EXISTENCE OF SOLUTIONS FOR NONLINEAR EVOLUTION EQUATIONS WITH INFINITE DELAY

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 51, Issue 1, 2014, pp.43-54
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2014.51.1.043

Title & Authors

EXISTENCE OF SOLUTIONS FOR NONLINEAR EVOLUTION EQUATIONS WITH INFINITE DELAY

Dong, Qixiang; Li, Gang;

Dong, Qixiang; Li, Gang;

Abstract

This paper is concerned with nonlinear evolution differential equations with infinite delay in Banach spaces. Using Kato`s approximating approach, existence and uniqueness of strong solutions are obtained.

Keywords

nonlinear evolution equation;m-accretive operator;approximate;strong solution;

Language

English

Cited by

References

1.

V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noord-hoff, Leyden, 1976.

2.

J. Dyson and R. V. Bressan, Functional differential equations and non-linear evolution operators, Proc. Roy. Soc. Edinburgh Ser. A 75 (1975/1976), no. 3, 223-234.

3.

J. Dyson and R. V. Bressan, Semigroups of translations associated with functional and functional-differential equations, Proc. Roy. Soc. Edinburgh Sect. A 82 (1978/79), no. 3-4, 171-188.

4.

Z. Fan, Existence and continuous dependence results for nonlinear differential inclusions with infinite delay, Nonlinear Anal. 69 (2008), no. 8, 2379-2392.

5.

W. Fitzgibbon, Representation and approximation of solutions to semilinear Volterra equations with delay, J. Differential Equations 32 (1979), no. 2, 233-249.

6.

C. Gori, V. Obukhovskii, M. Ragni, and P. Rubbioni, Existence and continuous dependence results for semilinear functional differential inclusions with infinite delay, Nonlinear Anal. 51 (2002), 765-782.

7.

J. K. Hale and J. Kato, Phace space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), no. 1, 11-41.

8.

H. R. Henriquez, Differentiability of solutions of second-order functional differential equations with unbounded delay, J. Math. Anal. Appl. 280 (2003), no. 2, 284-312.

9.

Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Infinite Delay, in Lecture Notes in Math. Vol. 1473, Springer-Verlag, Berlin, 1991.

10.

A. G. Kartsatos and M. E. Parrott Convergence of the Kato approximants for evolution equations involving functional perturbations, J. Differential Equations 47 (1983), no. 3, 358-377.

12.

J. Liang and T. J. Xiao, The Cauchy problem for nonlinear abstract functional differential equations with infinite delay, Comput. Math. Appl. 40 (2000), no. 6-7, 693-703.

13.

N. H. Pavel, Nonlinear evolution operators and semigroups, in Lecture Notes in Mathematics, Vol. 1260, Springer-Verlag, Berlin, 1987.

14.

K. Schumacher, Existence and continuous dependence for functional differential equations with unbounded delay, Arch. Ration. Mech. Anal. 67 (1978), no. 4, 315-335.

15.

C. C. Travis and G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395-418.

16.

C. C. Travis and G. F. Webb, Existence, stability and compactness in the ${\alpha}$ -norm for partial functional differential equations, Trans. Amer. Math. Soc. 240 (1978), 129-143.