| |
| | Institute of Mathematics of National Academy of Sciences of Armenia (Site not responding. Last check: 2007-10-08) |
 | | The paper studies the integral equation $f(x,y)=g(x,y)+\iint\limits_GK(x-x',y-y')f(x',y')\;dx'\;dy',$ where $G$ is an unbounded domain in $\R^2$, the kernel $K$ is nonnegative function satisfying the conservativity condition. |
| | We consider renewal equation $f(x)=g(x)+\int_0^x V(x-t)f(t)dt,$ where the kernel $V$ is completely monotone function and prove that if $g\in L_1(0,\y)$ is a completely monotone function of the form $g(x)=\int_a^b e^{-xs}G(s)d\si(s),$ and $G\ge 0$ is a continuous increasing function on $[a,b)$, then the solution is also completely monotone. |
| | For convolution-type integral equations on finite intervals with completely monotone kernels a method for construction of approximate solution is proposed. |
| math.sci.am /Journal/1997_1.html (464 words) |
|
