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REGULARITY OF SOLUTIONS OF QUASILINEAR DELAY INTEGRODIFFERENTIAL EQUATIONS
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 Title & Authors
REGULARITY OF SOLUTIONS OF QUASILINEAR DELAY INTEGRODIFFERENTIAL EQUATIONS
Park, Dong-Gun; Balachandran, Krishnan; Samuel, Francis Paul;
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 Abstract
We prove the existence and uniqueness of classical solutions for a quasilinear delay integrodifferential equation in Banach spaces. The result is established by using the semigroup theory and the Banach fixed point theorem.
 Keywords
contraction principle;mild and classical solution;semigroup theory;
 Language
English
 Cited by
 References
1.
D. Bahuguna, Quasilinear integrodifferential equations in Banach spaces, Nonlinear Anal. 24 (1995), no. 2, 175-183. crossref(new window)

2.
D. Bahuguna, Regular solutions to quasilinear integrodifferential equations in Banach spaces, Appl. Anal. 62 (1996), no. 1-2, 1-9. crossref(new window)

3.
K. Balachandran and D. G. Park, Existence of solutions of quasilinear integrodifferential evolution equations in Banach spaces, Bull. Korean Math. Soc. 46 (2009), no. 4, 691-700. crossref(new window)

4.
K. Balachandran and F. Paul Samuel, Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions, Electron. J. Differential Equations 2009 (2009), no. 6, 1-7.

5.
K. Balachandran and K. Uchiyama, Existence of local solutions of quasilinear integrodifferential equations in Banach spaces, Appl. Anal. 76 (2000), no. 1-2, 1-8. crossref(new window)

6.
K. Balachandran and K. Uchiyama, Existence of solutions of quasilinear integrodifferential equations with nonlocal condition, Tokyo J. Math. 23 (2000), no. 1, 203-210. crossref(new window)

7.
L. Byszewski, Theorem about existence and uniqueness of continuous solution of nonlocal problem for nonlinear hyperbolic equation, Appl. Anal. 40 (1991), no. 2-3, 173-180. crossref(new window)

8.
L. Byszewski, Uniqueness criterion for solution of abstract nonlocal Cauchy problem, J. Appl. Math. Stochastic Anal. 6 (1993), no. 1, 49-54. crossref(new window)

9.
L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), no. 2, 494-505. crossref(new window)

10.
M. G. Crandall and P. E. Souganidis, Convergence of difference approximations of quasilinear evolution equations, Nonlinear Anal. 10 (1986), no. 5, 425-445. crossref(new window)

11.
K. Furuya, Analyticity of solutions of quasilinear evolution equations, Osaka J. Math. 18 (1981), no. 3, 669-698

12.
K. Furuya, Analyticity of solutions of quasilinear evolution equations. II, Osaka J. Math. 20 (1983), no. 1, 217-236.

13.
M. Kanagaraj and K. Balachandran, Existence of solutions of quasilinear integrodifferential equations in Banach spaces, Far East J. Math. Sci. 4 (2002), no. 3, 337-350.

14.
S. Kato, Nonhomogeneous quasilinear evolution equations in Banach spaces, Nonlinear Anal. 9 (1985), no. 10, 1061-1071. crossref(new window)

15.
T. Kato, Quasi-linear equations of evolution, with applications to partial differential equations, Spectral theory and differential equations (Proc. Sympos., Dundee, 1974 dedicated to Konrad Jorgens), pp. 25-70. Lecture Notes in Math., Vol. 448, Springer, Berlin, 1975. crossref(new window)

16.
T. Kato, Abstract evolution equations, linear and quasilinear, revisited, Functional analysis and related topics, 1991 (Kyoto), 103-125, Lecture Notes in Math., 1540, Springer, Berlin, 1993. crossref(new window)

17.
A. Lunardi, Global solutions of abstract quasilinear parabolic equations, J. Differential Equations 58 (1985), no. 2, 228-242. crossref(new window)

18.
M. G. Murphy, Quasilinear evolution equations in Banach spaces, Trans. Amer. Math. Soc. 259 (1980), no. 2, 547-557.

19.
H. Oka, Abstract quasilinear Volterra integrodifferential equations, Nonlinear Anal. 28 (1997), no. 6, 1019-1045. crossref(new window)

20.
H. Oka and N. Tanaka, Abstract quasilinear integrodifferential equations of hyperbolic type, Nonlinear Anal. 29 (1997), no. 8, 903-925. crossref(new window)

21.
A. Pazy, Semigroups of Linear Operators and Applications to Partial DifferentialEquations, Springer, New York, 1983.

22.
A. Yagi, Abstract quasilinear evolution equations of parabolic type in Banach spaces, Boll. Un. Mat. Ital. B (7) 5 (1991), no. 2, 341-368.