Semiconservative Systems of Integral Equations with Two Kernels

N. B. Yengibaryan and A. G. Barseghyan

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-11

Abstract:

The solvability and the properties of solutions of nonhomogeneous and homogeneous vector integral equation ∫ ð ‘“ ( ð ‘¥ ) = ð ‘” ( ð ‘¥ ) + ∞ 0 ∫ 𠑘 ( ð ‘¥ − ð ‘¡ ) ð ‘“ ( ð ‘¡ ) ð ‘‘ ð ‘¡ + 0 − ∞ 𠑇 ( ð ‘¥ − ð ‘¡ ) ð ‘“ ( ð ‘¡ ) ð ‘‘ ð ‘¡ , where ð ¾ , 𠑇 are ð ‘› × ð ‘› matrix valued functions, ð ‘› ≥ 1 , with nonnegative integrable elements, are considered in one semiconservative (singular) case, where the matrix ∫ ð ´ = ∞ − ∞ ð ¾ ( ð ‘¥ ) ð ‘‘ ð ‘¥ is stochastic one and the matrix ∫ ð µ = ∞ − ∞ 𠑇 ( ð ‘¥ ) ð ‘‘ ð ‘¥ is substochastic one. It is shown that in certain conditions the nonhomogeneous equation simultaneously with the corresponding homogeneous one possesses positive solutions.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:917951

DOI: 10.1155/2011/917951

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