Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay

 Access to full text

 Full (PDF)

1. [1] N.U. Ahmed, Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics Series, 246. Longman Scientific & Technical, Harlow John Wiley & Sons, Inc. New York, 1991. 
2. [2] W.G. Aiello, H.I. Freedman, J. Wu, Analysis of a model representing stage-structured population growth with statedependent time delay. SIAM J. Appl. Math. 52 (3) (1992), 855–869. Zbl0760.92018
3. [3] S. Baghli and M. Benchohra, Perturbed functional and neutral functional evolution equations with infinite delay in Fréchet spaces, Electron. J. Differential Equations 2008 (69) (2008), 1–19. Zbl1190.34098
4. [4] S. Baghli and M. Benchohra, Global uniqueness results for partial functional and neutral functional evolution equations with infinite delay, Differential Integral Equations 23 (1&2) (2010), 31–50. Zbl1240.34378
5. [5] S. Baghli and M. Benchohra, Existence results for semilinear neutral functional differential equations involving evolution operators in Fréchet spaces, Georgian Math. J. 17 (2010), 1072–9176. Zbl1210.34109
6. [6] A. Caicedo, C. Cuevas, G. M. Mophou, and G. M. N’Guérékata, Asymptotic behavior of solutions of some semilinear functional differential and integro-differential equations with infinite delay in Banach spaces. J. Franklin Inst. 349 (2012), 1-24. [WoS] Zbl1260.34142
7. [7] T. A. Burton and C. Kirk, A fixed point theorem of Krasnoselskii type, Math. Nachrichten 189 (1998), 23–31. Zbl0896.47042
8. [8] C. Corduneanu, Integral Equations and Stability of Feedback Systems, Acadimic Press, New York, 1973. 
9. [9] B.C. Dhage, V. Lakshmikantham, On global existence and attractivity results for nonlinear functional integral equations, Nonlinear Anal. 72 (2010), 2219-2227. Zbl1197.45005
10. [10] J. P.C. dos Santos, On state-dependent delay partial neutral functional integro-differential equations, Appl. Math. Comput. 216 (2010) 1637–1644. Zbl1196.45013
11. [11] K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000. Zbl0952.47036
12. [12] X. Fu, Existence and stability of solutions to neutral equations with infinite delay, Electron. J. Differential Equations, Vol. 2013 (2013), No. 55, pp. 1–19. Zbl1293.34103
13. [13] J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977. Zbl0352.34001
14. [14] J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11–41. Zbl0383.34055
15. [15] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equation, Applied Mathematical Sciences 99, Springer-Verlag, New York, 1993. 
16. [16] E. Hernández M. and M. A. McKibben, On state-dependent delay partial neutral functional-differential equations, Appl. Math. Comput. 186 (2007), 294–301. Zbl1119.35106
17. [17] E. Hernández, M. A. McKibben and H. R. Henríquez, Existence results for partial neutral functional differential equations with state-dependent delay Math. Comput. Modelling 49 (2009), 1260–1267. Zbl1165.34420
18. [18] Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Unbounded Delay, Springer-Verlag, Berlin, 1991. Zbl0732.34051
19. [19] V. Kolmanovskii, and A. Myshkis, Introduction to the Theory and Application of Functional-Differential Equations. Kluwer Academic Publishers, Dordrecht, 1999. Zbl0917.34001
20. [20] V. Lakshmikantham, L. Wen and B. Zhang, Theory of Differential Equations with Unbounded Delay, Kluwer Acad. Publ., Dordrecht, 1994. Zbl0823.34069
21. [21] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. 
22. [22] N. Van Minh, Gaston M. N’Guérékata, and C. Preda. On the asymptotic behavior of the solutions of semilinear nonautonomous equations. Semigroup Forum 87 (2013), 18-34. [WoS] Zbl1280.34055
23. [23] J. Wu, Theory and Application of Partial Functional Differential Equations, Springer-Verlag, New York, 1996.