Paper title: |
Periodic Solution of Non-Linear Differential Equations with Non-Linear boundary conditions |
Published in: | Issue 1, (Vol. 19) / 2025 |
Publishing date: | 2025-04-15 |
Pages: | 8-13 |
Author(s): | BUTRIS Raad, SAEED Mayan |
Abstract. | In this paper, we investigate the existence, uniqueness and stability of the periodic solution for new non-linear system of differential equations with non-linear boundary conditions by using the numerical-analytic methods, which was introduced by Samoilenko. These investigations lead us to improving and extending the above method. Also we expand the results obtained by Samoilenko to change the periodic system of non-linear differential equations with initial condition to periodic a system of non-linear differential equations with non-linear boundary conditions. |
Keywords: | Existence, Uniqueness & Stability Solution, Periodic Solution, Nonlinear System Of Differential Equations, Non-linear Boundary Condition, Numerical Analytic Methods. |
References: | 1. Apostol, M. T. (1973). Mathematical Analysis, 2nd edition, Institute of Technology, Addison-Wesley, California. 2. Butris, R. N., Ava, SH. R. & Hewa, S. F. (2017). Existence, uniqueness and stability of periodic solution for nonlinear system of integro-differential equations science Journal of University of Zakho Vol. 5.No. 1 pp. 120-127, March- 2017. 3. Butris, R. N. (1994). Periodic solution for a system of second-order differential equations with boundary integral conditions, Univ. of Mosul, J.of Educ and Sci. Vol. 18. 4. Rama, M. M. (1981). Ordinary Differential Equations Theory and Applications, Britain. 5. Robert, M. M. and Robert. D. R., (1988).Numerical Solution of Boundary Value Problem for Ordinary Differential Equations, SIAM, In Applied Mathematics, Unit. 6. Samoilenko, A. M. & Ronto, N. I. (1976). A Numerical – Analytic Methods for Investigating of Periodic Solutions, Kiev, Ukraine. 7. Samoilenko, A. M. (1991). A numerical – analytic methods for Successive approximation of the problem with boundary integral condition, Kiev, Ukraine, Math. J. No. 9. 8. James, R. W. (2002). Periodic solution of ordinary differential equations with boundary nonlinearities, J.of the Julius Schauder Center Vol. 19, pp. 257-282. 9. Burrill, C. W. and Knudsen, J. R. (1969). Real variable, Holt Rinehart and Winson, Inc, USA. 10. Rafeq, A. Sh. (2009). Periodic solutions for some of nonlinear systems of integro –differential equations, M. Sc. Thesis, college of Science, Duhok University, Duhok. 11. Coddington, E. A. and Levinson, N. (1955). Theory of Ordinary Differential Equations, Mc Graw-Hill Book Company, New York. 12. Suham, K.H., & Shammo, S.K. (2013). Periodic solutions for some of non-linear systems of boundary value problems, M. Sc. Thesis, college of Education, Duhok University, Duhok. 13. Struble R. A. (1962). Non-Linear Differential Equations, McGraw – Hill Book company Inc., Newyork. 14. Sahla B. (2021). Abdi Periodic solutions of Volterra integro- differential equations with Retarded Argument, M. Sc. Thesis, college of Education , Duhok University, Duhok. 15. Aziz, M. A. (2006). Periodic solutions for some systems of nonlinear ordinary differential equations. Thesis. Collage of education. University of Mosul. 16. Mitropolsky Yu, A. & Martynyuk, D. I., (1979). For Periodic Solutions for the Oscillations Systems with Retarded Argument, Kiev, Ukraine. |
Back to the journal content |