ON SOLUTIONS OF NONHOMOGENEOUS SYSTEMS OF SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS

ЕКІНШІ РЕТТІ ДЕРБЕС ТУЫНДЫЛЫ БІРТЕКТІ ЕМЕС ДИФФЕРЕНЦИАЛДЫҚ ТЕҢДЕУЛЕР ЖҮЙЕСІНІҢ ШЕШІМДЕРІ ТУРАЛЫ
О РЕШЕНИЯХ НЕОДНОРОДНЫХ СИСТЕМ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ В ЧАСТНЫХ ПРОИЗВОДНЫХ ВТОРОГО ПОРЯДКА
Talipova M.Zh. Seilova R.D. Kaipova A.D.
2025 Kazakh-British Technical University

Herald of the Kazakh British Technical UNiversity
2025 #22 Issue 2 188 - 199 pp.

The aim of this work is to study a nonhomogeneous system of second-order partial differential equations that is close to the ordinary case. A particular solution of the considered system near the regular singular point (0,0) is sought in the form of a generalized power series in two variables using the Frobenius-Latysheva method. Various possible cases are demonstrated, where the systems of determining equations have simple or multiple roots. A theorem is presented for the particular solution of a “resonant” nonhomogeneous system of second-order partial differential equations. As an example, the solution of a nonhomogeneous Bessel system is given. The corresponding homogeneous system has solutions in the form of Bessel functions of two variables, while the particular solution of the nonhomogeneous system is expressed as a product of Bessel functions.

analytic function , determining equation , Frobenius-Latysheva method , nonhomogeneous system , polynomial , regular singular point , series , solution

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Aktobe Regional University named after K. Zhubanov, Kazakhstan

Aktobe Regional University named after K. Zhubanov

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