On nonlinear Volterra-Fredholm functional integrodifferential equations with nonlocal condition in Banach spaces
Downloads
DOI:
https://doi.org/10.26637/mjm104/007Abstract
In this paper we study the existence, uniqueness and continuous dependence of solutions of nonlinear Volterra-Fredholm functional integrodifferential equations with nonlocal condition in Banach space by using the Hausdorff’s measure of noncompactness and Darbo-Sadovskii fixed point theorem. An application is provided to illustrate the theory.
Keywords:
Volterra-Fredholm functional integrodifferential equation, nonlocal condition, Hausdorff’s measure of noncompactness, Darbo-Sadovskii fixed point theoremMathematics Subject Classification:
45J05, 34K30, 47H10- Pages: 61-75
- Date Published: 01-10-2013
- Vol. 1 No. 04 (2013): Malaya Journal of Matematik (MJM)
D. Bahuguna, and S. Agarwal, Approximations of solutions to neutral functional differential equations with nonlocal history conditions, J. Math. Anal. Appl., 317(2006), 583-602. DOI: https://doi.org/10.1016/j.jmaa.2005.07.010
K. Balachandran, and R. Sakthivel, Existence of solutions of neutral functional integrodifferential equation in Banach space, Proc. Indian Acad. Sci. Math. Sci., 109(1999), 325-332. DOI: https://doi.org/10.1007/BF02843536
K. Balachandran, and J.Y. Park, 2001. Existence of a mild solution of a functional integrodifferential equation with nonlocal condition, Bull. Korean Math. Soc., 38(1)(2001), 175-182.
J. Banas, and K. Goebel, Measure of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Math. Dekker, New York, Vol 60, 1980.
M. Benchohra, and S.K. Ntouyas, Nonlocal Cauchy problems for neutral functional Differential and integrodifferential inclusions, J. Math. Anal. Appl., 258(2001), 573-590. DOI: https://doi.org/10.1006/jmaa.2000.7394
L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Appl. Math. Stoc.Anal., 162(1991), 494-505. DOI: https://doi.org/10.1016/0022-247X(91)90164-U
L. Byszewski, and H. Akca, On a mild solution of a semilinear functional-differential evolution nonlocal problem, J. Appl. Math. Stoc.Anal., 10(1997), 265-271. DOI: https://doi.org/10.1155/S1048953397000336
L. Byszewiski, and H. Akca, Existence of solutions of a semilinear functional-differential evolution nonlocal problem, Nonlinear Analysis, 34(1998), 65-72. DOI: https://doi.org/10.1016/S0362-546X(97)00693-7
X. Fu X, and K. Ezzinbi, Existence of solutions for neutral functional differential evolution equations with nonlocal conditions, Nonlinear Anal., 54(2003), 215-227. DOI: https://doi.org/10.1016/S0362-546X(03)00047-6
E. Hernandez, and H.R. Henriquez, Existence results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl., 221(1998), 452-475. DOI: https://doi.org/10.1006/jmaa.1997.5875
E. Hernandez, Existence results for a class of semi-linear evolution equations, Electron. J. Differential Equations, Vol 2001, pp. 1-14.
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
D. Qixiang, F. Zhenbin, and Gang Li, Semilinear differential equations with nonlocal conditions in Banach spaces, International J. Nonlinear Science, 2(3)(2006), 131-139.
D. Qixiang, F. Zhenbin, and Gang Li, Existence of solutions to nonlocal neutral functional differential and integrodifferential equations, International J. Nonlinear Science, 5(2)(2008), 140-151.
Y. Runping, and Z. Guowei, Neutral functional differential equations of second order with infinite delays, Electronic Journal of Differential Equations, Vol 2010, No.36, pp. 1-12.
X. Xue, Nonlinear differential equations with nonlocal conditions in Banach spaces, Nonlinear Anal., 63(2005), 575-586. DOI: https://doi.org/10.1016/j.na.2005.05.019
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
- Taufiq K. A. Khairuddin, William R. B. Lionheart, Fitting ellipsoids to objects by the first order polarization tensor , Malaya Journal of Matematik: Vol. 1 No. 04 (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.
