ON COUPLED INTEGRAL H-LIKE EQUATIONS OF CHANDRASEKHAR

Abstract

A recently proposed ''simple transport model'' equation with an ''angular shift'' a (0 less than or equal to alpha less than or equal to 1) leads to a coupled integral H-like equation of Chandrasekhar. Such coupled H-like equations can be treated in terms of a one-parameter (k(1), 0 < k(1) < 1) family. From there an a priori bound can be obtained, which is independent of k(1), alpha, and c (0 less than or equal to c less than or equal to 1). Here c denotes the average total number of particles emerging from a collision. Consequently, we conclude that positive solutions of such coupled integral H-like equations exist. Moreover, we show that such equations have a unique positive solution pair for c = 0 or c = 1 and alpha = 0 or alpha = 1, and that the equations have exactly two positive solution pairs for 0 < c < 1 and 0 less than or equal to alpha < 1 or c = 1 and alpha sufficiently close to 1.