Positive Solutions of Impulsive Dynamic System on Time Scales
Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 214-224

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, some criteria for the existence of positive solutions of a class of systems of impulsive dynamic equations on time scales are obtained by using a fixed point theorem in cones.
DOI : 10.4153/CMB-2011-125-1
Mots-clés : 39A10, 34B15, time scale, positive solution, fixed point, impulsive dynamic equation
Wang, Da-Bin. Positive Solutions of Impulsive Dynamic System on Time Scales. Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 214-224. doi: 10.4153/CMB-2011-125-1
@article{10_4153_CMB_2011_125_1,
     author = {Wang, Da-Bin},
     title = {Positive {Solutions} of {Impulsive} {Dynamic} {System} on {Time} {Scales}},
     journal = {Canadian mathematical bulletin},
     pages = {214--224},
     year = {2012},
     volume = {55},
     number = {1},
     doi = {10.4153/CMB-2011-125-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-125-1/}
}
TY  - JOUR
AU  - Wang, Da-Bin
TI  - Positive Solutions of Impulsive Dynamic System on Time Scales
JO  - Canadian mathematical bulletin
PY  - 2012
SP  - 214
EP  - 224
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-125-1/
DO  - 10.4153/CMB-2011-125-1
ID  - 10_4153_CMB_2011_125_1
ER  - 
%0 Journal Article
%A Wang, Da-Bin
%T Positive Solutions of Impulsive Dynamic System on Time Scales
%J Canadian mathematical bulletin
%D 2012
%P 214-224
%V 55
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-125-1/
%R 10.4153/CMB-2011-125-1
%F 10_4153_CMB_2011_125_1

[1] [1] Agarwal, R. P. and Bohner, M., Basic calculus on time scales and some of its applications. Results Math. 35(1999), no. 1–2, 3–22. Google Scholar

[2] [2] Agarwal, R. P. and O’Regan, D., Multiple nonnegative solutions for second order impulsive differential equations. Appl. Math. Comput. 114(2000), no. 1, 51–59. doi:10.1016/S0096-3003(99)00074-0 Google Scholar

[3] [3] Agarwal, R. P., Otero-Espinar, V., Perera, K., and Vivero, D. R., Multiple positive solutions in the sense of distributions of singular BVPs on time scales and an application to Emden-Fowler equations. Adv. Difference Equ. , Art. ID 796851, 1–13. Google Scholar

[4] [4] Agarwal, R. P., Otero-Espinar, V., Perera, K., and Vivero, D. R., Wirtinger's inequalities on time scales. Canad. Math. Bull. 51(2008), no. 2, 161–171. doi:10.4153/CMB-2008-018-6 Google Scholar

[5] [5] Akhmet, M. U. and Turan, M., The differential equations on time scales through impulsive differential equations. Nonlinear Anal. 65(2006), no. 11, 2043–2060. doi:10.1016/j.na.2005.12.042 Google Scholar

[6] [6] Akhmet, M. U. and Turan, M., Differential equations on variable time scales. Nonlinear Anal. 70(2009), no. 3, 1175–1192. doi:10.1016/j.na.2008.02.020 Google Scholar

[7] [7] Bohner, M. and Peterson, A., Dynamic equations on time scales. An introduction with applications. Birkhäuser Boston Inc., Boston, MA, 2001. Google Scholar

[8] [8] Bohner, M. and Peterson, A., Advances in dynamic equations on time scales. Birkhäuser Boston Inc., Boston, MA, 2003. Google Scholar

[9] [9] Benchohra, M., Henderson, J., Ntouyas, S. K., and Ouahab, A., On first order impulsive dynamic equations on time scales. J. Difference Equ. Appl. 10(2004), no. 6, 541–548. doi:10.1080/10236190410001667986 Google Scholar

[10] [10] Benchohra, M., Ntouyas, S. K., and Ouahab, A., Existence results for second order boundary value problem of impulsive dynamic equations on time scales. J. Math. Anal. Appl. 296(2004), no. 1, 65–73. doi:10.1016/j.jmaa.2004.02.057 Google Scholar

[11] [11] Benchohra, M., Henderson, J., and Ntouyas, S. K., Impulsive differential equations and inclusions. Contemporary Mathematics and Its Applications, 2, Hindawi Publishing Corporation, New York, 2006. Google Scholar

[12] [12] Chen, H. and Wang, H., Triple positive solutions of boundary value problems for p-Laplacian impulsive dynamic equations on time scales. Math. Comput. Modelling 47(2008), no. 9–10, 917–924. doi:10.1016/j.mcm.2007.06.012 Google Scholar

[13] [13] Guo, D. J. and Lakshmikantham, V., Nonlinear problems in abstract cones. Notes and Reports in Mathematics in Science and Engineering, 5, Academic Press, Inc., Boston, MA, 1988. Google Scholar

[14] [14] Geng, F., Zhu, D., and Lu, Q., A new existence result for impulsive dynamic equations on timescales. Appl. Math. Lett. 20(2007), no. 2, 206–212. doi:10.1016/j.aml.2006.03.013 Google Scholar

[15] [15] Geng, F., Xu, Y., and Zhu, D., Periodic boundary value problems for first-order impulsive dynamic equations on time scales. Nonlinear Anal. 69(2008), no. 11, 4074–4087. doi:10.1016/j.na.2007.10.038 Google Scholar

[16] [16] Graef, J. R. and Ouahab, A., Extremal solutions for nonresonance impulsive functional dynamic equations on time scales. Appl. Math. Comput. 196(2008), no. 1, 333–339. doi:10.1016/j.amc.2007.05.056 Google Scholar

[17] [17] Hilger, S., Analysis on measure chains—a unified approach to continuous and discrete calculus. Results Math. 18(1990), no. 1–2, 18–56. Google Scholar

[18] [18] He, Z. and Yu, J., Periodic boundary value problem for first-order impulsive functional differential equations. J. Comput. Appl. Math. 138(2002), no. 2, 205–217. doi:10.1016/S0377-0427(01)00381-8 Google Scholar

[19] [19] He, Z. and Zhang, X., Monotone iterative technique for first order impulsive differential equations with periodic boundary conditions. Appl. Math. Comput. 156(2004), no. 3, 605–620. doi:10.1016/j.amc.2003.08.013 Google Scholar

[20] [20] Jiao, J. J., Chen, L.-S., Nieto, J. J., and Torres, A., Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey. Appl. Math. Mech. (English Ed.) 29(2008), no. 5, 653–663. doi:10.1007/s10483-008-0509-x Google Scholar

[21] [21] Kaymakcalan, B., Lakshmikantham, V., and Sivasundaram, S., Dynamical systems on measure chains. Mathematics and its Applications, 370, Kluwer Academic Publishers Group, Dordrecht, 1996. Google Scholar

[22] [22] Khan, R. A., Nieto, J. J., and Otero-Espinar, V., Existence and approximation of solution of three-point boundary value problems on time scales. J. Difference Equ. Appl. 14(2008), no. 7, 723–736. doi:10.1080/10236190701840906 Google Scholar

[23] [23] Krasnosel’skii, M. A., Positive solutions of operator equations. P. Noordhoff Ltd., Groningen, 1964. Google Scholar

[24] [24] Lakshmikantham, V., Bainov, D. D., and Simeonov, P. S., Theory of impulsive differential equations. Series in Modern Applied Mathematics, 6, World Scientific, Teaneck, NJ, 1989. Google Scholar

[25] [25] Li, J., Nieto, J. J., and Shen, J., Impulsive periodic boundary value problems of first-order differential equations. J. Math. Anal. Appl. 325(2007), no. 1, 226–236. doi:10.1016/j.jmaa.2005.04.005 Google Scholar

[26] [26] Li, J.-L. and Shen, J.-H., Existence of positive periodic solutions to a class of functional differential equations with impulses. Math. Appl. 17(2004), no. 3, 456–463. Google Scholar

[27] [27] Li, J.-L. and Shen, J.-H., Existence results for second-order impulsive boundary value problems on time scales. Nonlinear Anal. 70(2009), no. 4, 1648–1655. doi:10.1016/j.na.2008.02.047 Google Scholar

[28] [28] Liu, H. and Xiang, X., A class of the first order impulsive dynamic equations on time scales. Nonlinear Anal. 69(2008), no. 9, 2803–2811. doi:10.1016/j.na.2007.08.052 Google Scholar

[29] [29] Nieto, J. J., Impulsive resonance periodic problems of first order. Appl. Math. Lett. 15(2002), no. 4, 489–493. doi:10.1016/S0893-9659(01)00163-X Google Scholar

[30] [30] Nieto, J. J., Periodic boundary value problems for first-order impulsive ordinary differential equations. Nonlinear Anal. 51(2002), no. 7, 1223–1232. doi:10.1016/S0362-546X(01)00889-6 Google Scholar

[31] [31] Nieto, J. J. and O’Regan, D., Variational approach to impulsive differential equations. Nonlinear Anal. Real World Appl. 10(2009), no. 2, 680–690. doi:10.1016/j.nonrwa.2007.10.022 Google Scholar

[32] [32] Di Piazza, L. and Satco, B., A new result on impulsive differential equations involving non-absolutely convergent integrals. J. Math. Anal. Appl. 352(2009), no. 2, 954–963. doi:10.1016/j.jmaa.2008.11.048 Google Scholar

[33] [33] Zavalishchin, S. T. and Sesekin, A. N., Dynamic impulse systems. Theory and applications. Mathematics and Its Applications, 394, Kluwer Academic Publishers Group, Dordrecht, 1997. Google Scholar

[34] [34] Sun, J.-P. and Li, W.-T., Existence of solutions to nonlinear first-order PBVPs on time scales. Nonlinear Anal. 67(2007), no. 3, 883–888. doi:10.1016/j.na.2006.06.046 Google Scholar

[35] [35] Sun, J.-P. and Li, W.-T., Existence and multiplicity of positive solutions to nonlinear first-order PBVPs on time scales. Comput. Math. Appl. 54(2007), no. 6, 861–871. doi:10.1016/j.camwa.2007.03.009 Google Scholar

[36] [36] Wang, D.-B., Positive solutions for nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales. Comput. Math. Appl. 56(2008), no. 6, 1496–1504. doi:10.1016/j.camwa.2008.02.038 Google Scholar

[37] [37] Zeng, G., Wang, F., and Nieto, J. J., Complexity of a delayed predator-prey model with impulsive harvest and Holling type II functional response. Adv. Complex Syst. 11(2008), no. 1, 77–97. doi:10.1142/S0219525908001519 Google Scholar

[38] [38] Zhang, H., Chen, L., and Nieto, J. J., A delayed epidemic model with stage-structure and pulses for pest management strategy. Nonlinear Anal. RealWorld Appl. 9(2008), no. 4, 1714–1726. doi:10.1016/j.nonrwa.2007.05.004 Google Scholar

[39] [39] Zhang, N., Dai, B., and Qian, X., Periodic solutions for a class of higher-dimension functional differential equations with impulses. Nonlinear Anal. 68(2008), no. 3, 629–638. doi:10.1016/j.na.2006.11.024 Google Scholar

Cité par Sources :