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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.
##### MSC:
 45F15 Systems of singular linear integral equations 45M20 Positive solutions of integral equations
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##### References:
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