## Mental Enlightenment Scientific-Methodological Journal

#### Abstract

The study of spectral properties, in particular bound states, of multiparticle operators of quantum mechanics and solid state physics is closely related to the problem of solving integral equations with partial integrals (partial integral equations) for functions of three variables. In this article, we study the question of the existence and uniqueness of the solution of a linear partial integral equation for functions of three variables with degenerate kernels and many parameters in a complex Hilbert space. It is proved that under natural conditions, equation (1) has a unique solution, which is expressed through the data and their integrals of the considered equation. The general view of the solution is found. When solving the partial integral equation under study, the Fredholm method was developed for solving a linear integral equation of the second kind with a parameter.

#### First Page

40

#### Last Page

49

#### References

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#### Recommended Citation

Soatov, Ulugbek
(2021)
"ON THE SOLUTION OF A LINEAR PARTIALLY INTEGRAL EQUATION IN THE SPACE L2 ([a, b] 3),"
*Mental Enlightenment Scientific-Methodological Journal*: Vol. 2021
:
Iss.
1
, Article 5.

Available at:
https://uzjournals.edu.uz/tziuj/vol2021/iss1/5