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# On solvability of a partial integral equation in the space ${L_2(\Omega \times\Omega)}$

### Abstract

In this paper we investigate solvability of a partial integral equation in the space $L_2(\Omega\times\Omega),$ where $\Omega=[a,b]^ u.$ We define a determinant for the partial integral equation as a continuous function on $\Omega$ and for a continuous kernels of the partial integral equation we give explicit description of the solution.

### Article Information

 Title On solvability of a partial integral equation in the space ${L_2(\Omega \times\Omega)}$ Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 4, 323-329 MathSciNet MR2469071 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

Yu. Kh. Eshkabilov
National University of Uzbekistan, Tashkent, Uzbekistan

### Citation Example

Yu. Kh. Eshkabilov, On solvability of a partial integral equation in the space ${L_2(\Omega \times\Omega)}$, Methods Funct. Anal. Topology 14 (2008), no. 4, 323-329.

### BibTex

@article {MFAT421,
AUTHOR = {Eshkabilov, Yu. Kh.},
TITLE = {On solvability of a partial integral equation in the space ${L_2(\Omega \times\Omega)}$},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {4},
PAGES = {323-329},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=421},
}