A Construction of analog of Fredgolm theorems for one class of first order

S. K. Zaripov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 236-248.

Résumé

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.

Détail

Keywords: integro-differential equation, boundary singular points, manifold solution, integral representation, characteristic equation.

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