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Semiconservative systems of integral equations with two kernels. (English) Zbl 1223.45004
Summary: The solvability and the properties of solutions of nonhomogeneous and homogeneous vector integral equation \(f(x) = g(x) + \int_0^{\infty} k(x - t) f(t) dt + \int_{-\infty}^0 T(x - t)f(t)dt\), where \(K, T\) are \(n \times n\) matrix valued functions, \(n \geq 1\), with nonnegative integrable elements, are considered in one semiconservative (singular) case, where the matrix \(A = \int_{-\infty}^{\infty} K(x)dx\) is stochastic one and the matrix \(B = \int^{\infty}_{-\infty} T(x)dx\) is substochastic one. It is shown that in certain conditions the nonhomogeneous equation simultaneously with the corresponding homogeneous one possesses positive solutions.
45F15 Systems of singular linear integral equations
45M20 Positive solutions of integral equations
Full Text: DOI
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