellina A.: Differential Inclusions. Springer, Berlin-Heidelberg, 1984. MR 0755330 | Zbl 0538.34007
[2] Bounkhel M., Thibault L.: Nonconvex sweeping process and prox-regularity in Hilbert space. J. Nonlinear Convex Anal. 6 (2005), no. 2, 359–374. MR 2159846 | Zbl 1086.49016
[3] Castaing C., Valadier M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, 580, Springer, Berlin-Heidelberg-New York, 1977. DOI 10.1007/BFb0087688 | MR 0467310 | Zbl 0346.46038
[4] Castaing P., Monteiro Marques M.D.P.: Topological properties of solution sets for sweeping process with delay. Portugal. Math. 54 (1997), 485–507. MR 1489988
[5] Clarke F.H., Stern R.J., Wolenski P.R.: Proximal smoothness and the lower $C^2$ property. J. Convex Anal. 2 (1995), no. 1–2, 117–144. MR 1363364
[6] Edmond J.F.: Delay perturbed sweeping process. Set-Valued Anal. 14 (2006), no. 3, 295-317. DOI 10.1007/s11228-006-0021-9 | MR 2252653 | Zbl 1122.34060
[7] Edmond J.F., Thibault L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. J. Differential Equations 226 (2006), 135–179. DOI 10.1016/j.jde.2005.12.005 | MR 2232433 | Zbl 1110.34038
[8] Haddad T., Thibault L.: Mixed semicontinuous perturbations of nonconvex sweeping process. Math. Program. 123 (2010), no. 1, Ser. B, 225–240. DOI 10.1007/s10107-009-0315-4 | MR 2577329
[9] Moreau J.J.: Evolution problem associated with a moving convex set in a Hilbert space. J. Differential Equations 26 (1977), 347–374. DOI 10.1016/0022-0396(77)90085-7 | MR 0508661 | Zbl 0351.34038
[10] Moreau J.J.: Application of convex analysis to the treatment of elasto-plastic systems. in Applications of Methods of Functional Analysis to Problems in Mechanics (Germain and Nayroles, Eds.), Lecture Notes in Mathematics, 503, Springer, Berlin, 1976, pp. 56–89.
[11] Moreau J.J.: Unilateral contact and dry friction in finite freedom dynamics. in Nonsmooth Mechanics (J.J. Moreau and P.D. Panagiotopoulos, Eds.), CISM Courses and Lectures, 302, Springer, Vienna-New York, 1988, pp. 1–82. Zbl 0703.73070
[12] Poliquin R.A., Rockafellar R.T., Thibault L.: Local differentiability of distance functions. Trans. Amer. Math. Soc. 352 (2000), no. 11, 5231–5249. DOI 10.1090/S0002-9947-00-02550-2 | MR 1694378 | Zbl 0960.49018
[13] Thibault L.: Sweeping process with regular and nonregular sets. J. Differential Equations 193 (2003), 1–23. DOI 10.1016/S0022-0396(03)00129-3 | MR 1994056 | Zbl 1037.34007
[14] Valadier M., Duc Ha T.X., Castaing C.: Evolution equations governed by the sweeping process. Set Valued Anal. 1 (1993), 109–139. MR 1239400 | Zbl 0813.34018
[15] Zhu Q.: On the solution set of differential inclusions in Banach space. J. Differential Equations 93 (1991), 213–237. DOI 10.1016/0022-0396(91)90011-W | MR 1125218 | Zbl 0735.34017
Partner of
EuDML logo