This article is cited in 9 papers

Boundary value problems for the loaded third order equations of the hyperbolic and mixed types

U. I. Baltayeva^a, B. I. Islomov<sup>b

a</sup> Urgench State University, Urgench, Uzbekistan
^b Institute for Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

Abstract: In this paper, the unique solvability is proved for the solution of boundary value problems of a loaded third order differential equation with hyperbolic and parabolic-hyperbolic operators. The boundary value problems for loaded differential equations are reduced to the Volterra integral equation of the second kind. On this basis, existence and uniqueness of the solution of boundary value problems is proved by the method of integral equations.

Keywords: loaded equation, equations of the mixed type, integral equation, integral equation with a shift, Bessel's functions.

UDC: 517.946

Received: 07.07.2011

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