On an integral equation of transport theory in an inhomogeneous medium. (Russian) Zbl 0635.45009

Arabadzhyan, L. G.

Differ. Uravn. 23, No. 9, 1618-1622 (1987).

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.Tvrdý

MSC:

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

Keywords:

transport theory; Milne problem; nonnegative solutions