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arXiv · 0803.1899

The necessary and sufficient condition for solvability of a partial integral equation

Eshkabilov Yu. Kh
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Abstract

Let $T_1: L_2(Ω^2) \to L_2(Ω^2)$ be a partial integral operator with the kernel from $C(Ω^3)$ where $Ω=[a,b ]^ν.$ In this paper we investigate solvability of a partial integral equation $f-\varkappa T_1 f=g_0$ in the space $L_2(Ω^2)$ in the case when $\varkappa$ is a characteristic number. We proved the theorem describing the necessary and sufficient condition for solvability of the partial integral equation $f-\varkappa T_1 f=g_0.$

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Eshkabilov Yu. Kh. 2008-03-13. The necessary and sufficient condition for solvability of a partial integral equation. https://arxiv.org/abs/0803.1899

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