On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions
Tóm tắt
This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases.
Tài liệu tham khảo
Benchora, M., Henderson, J., Ntouyas, S.K.: Impulsive Differential Equations and Inclusions. Hindawi, New York (2006)
Haddad, W.M., Chellabonia, V., Nersesov, S.G., Sergey, G.: Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control. Princeton University Press, Princeton (2006)
Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
Belarbi, A., Benchora, M.: Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times. J. Math. Anal. Appl. 327, 1116–1129 (2007)
Benchora, M., Gōrniewicz, L., Ntouyas, S.K., Ouahab, A.: Existence results for impulsive hyperbolic differential inclusions. Appl. Anal. 82, 1085–1097 (2003)
Chang, Y.K., Li, W.T.: Existence results for second order impulsive functional differential inclusions. J. Math. Anal. Appl. 301, 477–490 (2005)
Chang, Y.K., Qi, L.M.: Existence results for second order impulsive functional differential inclusions. J. Appl. Math. Stoch. Anal. 2006, 1–12 (2006)
Chang, Y.K., Li, W.T.: Existence results for impulsive dynamic equations on time scales with nonlocal initial conditions. Math. Comput. Model. 43, 377–384 (2006)
Migorski, S., Ochal, A.: Nonlinear impulsive evolution inclusions of second order. Dyn. Syst. Appl. 16, 155–173 (2007)
Nieto, J.J.: Impulsive resonance periodic problems of first order. Appl. Math. Lett. 15, 489–493 (2002)
Li, J., Nieto, J.J., Shen, J.: Impulsive periodic boundary value problems of first-order differential equations. J. Math. Anal. Appl. 325, 226–236 (2007)
Nieto, J.J., Rodriguez-Lopez, R.: New comparison results for impulsive integro-differential equations and applications. J. Math. Anal. Appl. 328, 1343–1368 (2007)
Nieto, J.J., O’regan, D.: Variational approach to impulsive differential equations, Nonlinear Anal. doi:10.1016/j.nonrwa.2007.10.022
Li, S.: Estimation of coefficients in a hyperbolic equation with impulsive inputs. J. Inverse Ill-Posed Probl. 14, 891–904 (2006)
Sun, J., Zhang, Y.: Impulsive control of a nuclear spin generator. J. Comput. Appl. Math. 157, 235–242 (2003)
Liu, X., Willms, A.R.: Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft. Math. Probl. Eng. 2, 277–299 (1996)
Miele, A., Weeks, M.W., Ciarcia, M.: Optimal trajectories for spacecraft rendezvous. J. Optim. Theory Appl. 132, 353–376 (2007)
Miele, A., Ciarcia, M., Weeks, M.W.: Guidance trajectories for spacecraft rendezvous. J. Optim. Theory Appl. 132, 377–400 (2007)
Cui, B., Han, M.: Oscillation theorems for nonlinear hyperbolic systems with impulses. Nonlinear Anal. 98, 94–102 (2008)
Erbe, L.H., Freedman, H.I., Liu, X., Wu, J.H.: Comparison principles for impulsive parabolic equations with applications to models of single species growth. Aust. Math. Soc. J. Ser. B. 32, 382–400 (1991)
Yan, J., Zhao, A., Nieto, J.J.: Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka–Volterra systems. Math. Comput. Model. 40, 509–518 (2004)
Zhang, H., Chen, L., Nieto, J.J.: A delayed epidemic model with stage-structure and pulses for pest management strategy, Nonlinear Anal. doi:10.1016/j.nonrwa.2007.05.004
Gao, S., Chen, L., Nieto, J.J., Torres, A.: Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. Vaccine 24, 6037–6045 (2006)
Sun, J., Qiao, F., Wu, Q.: Impulsive control of a financial model. Phys. Lett. A 335, 282–288 (2005)
Company, R., Jodar, L., Rubio, G., Villanueva, R.J.: Explicit solution of Black-Scholes option pricing mathematical models with an impulsive payoff function. Math. Comput. Model. 45, 80–92 (2007)
Belarbi, A., Benchohra, M.: Existence theory for perturbed hyperbolic differential inclusions. Electron. J. Differ. Equ. 2006, 1–11 (2006)
Benchohra, M., Ntouyas, S.K.: The method of lower and upper solutions to the Darboux problem for partial differential inclusions. Miskolc Math. Notes 4, 81–88 (2003)
Henderson, J., Ouahab, A.: Impulsive hyperbolic differential inclusions with infinite delay and variable moments. Commun. Appl. Nonlinear Anal. 13, 61–78 (2006)
Bohnenblust, H.F., Karlin, S.: On a theorem of Ville. In: Contributions to the Theory of Games, vol. 1, pp. 155–160. Princeton University Press, Princeton (1950)
Dugundij, J., Granas, A.: Fixed Point Theory. Monografie Mat. PWN, Warsaw (1982)
Bressan, A., Colombo, G.: Existence and selections of maps with decomposable values. Studia Math. 90, 69–86 (1988)
Deimling, K.: Multivalued Differential Equations. De Gruyter, Berlin (1992)
Hu, S., Papageorgiou, N.: Handbook of Multivalued Analysis. Kluwer, Dordrecht/Boston (1997)
Lasota, A., Opial, Z.: An application of the Kakutani–Ky Fan theorem in the theory of ordinary differential equations. Acad. Polonaise Sci. Sér. Sci. Math. Astron. Phys. 13, 781–786 (1965)
Nieto, J.J.: Basic theory for nonresonance impulsive periodic problems of first order. J. Math. Anal. Appl. 205, 423–433 (1997)