On mild solutions of nonlocal semilinear functional integro-differential equations
Downloads
DOI:
https://doi.org/10.26637/mjm103/005Abstract
In the present paper, we investigate the existence, uniqueness and continuous dependence on initial data of mild solutions of first order nonlocal semilinear functional integro-differential equations of more general type with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.
Keywords:
Existence, delay, functional, integro-differential equation, fixed point, semigroup theoryMathematics Subject Classification:
45J05, 47H10, 47B38- Pages: 27-33
- Date Published: 01-07-2013
- Vol. 1 No. 03 (2013): Malaya Journal of Matematik (MJM)
T. A. Burton, Volterra Integral and Differential Equations, Academic Press, New York, 1983.
L. Byszewski, On mild solution of a semilinear functional differential evolution nonlocal problem, J. Appl. Maths and Stoch. Anal., 10(3)(1997), 265-271. DOI: https://doi.org/10.1155/S1048953397000336
L. Byszewski and H. Akca, Existence of solutions of a semilinear functional evolution nonlocal problem, Nonlinear Anal., 34(1998), 65-72. DOI: https://doi.org/10.1016/S0362-546X(97)00693-7
L. Byszewski and V. Lakshamikantham, Theorems about the existence and uniqueness of a solution of a nonlocal abstract cauchy problem in a Banach space, Applicable Analysis, 40(1990), 11-19. DOI: https://doi.org/10.1080/00036819008839989
C. Corduneanu, Integral Equations and Stability of Feedback System, Academic Press, New York, 1973.
M. B. Dhakne, Global existence of solution of nonlinear functional integral equations, Indian J. Pure Appl. Math., 30(7)(1999), 735-744.
M. B. Dhakne and G. B. Lamb, Existence results for abstract nonlinear integrodifferential equations, Ganit,J. Bangladesh Math. Soc., 21(2001), 29-37.
J.K. Hale, Theory of Functional Differential Equations, Springer,1977. DOI: https://doi.org/10.1007/978-1-4612-9892-2
Y. Lin and J.H. Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Analysis, 26(1996), 1023-1033. DOI: https://doi.org/10.1016/0362-546X(94)00141-0
C. Lizama and J. Pozo, Existence of mild solutions for a semilinear integrodifferential equation with nonlocal initial conditions, Abstract and Applied Analysis, Vol. 2012, Article Id. 647103, 15 pages. DOI: https://doi.org/10.1155/2012/647103
S. K. Ntouyas, Initial and boundary value problems for functional differential equations via the topological transversality method: A survey, Bull. Greek Math. Soc.,, 1998, 1-39.
S. K. Ntouyas, Nonlocal initial and boundary value problems: A survey, Handbook of Differential Equations: Ordinary Differential Equations, 2(2006), 461-557. DOI: https://doi.org/10.1016/S1874-5725(05)80008-2
B. G. Pachpatte, Inequalities for Differential and Integral Equations, Academic press, 1998.
B. G. Pachpatte, Global existence results for certain Integrodifferential equations, Demonstratio Mathematica, XXIX(1)(1996), 23-30. DOI: https://doi.org/10.1515/dema-1996-0105
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983. DOI: https://doi.org/10.1007/978-1-4612-5561-1
A.H. Siddiqi, Functional Analysis with Applications, Tata McGraw-Hill publishing ltd, New Delhi, 1986.
Y. Yang and J. Wang, On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces, Opscula Mathematica, 31(3)(2011), 443-455. DOI: https://doi.org/10.7494/OpMath.2011.31.3.443
X. Xue, Existence of solutions for semilinear nonlocal Cauchy problems in Banach spaces,Electronic Journal of Differential Equations, 64(2005), 1-7.
- NA
Similar Articles
- A.M.A. El-Sayed , S.M. Salman, Chaos and bifurcation of the Logistic discontinuous dynamical systems with piecewise constant arguments , Malaya Journal of Matematik: Vol. 1 No. 03 (2013): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2013 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
