[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2015.28.3.365

EXITSENCE OF MILD SOLUTIONS FOR SEMILINEAR MIXED VOLTERRA-FREDHOLM FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCALS

LEE, HYUN MORK (Department of Mathematics Chungnam National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.28, no.3, 2015 , pp. 365-375 More about this Journal

Abstract

Of concern is the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear mixed Volterra-Fredholm functional integrodifferential equation. Our analysis is based on the theory of a strongly continuous semigroup of operators and the Banach fixed point theorem.

Keywords

Volterra-Fredholm equation; strongly continuous semi-group; Pachpatte's inequality; Gronwall inequality; continuous dependence; Banach fixed point theorem; nonlocal conditions;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
Cited By KSCI

1	K. Balachandran and M.Chandrasekaran, Existence of solutions of nonlinear integrodifferential equation with nonlocal conditions, Indian J. Appl. Stoch. Anal. 10 (1997), 27-288.
2	K. Balachandran and J. Y. Park, Existence of a mild solution of a functional integrodifferential equation with nonlocal condition, Bull. Korean Math. Soc. 38 (2001), no. 1, 175-182.
3	L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505. DOI
4	L. Byszewski, Existence, uniqueness and asymptotic satbility of solutions of abstract nonlocal Cauchy problem, Dynamic Systems and Applications 5 (1996), 595-605.
5	L. Byszewski and H. Akca, On a mild solution of a semilinear funtional-differential evolution nonlocal problem, J. Appl. Math. Stoch. Anal. 10 (1997), 265-271. DOI ScienceOn
6	S. K. Choi, H. H. Jang, N. Koo, and C. Yun existence of solutions in the ${\alpha}$ -norm for neutral differential equations with nonlocal conditions, J. Chungchenong Math. Soc. 27 (2014), 89-97. DOI ScienceOn
7	H. H. Jang, existence of mild solutions in the ${\alpha}$ -norm for some partial functional integrodifferential equations with nonlocal conditions, J. Chungchenong Math. Soc. 27 (2014), 393-401. DOI ScienceOn
8	K. D. Kucche and M. B. Dhakne, Existence of a Mild Solution of Mixed Volterra-Fredholm Functional Integrodifferential Equation with Nonlocal condition, Applied Mathematics and Computation 5 (2011), no. 8, 359-366.
9	K. D. Kucche and M. B. Dhakne,On existence results and qualitative properties of mild solution of semilinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces, Applied Mathematics and Computation 219 (2013), 10806-10816. DOI ScienceOn
10	Y. Lin and J. H. Liu, Semilinear integrodifferential equatioins with nonlocal Cauchy problem, Nonlinear Analysis, Methods and Appl. 26 (1996), 1023-1033. DOI ScienceOn
11	B. G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, New York, 1998.
12	B. G. Pachpatte, Integral and finite difference inequalities and applications, North-holland Mathematics Studies 205 Elesevier Science, B. V., Amsterdam (2006).
13	A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences 44, Springer-Verlag, New York, 1983.