Geodesic
Solvability of a Class of Integro-Differential Equations of First Order with Variable Coefficients
Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 933-940

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In the present paper, we consider a class of linear integro-differential equations of first order with a stochastic kernel and with variable coefficients on the semiaxis. These equations have important applications in physical kinetics. By combining special factorization methods with methods involving integral Fredholm equations of the second kind, we can construct solutions of such equations in the Sobolev space $W^1_1(\mathbb R^+)$. In certain singular cases, we can also describe the structure of the obtained solutions.
Keywords: integro-differential equation of first order, stochastic kernel, integral Fredholm equation of the second kind, factorization method, Sobolev space $W^1_1(\mathbb R^+)$. 
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     author = {Kh. A. Khachatryan},
     title = {Solvability of a {Class} of {Integro-Differential} {Equations} of {First} {Order} with {Variable} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {933--940},
     publisher = {mathdoc},
     volume = {83},
     number = {6},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a11/}
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Kh. A. Khachatryan. Solvability of a Class of Integro-Differential Equations of First Order with Variable Coefficients. Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 933-940. http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a11/