| 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:
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| 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:
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[7] Dugundji, J., Granas, A.: Fixed Point Theory. I: Monografie Matematyczne.PWN Warszawa (1982). MR 0660439 |
| Reference:
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[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:
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[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:
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[14] Winter, A.: The nonlocal existence problem for ordinary differential equations.Am. J. Math. 67 (1945), 277-284. 10.2307/2371729 |
| . |
