Solvability and construction of solutions of integral equations

  • С. А. Айсагалиев al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
  • С. С. Айсагалиева al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan
  • А. А. Кабидолданова al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan

Abstract

A class of integral equations with respect to one variable function as well as to multivariablefunction that are solvable for any right hand side of an equation has been singled out. A necessaryand sufficient condition for existence of a solution has been obtained for the class of integralequations and the general form of their exact solutions has been found. Necessary and sufficientconditions for existence of solutions to the mentioned equations with a given right hand sideare obtained by reducing them to solving an extremal problem. An algorithm for solving theextremal problem by constructing a minimizing sequence has been developed and a convergencerate estimation has been obtained. A solvability criterion as a requirement on infimum of functionalhas been formulated. A necessary and sufficient condition for solvability of an integral equationwith parameter has been obtained and its general solution has been found.

References

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Published
2017-11-24
How to Cite
АЙСАГАЛИЕВ, С. А.; АЙСАГАЛИЕВА, С. С.; КАБИДОЛДАНОВА, А. А.. Solvability and construction of solutions of integral equations. KazNU Bulletin. Mathematics, Mechanics, Computer Science Series, [S.l.], v. 89, n. 2, p. 3-18, nov. 2017. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/347>. Date accessed: 17 aug. 2018.
Keywords: integral equation, general solution, existence of a solution, necessary and sufficient condition, solvability criterion, extremal problem, minimizing sequence