EXISTENCE OF MILD SOLUTIONS IN THE α-NORM FOR SOME PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

다국어 초록 (Multilingual Abstract)

In this work, we discuss the existence of mild solutionsin the α-norm for some partial functional integrodifferential equa-tions with in¯nite delay. We assume that the linear part generatesan analytic semigroup on a Banach space X and the nonlinear partis a Lipschitz continuous function with respect to the fractionalpower norm of the linear part.

참고문헌 (Reference)

1 L. Byszewski, "Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem" 162 : 494-505, 1991

2 Y. Lin, "Semilinear integrodifferential equations with nonlocal Cauchy problem" 26 : 1023-1033, 1996

3 A. Pazy, "Semigroups of linear operators and applications to partial differential equations" Springer-Verlag 1983

4 J. K. Hale, "Phase space for retarded equations with unbounded delay" 21 : 11-41, 1978

5 L. Byszewski, "On a mild solution of a semilinear functional-differential evolution nonlocal problem" 10 : 265-271, 1997

6 M. Adimy, "Local existence and stability for some partial functional differential equations with infinite delay, Nonlinear Analysis Theory" 48 : 323-348, 2002

7 J. K. Hale, "Introduction to Functional Differential Equations" Springer-Verlag 1993

8 H. Bouzahir, "Global Attractor for a class of partial functional differential equations with infinite delay" 29 : 63-71, 2001

9 L. Byszewski, "Existence, uniqueness and asymptotic stability of solutions of abstract nonlocal Cauchy problem" 5 : 595-605, 1996

10 C. C. Tarvis, "Existence, stability and compactness in the α α-norm for partial functional differential equations" 240 : 129-143, 1978

11 K. Balachandran, "Existence of solutions of nonlin-ear integrodifferential equation with nonlocal conditions" 10 : 27-288, 1997

12 K. Balachandran, "Existence of solution of a delay differential equation with nonlocal condition" 27 : 443-449, 1996

13 R. Benkhalti, "Existence of a periodic solution for some partial functional differential equations with infinite delay" 256 : 257-280, 2001

14 K. Balachandran, "Existence of a mild solution of a functional integrodifferential equation with nonlocal condition" 38 : 175-182, 2001

15 M. Adimy, "Existence for a class of partial functional differential equations with infinite delay, Nonlinear Analysis Theory" 46 : 91-112, 2001

16 R. Benkhalti, "Existence and stability in the α α-norm for some partial functional differential equations with infinite delay" 19 : 545-572, 2006

17 M. Adimy, "Existence and stability in the α α-norm for some partial functional differential equations of neutral type" 185 (185): 437-460, 2006

18 R. Benkhalti, "Existence and stability for some partial neutral functional differential equations" 17 : 1426-1436, 2004

19 K. Ezzinbi, "Existence and stability for some partial functional differential equations with infinite delay" 2003 : 1-13, 2003

20 J. K. Hale, "Asymptotic Behavior of Dissipative Systems" Amer. Math. Soc. 1988