Previous |  Up |  Next

Article

Title: Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition (English)
Author: Tidke, Haribhau L.
Author: Dhakne, Machindra B.
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 57
Issue: 3
Year: 2012
Pages: 297-307
Summary lang: English
.
Category: math
.
Summary: The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions. (English)
Keyword: global existence
Keyword: Volterra-Fredholm integrodifferential equation
Keyword: Leray-Schauder alternative
Keyword: nonlocal condition
Keyword: nonlinear
Keyword: mild solutions
MSC: 34K30
MSC: 45B05
MSC: 45D05
MSC: 45G10
MSC: 45J05
MSC: 45N05
MSC: 47D09
MSC: 47G20
idZBL: Zbl 1265.45012
idMR: MR2984604
DOI: 10.1007/s10492-012-0017-8
.
Date available: 2012-06-08T10:02:45Z
Last updated: 2020-07-02
Stable URL: http://hdl.handle.net/10338.dmlcz/142854
.
Reference: [1] Balachandran, K., Chandrasekaran, M.: Existence of solutions of nonlinear integrodifferential equation with nonlocal condition.J. Appl. Math. Stochastic Anal. 10 (1997), 279-288. Zbl 0986.45005, MR 1468123, 10.1155/S104895339700035X
Reference: [2] Balachandran, K.: Existence and uniqueness of mild and strong solutions of nonlinear integrodifferential equations with nonlocal condition.Differ. Equ. Dyn. Syst. 6 (1998), 159-165. MR 1660213
Reference: [3] Byszewski, L.: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem.J. Math. Anal. Appl. 162 (1991), 494-505. Zbl 0748.34040, MR 1137634, 10.1016/0022-247X(91)90164-U
Reference: [4] Byszewski, L.: Existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem.Zesz. Nauk. Politech. Rzesz. 121, Mat. Fiz. 18 (1993), 109-112. Zbl 0858.34045, MR 1274697
Reference: [5] Dhakne, M. B., Kendre, S. D.: On a nonlinear Volterra integrodifferential equation in Banach spaces.Math. Inequal. Appl. 9 (2006), 725-735. Zbl 1108.45009, MR 2268180
Reference: [6] Dhakne, M. B., Kendre, S. D.: On an abstract nonlinear integrodifferential equation. Proceedings of Second International Conference on Nonlinear Systems, December 2007.Bulletin of Marathwada Mathematical Society 8 (2007), 12-22.
Reference: [7] Dugundji, J., Granas, A.: Fixed Point Theory. I: Monografie Matematyczne.PWN Warszawa (1982). MR 0660439
Reference: [8] Ntouyas, S. K., Tsamatos, P. C.: Global existence for semilinear evolution equations with nonlocal conditions.J. Math. Anal. Appl. 210 (1997), 679-687. Zbl 0884.34069, MR 1453198, 10.1006/jmaa.1997.5425
Reference: [9] Ntouyas, S. K., Tsamatos, P. C.: Global existence for second-order semilinear ordinary and delay integrodifferential equations with nonlocal conditions.Appl. Anal. 67 (1997), 245-257. Zbl 0906.35110, MR 1614061, 10.1080/00036819708840609
Reference: [10] Pachpatte, B. G.: Applications of the Leray-Schauder alternative to some Volterra integral and integrodifferential equations.Indian J. Pure Appl. Math. 26 (1995), 1161-1168. Zbl 0852.45012, MR 1364736
Reference: [11] Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations.Springer New York (1983). Zbl 0516.47023, MR 0710486
Reference: [12] Tidke, H. L., Dhakne, M. B.: On global existence of solutions of abstract nonlinear mixed integrodifferential equation with nonlocal condition.Commun. Appl. Nonlinear Anal. 16 (2009), 49-59. Zbl 1179.45021, MR 2490243
Reference: [13] Tidke, H. L.: Existence of global solutions to nonlinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions.Electron. J. Differ. Equ., paper No. 55 2009 (2009), 1-7. Zbl 1165.45010, MR 2505113
Reference: [14] Winter, A.: The nonlocal existence problem for ordinary differential equations.Am. J. Math. 67 (1945), 277-284. 10.2307/2371729
.

Files

Files Size Format View
AplMat_57-2012-3_6.pdf 240.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo