Title | FIRST-ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS |
Publication Type | Journal Article |
Year of Publication | 2007 |
Authors | JANKOWSKI, TADEUSZ |
Secondary Title | Communications in Applied Analysis |
Volume | 11 |
Issue | 3 |
Start Page | 359 |
Pagination | 378 |
Date Published | 08/2007 |
Type of Work | scientific: mathematics |
ISSN | 1083–2564 |
AMS | 34A37, 34B15 |
Abstract | Problems of existence of solutions and quasi–solutions of first order impulsive functional differential equations with nonlinear two–point boundary conditions are discussed in this paper. Also impulsive differential inequalities with positive linear operators are investigated. The results are very general and some known results can be obtained from ours as special cases. Two examples are added to illustrate the obtained results.
|
URL | http://www.acadsol.eu/en/articles/11/3/2.pdf |
Short Title | FUNCTIONAL DIFFERENTIAL EQUATIONS |
Refereed Designation | Refereed |
Full Text | REFERENCES[1] R. P. Agarwal, D. Franco and D. O’Regan, Singular boundary value problems for first and second order impulsive differential equations, Aequations Math., 69: 83–96, 2005.
[2] L. Chen and J. Sun, Nonlinear boundary value problem of first order impulsive functional differential equations, J.Math. Anal. Appl., 318:726–741, 2006. [3] C. Corduneanu, Functional Equations with Causal Operators, Stability and Control, Methods and Applications, Vol. 16, Taylor and Francis, London, 2002. [4] W. Ding, J. Mi and M. Han, Periodic boundary value problems for the first order impulsive functional differential equations, Appl. Math. Comput., 165:433–446, 2005. [5] Z. Drici, F. A. McRae and J. V. Devi, Differential equations with causal operators in a Banach space, Nonlinear Anal., 62:301–313, 2005. [6] Z. Drici, F. A. McRae and J. V. Devi, Monotone iterative technique for periodic boundary value problems with causal operators, Nonlinear Anal., 64:1271–1277, 2006. [7] Z. Drici, F. A. McRae and J. V. Devi, Set differential equations with causal operators, Math. Probl. Eng., 2:185–194, 2005. [8] Z. He and J. Yu, Periodic boundary value problem for first–order impulsive functional differential equations, J. Comput. Appl. Math., 138:205–217, 2002. [9] T. Jankowski, On delay differential equations with nonlinear boundary conditions, Boundary Value Problems, 2005:201–214, 2005. [10] T. Jankowski, Advanced differential equations with nonlinear boundary conditions, J. Math. Anal. Appl., 304:490–503, 2005. [11] T. Jankowski, Solvability of three point boundary value problems for second order differential equations with deviating arguments, J. Math. Anal. Appl., 312:620–636, 2005. [12] T. Jankowski, Boundary value problems for first order differential equations of mixed type, Nonlinear Anal., 64:1984–1997, 2006.
[13] T. Jankowski, First–order impulsive ordinary differential equations with advanced arguments, J.Math. Anal. Appl., 331:1–12, 2007. [14] T. Jankowski, Nonlinear boundary value problems for second order differential equations with causal operators, J. Math. Anal., Appl., 332:1379–1391, 2007. [15] T. Jankowski, Boundary value problems with causal operators, Nonlinear Anal., in press. [16] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Non-linear Differential Equations, Pitman, Boston, 1985. [17] V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Ordinary Differential Equations, World Scientific, Singapore, 1989. [18] R. Liang and J. Shen, Periodic boundary value problem for the first order impulsive functional differential equations, J. Comput. Appl. Math., 202:498–510, 2007. [19] J. J. Nieto and R. Rodrıquez–Lopez, Periodic boundary value problem for non–Lipschitzian impulsive functional differential equations, J. Math. Anal. Appl., 318:593–610, 2006. [20] A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. [21] F. Zhang, Z. Ma and J. Yan, Boundary value problems for first order impulsive delay differential equations with a parameter, J. Math. Anal. Appl., 290:213–223, 2004. [22] F. Zhang, M. Li and J. Yan, Nonhomogeneous boundary value problem for first–order impulsive differential equations with delay, Comput. Math. Appl., 51:927–936, 2006. |