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On an integral equation of transport theory in an inhomogeneous medium. (Russian) Zbl 0635.45009
The author investigates the equation (1) \(y(x)=\lambda (x)\cdot \int^{\infty}_{r}K(x-s)y(s)ds,\) where \(0\leq K\in L_ 1(- \infty,\infty)\), \(\int^{\infty}_{-\infty}K(s)ds=1\), \(0\leq \lambda (x)<1\) on (r,\(\infty)\). Under some additional assumptions on the functions \(\lambda\) (x) and K(x) he proves the existence of nonnegative solutions to (1) in the cases \(r=0\) and \(r=-\infty\).
Reviewer: M.TvrdĂ˝

MSC:
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
82C70 Transport processes in time-dependent statistical mechanics
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