UDC 517. 95
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4 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
lyashko.natali@gmail.com
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5 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
myksyd@knu.ua
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INTEGRAL OPERATORS THAT DETERMINE THE SOLUTION
OF AN ITERATED HYPERBOLIC-TYPE EQUATION
Abstract. Integral operators that translate arbitrary functions into regular solutions of the hyperbolic equation of the second and higher orders are constructed. The Cauchy problem for the fourth-order hyperbolic equation is solved. The use of the theory of special functions helped us to obtain the image of solutions of partial derivative equations in a form convenient for the analysis. Along the way, solvable integral equations with special functions in the kernel are solved.
Keywords: integral operator, hyperbolic type iterated equations, regular solutions, mathematical induction.
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