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...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/917951 |
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| author | N. B. Yengibaryan A. G. Barseghyan |
| author_facet | N. B. Yengibaryan A. G. Barseghyan |
| author_sort | N. B. Yengibaryan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5480ce0ec8bd4d73a603930544502377 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5480ce0ec8bd4d73a6039305445023772025-02-03T06:48:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/917951917951Semiconservative Systems of Integral Equations with Two KernelsN. B. Yengibaryan0A. G. Barseghyan1Institute of Mathematics of National Academy of Sciences of Armenia, 24b Marshal Baghramian Avenue, 0019 Yerevan, ArmeniaInstitute of Mathematics of National Academy of Sciences of Armenia, 24b Marshal Baghramian Avenue, 0019 Yerevan, ArmeniaThe 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.http://dx.doi.org/10.1155/2011/917951 |
| spellingShingle | N. B. Yengibaryan A. G. Barseghyan Semiconservative Systems of Integral Equations with Two Kernels International Journal of Mathematics and Mathematical Sciences |
| title | Semiconservative Systems of Integral Equations with Two Kernels |
| title_full | Semiconservative Systems of Integral Equations with Two Kernels |
| title_fullStr | Semiconservative Systems of Integral Equations with Two Kernels |
| title_full_unstemmed | Semiconservative Systems of Integral Equations with Two Kernels |
| title_short | Semiconservative Systems of Integral Equations with Two Kernels |
| title_sort | semiconservative systems of integral equations with two kernels |
| url | http://dx.doi.org/10.1155/2011/917951 |
| work_keys_str_mv | AT nbyengibaryan semiconservativesystemsofintegralequationswithtwokernels AT agbarseghyan semiconservativesystemsofintegralequationswithtwokernels |