Necessary and sufficient condition for solvability of a partial integral equation

Abstract

Let $T_1: L_2(\Omega^2) \to L_2(\Omega^2)$ be a partial integral operator [4,7] with the kernel from $C(\Omega^3)$ where $\Omega=[a,b ]^ u$, $ u \in N$ is fixed. In this paper we investigate solvability of the partial integral equation $f-\varkappa T_1 f=g_0$ in the space $L_2(\Omega^2)$ in the case where $\varkappa$ is a cha ac eristic number. We prove a the theorem that gives a necessary and sufficient condition for solvability of the partial integral equation $f-\varkappa T_1 f=g_0.$

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Article Information

Title	Necessary and sufficient condition for solvability of a partial integral equation
Source	Methods Funct. Anal. Topology, Vol. 15 (2009), no. 1, 67-73
MathSciNet	MR2502640
Copyright	The Author(s) 2009 (CC BY-SA)

Authors Information

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

Citation Example

Yu. Kh. Eshkabilov, Necessary and sufficient condition for solvability of a partial integral equation, Methods Funct. Anal. Topology 15 (2009), no. 1, 67-73.

BibTex

@article {MFAT426,
    AUTHOR = {Eshkabilov, Yu. Kh.},
     TITLE = {Necessary and sufficient condition for solvability of a partial integral equation},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {15},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {67-73},
      ISSN = {1029-3531},
  MRNUMBER = {MR2502640},
       URL = {http://mfat.imath.kiev.ua/article/?id=426},
}