Nonlinear boudary value problem in the case of parametric resonance

• Main Authors: Sergey Mikhaylovich Chujko, O. V. Nesmelova (Starkova), D. V. Sysoev
• Format: Article
• Language: Russian
• Published: Institute of Computer Science 2015-08-01
• Series: Компьютерные исследования и моделирование
• Subjects: seminonlinear boundary value problem; matrix differential equations; generalized Green’s operator; parametric excitation
• Online Access: http://crm.ics.org.ru/uploads/crmissues/crm_2015_4/150703.pdf
• ISSN: 2076-7633; 2077-6853

We construct necessary and sufficient conditions for the existence of solution of seminonlinear matrix boundary value problem for a parametric excitation system of ordinary differential equations. The convergent iteration algorithms for the construction of the solutions of the semi-nonlinear matrix boundary value problem for a parametric excitation system differential equations in the critical case have been found. Using the convergent iteration algorithms we expand solution of seminonlinear periodical boundary value problem for a parametric excitation Riccati type equation in the neighborhood of the generating solution. Estimates for the value of residual of the solutions of the seminonlinear periodical boundary value problem for a parametric excitation Riccati type equation are found.