One-sided Perron Differential Inclusions

详细信息    查看全文

• 作者：Tzanko Donchev (1) (2)
  Alina Ilinca Lazu (1) (3)
  Ammara Nosheen (2)
  
• 关键词：Differential inclusions ; One ; sided Perron multifunction ; State constraints ; Solution map ; 34A60 ; 49J21 ; 93B03
• 刊名：Set-Valued and Variational Analysis
• 出版年：2013
• 出版时间：June 2013
• 年：2013
• 卷：21
• 期：2
• 页码：283-296
• 全文大小：346KB
• 参考文献：1. Cannarsa, P., Castelpietra, M.: Lipschitz continuity and local semiconcavity for exit time problems with state constraints. J. Differ. Equ. 245(3), 616-36 (2008) CrossRef
  2. Carj?, O., Lazu, A.: Lower semi-continuity of the solution set for semilinear differential inclusions. J. Math. Anal. Appl. 385, 865-73 (2012) CrossRef
  3. Carj?, O., Lazu, A.: On the regularity of the solution map for differential inclusions. Dyn. Syst. Appl. 21, 457-66 (2012)
  4. Carj?, O., Necula, M., Vrabie, I.: Viability, Invariance and Applications. Elsevier Science B.V., Amsterdam (2007)
  5. Carj?, O., Necula, M., Vrabie, I.: Necessary and sufficient conditions for viability for semilinear differential inclusions. Trans. Am. Math. Soc. 361, 343-90 (2009) CrossRef
  6. Carj?, O., Ursescu, C.: The characteristics method for a first order partial differential equation. An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 39, 367-96 (1993)
  7. Clarke, F., Ledyaev, Yu., Stern, R., Wolenski, P.: Qualitative properties of trajectories of control systems: a survey. J. Dyn. Control Syst. 1, 1-8 (1995) CrossRef
  8. Clarke, F., Ledyaev, Yu., Stern, R., Wolenski, P.: Nonsmooth Analysis and Control Theory. Springer, New York (1998)
  9. De Blasi, F., Pianigiani, G., Baire’s category and relaxation problems for locally lipschitzean differential inclusions in finite and infinite time intervals. Nonlinear Anal. TMA, 72, 288-01 (2009) CrossRef
  10. Deimling, K.: Multivalued Differential Equations. De Grujter, Berlin (1992) CrossRef
  11. Donchev, T.: Properties of the reachable set of control systems. Syst. Control Lett. 46, 379-86 (2002) CrossRef
  12. Donchev, T.: Generic properties of multifunctions: applications to differential inclusions. Nonlinear Anal. 74, 2585-590 (2011) CrossRef
  13. Donchev, T., Farkhi, E.: On the theorem of Filippov-Plis and some applications. Control Cybern. 38, 1-1 (2009)
  14. Donchev, T., Rios, V., Wolenski, P.: Strong invariance and one-sided Lipschitz multifunctions. Nonlinear Anal. 60(5), 849-62 (2005) CrossRef
  15. Donchev, T., Rios, V., Wolenski, P.: Strong invariance for discontinuous Hilbert space differential inclusions. An. Stiint. Univ. Al. I. Cuza Iasi, Ser. Noua, Mat. 51(2), 265-79 (2005)
  16. Filippov, A.: Differential equations with discontinuous right-hand side. Mat. Sb. (N.S.) 51(93), 99-28 (1960) (in Russian); English translation: Amer. Math. Soc. Translat. Ser. II 42, 199-31 (1964)
  17. Filippov, A.: Classical solutions of differential equations with multi-valued right-hand side. SIAM J. Control 5, 609-21 (1967) CrossRef
  18. Frankowska, H.: A priori estimates for operational differential inclusions. J. Differ. Equ. 84(1), 100-28 (1990) CrossRef
  19. Frankowska, H., Rampazzo, F.: Filippov’s and Filippov-Wazewski’s theorems on closed domains. J. Differ. Equ. 161, 449-78 (2000) CrossRef
  20. Krastanov, M.: Forward invariant sets, homogeneity and small-time local controllability. In: Jakubczyk, B., et al. (eds.) Geometry in Nonlinear Control and Differential Inclusions, vol.?32, pp.?287-00. Banach Center Publ., Polish Acad. Sci., Warsaw (1995)
  21. Nour, C., Stern, R.: Regularity of the state constrained minimal time function. Nonlinear Anal. 66, 62-2 (2007) CrossRef
  22. Nour, C., Stern, R.: The state constrained bilateral minimal time function. Nonlinear Anal. 69, 3549-558 (2008) CrossRef
  23. Plis, A.: On trajectories of orientor fields. Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys. 13, 571-73 (1965)
  24. Soner, H.: Optimal control problems with state-space constraints I. SIAM J. Control Optim. 24, 551-61 (1986)
  25. Tolstonogov, A.: Differential Inclusions in a Banach Space. Kluwer, Dordrecht (2000) CrossRef
  26. Veliov, V.: Differential inclusions with stable subinclusions. Nonlinear Anal. 23, 1027-038 (1994) CrossRef
  27. Zhu, Q.: On the solution set of the differential inclusions in Banach spaces. J. Differ. Equ. 93, 213-37 (1991) CrossRef
  
• 作者单位：Tzanko Donchev (1) (2)
  Alina Ilinca Lazu (1) (3)
  Ammara Nosheen (2)
  
  1. Department of Mathematics, University Al. I. Cuza, Ia?i, 700506, Romania
  2. Abdus Salam School of Mathematical Sciences, 68-B New Muslim Town, Lahore, Pakistan
  3. Department of Mathematics, Gh. Asachi Technical University, Ia?i, 700506, Romania
  
• ISSN：1877-0541

文摘

The main qualitative properties of the solution set of almost lower (upper) semicontinuous one-sided Perron differential inclusion with state constraints in finite dimensional spaces are studied. Using the technique introduced by Veliov (Nonlinear Anal 23:1027-038, 1994) we give sufficient conditions for the solution map of the above state constrained differential inclusion to be continuous in the sense of Hausdorff metric. An application on the propagation of the continuity of the state constrained minimum time function associated with the nonautonomous differential inclusion and the target zero is given. Some relaxation theorems are proved, which are used afterward to derive necessary and sufficient conditions for invariance.