Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition

Haribhau L. Tidke; Machindra B. Dhakne

Applications of Mathematics (2012)

  • Volume: 57, Issue: 3, page 297-307
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Tidke, Haribhau L., and Dhakne, Machindra B.. "Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition." Applications of Mathematics 57.3 (2012): 297-307. <http://eudml.org/doc/246432>.

@article{Tidke2012,
abstract = {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.},
author = {Tidke, Haribhau L., Dhakne, Machindra B.},
journal = {Applications of Mathematics},
keywords = {global existence; Volterra-Fredholm integrodifferential equation; Leray-Schauder alternative; nonlocal condition; nonlinear; mild solutions; global existence; Volterra-Fredholm integro-differential equation; Leray-Schauder alternative; nonlocal condition; nonlinear; mild solutions},
language = {eng},
number = {3},
pages = {297-307},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition},
url = {http://eudml.org/doc/246432},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Tidke, Haribhau L.
AU - Dhakne, Machindra B.
TI - Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 297
EP - 307
AB - 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.
LA - eng
KW - global existence; Volterra-Fredholm integrodifferential equation; Leray-Schauder alternative; nonlocal condition; nonlinear; mild solutions; global existence; Volterra-Fredholm integro-differential equation; Leray-Schauder alternative; nonlocal condition; nonlinear; mild solutions
UR - http://eudml.org/doc/246432
ER -

References

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  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. (2007) 
  7. Dugundji, J., Granas, A., Fixed Point Theory. I: Monografie Matematyczne, PWN Warszawa (1982). (1982) MR0660439
  8. Ntouyas, S. K., Tsamatos, P. C., 10.1006/jmaa.1997.5425, J. Math. Anal. Appl. 210 (1997), 679-687. (1997) Zbl0884.34069MR1453198DOI10.1006/jmaa.1997.5425
  9. Ntouyas, S. K., Tsamatos, P. C., 10.1080/00036819708840609, Appl. Anal. 67 (1997), 245-257. (1997) Zbl0906.35110MR1614061DOI10.1080/00036819708840609
  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. (1995) Zbl0852.45012MR1364736
  11. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer New York (1983). (1983) Zbl0516.47023MR0710486
  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. (2009) Zbl1179.45021MR2490243
  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. (2009) Zbl1165.45010MR2505113
  14. Winter, A., 10.2307/2371729, Am. J. Math. 67 (1945), 277-284. (1945) DOI10.2307/2371729

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