Semiconservative Systems of Integral Equations with Two Kernels

The solvability and the properties of solutions of nonhomogeneous and homogeneous vector integral equation f x g x ∫∞ 0 k x − t f t dt ∫0 −∞ T x − t f t dt, where K, T are n × n matrix valued functions, n ≥ 1, with nonnegative integrable elements, are considered in one semiconservative singular case, where the matrix A ∫∞ −∞ K x dx is stochastic one and the matrix B ∫∞ −∞ T x dx is substochastic one. It is shown that in certain conditions the nonhomogeneous equation simultaneously with the corresponding homogeneous one possesses positive solutions.