Semiconservative Systems of Integral Equations with Two Kernels

Abstract EN

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+∫−∞0T(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.