Geodesic
A Construction of analog of Fredgolm theorems for one class of first order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 236-248

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The integral representations of the solution manifold for one class of the first order model integro-differential equation with logarithmic singularity in the kernel are constructed using arbitrary constants. The cases when the given integro-differential equation has unique solution are found. The analogue of Fredholm theorem is built for given integro-differential equation. The method of solving this problem can be used for the solving of higher order model and non-model integro-differential equations with singular coefficients.
Keywords: integro-differential equation, boundary singular points, manifold solution, integral representation, characteristic equation. 
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     author = {S. K. Zaripov},
     title = {A {Construction} of analog of {Fredgolm} theorems for one class of first order},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {236--248},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2017_21_2_a2/}
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S. K. Zaripov. A Construction of analog of Fredgolm theorems for one class of first order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 236-248. http://geodesic.mathdoc.fr/item/VSGTU_2017_21_2_a2/