Existence results for an impulsive abstract partial differential equation with state-dependent delay

Computers and Mathematics with Applications

Volumn 52, Issue 3-4, 2006, Pages 411-420

  Hernaindez E ^a   Pierri, M ^a   Goncalves, G ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Abstract functional differential equations; Impulsive differential equations; State dependent delay

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL PROGRAMMING; PROBLEM SOLVING;

ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS; IMPULSIVE DIFFERENTIAL EQUATIONS; STATE DEPENDENT DELAYS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33750455453     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.03.022     Document Type: Article

References (28)

1. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of impulsive differential equations. Series in Modern Applied Mathematics Volume 6 (1989), World Scientific, Teaneck, NJ
2. Ranco D., and Nieto J. Maximum principles for periodic impulsive first order problems. Positive solutions of nonlinear problems. J. Comput. Appl. Math. 88 1 (1998) 149-159
3. He Z., and Yu J. Periodic boundary value problem for first-order impulsive functional differential equations. J. Comput. Appl. Math. 138 2 (2002) 205-217
4. Luo Z., and Shen J. Stability results for impulsive functional differential equations with infinite delays. J. Comput. Appl. Math. 131 1/2 (2001) 55-64
5. Sun J., and Zhang Y. Impulsive control of a nuclear spin generator. J. Comput. Appl. Math. 157 1 (2003) 235-242
6. Lakshmikantham V., and Drici Z. Positivity and boundedness of solutions of impulsive reaction-diffusion equations. Positive solutions of nonlinear problems. J. Comput. Appl. Math. 88 1 (1998) 175-184
7. Liu J.H. Nonlinear impulsive evolution equations. Dynam. Contin. Discrete Impuls. Systems 6 1 (1999) 77-85
8. Rogovchenko Y.V. Impulsive evolution systems: Main results and new trends. Dynam. Contin. Discrete Impuls. Systems 3 1 (1997) 57-88
9. Rogovchenko Y.V. Nonlinear impulse evolution systems and applications to population models. J. Math. Anal. Appl. 207 2 (1997) 300-315
10. Hale J.K., and Verduyn Lunel S.M. Introduction to Functional-Differential Equations. Appl. Math. Sci Volume 99 (1993), Springer-Verlag, New York
11. Wu J. Theory and Applications of Partial Functional-Differential Equations. Applied Mathematical Sciences Volume 119 (1996), Springer-Verlag, New York
12. Arino O., Boushaba K., and Boussouar A. A mathematical model of the dynamics of the phytoplanktonnutrient system. Spatial heterogeneity in ecological models. Alcal'a de Henares (1998)
13. Nonlinear Analysis RWA 1 1 (2000) 69-87
14. Aiello W.G., Freedman H.I., and Wu J. Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J. Appl. Math. 52 3 (1992) 855-869
15. Cao Y., Fan J., and Card T.C. The effects of state-dependent time delay on a stage-structured population growth model. Nonlinear Analysis TMA 19 2 (1992) 95-105
16. Domoshnitsky A., Drakhlin M., and Litsyn E. On equations with delay depending on solution. Nonlinear Analysis TMA 49 5 (2002)) 689-701
17. Chen F., Sun D., and Shi J. Periodicity in a food-limited population model with toxicants and state dependent delays. J. Math. Anal. Appl. 288 1 (2003) 136-146
18. Hartung F. Linearized stability in periodic functional differential equations with state-dependent delays. J. Comput. Appl. Math. 174 2 (2005) 201-211
19. Hartung F., Herdman T.L., and Turi J. Parameter identification in classes of neutral differential equations with state-dependent delays. Nonlinear Analysis TMA, Ser. A: Theory Methods 39 3 (2000) 305-325
20. Yang Z., and Cao J. Existence of periodic solutions in neutral state-dependent delays equations and models. J. Comput. Appl. Math. 174 1 (2005) 179-199
21. Willé D.R., and Baker C.T.H. Stepsize control and continuity consistency for state-dependent delay-differential equations. J. Comput. Appl. Math. 53 2 (1994) 163-170
22. Rezounenko A.V., and Wu J. A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors. Journal of Computational and Applied Mathematics 190 1-2 (2006) 99-113
23. Hernández E., Prokopczyk A., and Ladeira L. A note on partial functional differential equations with statedependent delay. Nonlinear Analysis: Real World Applications 7 4 (2006) 510-519
24. Pazy A. Semigroups of linear operators and applications to partial differential equations. Applied Mathematical Sciences Volume 44 (1983), Springer-Verlag, New York
25. Hino Y., Murakami S., and Naito T. Functional differential equations with infinite delay. Lecture Notes in Mathematics Volume 1473 (1991), Springer-Verlag, Berlin
26. Hale J.K., and Kato J. Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21 1 (1978) 11-41
27. Granas A., and Dugundji J. Fixed Point Theory (2003), Springer-Verlag, New York
28. Martin R.H. Nonlinear Operators and Differential Equations in Banach Spaces (1987), Robert E. Krieger Publ., Malabar, FL