Mathematics

On some integral equations on the half-axis with kernels composed of exponentials

A. G. Galumian

Yerevan State University

Abstract: Consider the equation
$$y(x)=\int\limits_{0}^{+\infty}K(x, t)y(t)dt +f(x)~(x>0).\qquad{(1)}$$
In the case of a difference $(K= K(x-t))$ or a difference-sum $(K=K_1(x-t)+K_2(x+t))$ kernel, a theory of solvability of equation (1) has been constructed and various methods for solving it have been developed. In the case of a difference kernel representable through exponentials, the theory has been advanced especially far. However, all these approaches turn out to be essentially ineffective if the kernel has the form $(K= K(ax+bt)) (a\neq ± b)$. Let us begin the study of some classes of equations of the latter type.

UDC: 517.984

Received: 07.04.1984
Accepted: 25.03.1985