Existence, Uniqueness and Stability of Periodic Solution for Nonlinear System of Integro-Differential Equations
DOI:
https://doi.org/10.25271/2017.5.1.312Keywords:
Existence, Uniqueness & Stability solution, Periodic Solution, Nonlinear System of Integro-differential Equations, Numerical-Analytic MethodsAbstract
In this paper, we investigate the existence, uniqueness, and stability of the periodic solution for the system of nonlinear integro-differential equations by using the numerical-analytic methods for investigating the solutions and the periodic solutions of ordinary differential equations, which are given by A. Samoilenko.
References
Aziz, M. A. (2006). Periodic solutions for some systems of non-linear ordinary differential equations (Doctoral dissertation, M. Sc. Thesis, college of Education, University of Mosul).
Apostol, M. T. (1973). Mathematical Analysis, 2nd edition, Institute of Technology, Addison-Wesley, California.
Burrill, C. W. and Knudsen, J. R. (1969). Real variable, Holt Rinehart and Winson, Inc, USA.
Butris, R. N., & Dawoud, S. A. Solution of Integro-differential Equation of the first order with the operators. International Journal of Scientific Engineering and Applied Science, India,(IJSEAS), 1.
Byszewski, L., & Akca, H. (1997). On a mild solution of a semilinear functional-differential evolution nonlocal problem. International Journal of Stochastic Analysis, 10(3), 265-271.
Lipshutz, D., & Williams, R. J. (2015). Existence, uniqueness, and stability of slowly oscillating periodic solutions for delay differential equations with nonnegativity constraints. SIAM Journal on Mathematical Analysis, 47(6), 4467-4535.
Hu, J., & Li, W. P. (2005). Theory of Ordinary Differential Equations. Existence, Uniqueness and Stability. Publications of Department of Mathematics. The Hong Kong University of Science and Technology.
Korol’, I. I. (2010). Numerical-analytic method for the investigation of boundary-value problems for semilinear systems of differential equations. Nonlinear Oscillations, 13(1), 45-56.
Korol', I. I. (2005). On periodic solutions of one class of systems of differential equations. Ukrainian Mathematical Journal, 57, 583-599.
Rama, M. M., & Rao, M. (1981). Ordinary differential equations theory and applications. United Kingdom.
Samoĭlenko, A.M. (1966) A numerical-analytic method for investigation of periodic systems of ordinary differential equations. II, Ukrain. Mat. Zh. 18 (2), 50–59.
Samoĭlenko, A.M. (1965). A numerical-analytic method for investigation of periodic systems of ordinary differential equations. I, Ukrain. Mat. Zh. 17 (4), 82–93.
Tidke, H. L., & More, R. T. (2015). Existence and uniqueness of solution of integrodifferential equation in cone metric space. SOP Trans. Appl. Math, 2(1), 13-19.
Apostol, M. T. (1973). Mathematical Analysis, 2nd edition, Institute of Technology, Addison-Wesley, California.
Burrill, C. W. and Knudsen, J. R. (1969). Real variable, Holt Rinehart and Winson, Inc, USA.
Butris, R. N., & Dawoud, S. A. Solution of Integro-differential Equation of the first order with the operators. International Journal of Scientific Engineering and Applied Science, India,(IJSEAS), 1.
Byszewski, L., & Akca, H. (1997). On a mild solution of a semilinear functional-differential evolution nonlocal problem. International Journal of Stochastic Analysis, 10(3), 265-271.
Lipshutz, D., & Williams, R. J. (2015). Existence, uniqueness, and stability of slowly oscillating periodic solutions for delay differential equations with nonnegativity constraints. SIAM Journal on Mathematical Analysis, 47(6), 4467-4535.
Hu, J., & Li, W. P. (2005). Theory of Ordinary Differential Equations. Existence, Uniqueness and Stability. Publications of Department of Mathematics. The Hong Kong University of Science and Technology.
Korol’, I. I. (2010). Numerical-analytic method for the investigation of boundary-value problems for semilinear systems of differential equations. Nonlinear Oscillations, 13(1), 45-56.
Korol', I. I. (2005). On periodic solutions of one class of systems of differential equations. Ukrainian Mathematical Journal, 57, 583-599.
Rama, M. M., & Rao, M. (1981). Ordinary differential equations theory and applications. United Kingdom.
Samoĭlenko, A.M. (1966) A numerical-analytic method for investigation of periodic systems of ordinary differential equations. II, Ukrain. Mat. Zh. 18 (2), 50–59.
Samoĭlenko, A.M. (1965). A numerical-analytic method for investigation of periodic systems of ordinary differential equations. I, Ukrain. Mat. Zh. 17 (4), 82–93.
Tidke, H. L., & More, R. T. (2015). Existence and uniqueness of solution of integrodifferential equation in cone metric space. SOP Trans. Appl. Math, 2(1), 13-19.
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Published
2017-03-30
How to Cite
Butris, R. N., Rafeeq, A. S., & Faris, H. S. (2017). Existence, Uniqueness and Stability of Periodic Solution for Nonlinear System of Integro-Differential Equations. Science Journal of University of Zakho, 5(1), 120–127. https://doi.org/10.25271/2017.5.1.312
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Science Journal of University of Zakho
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Copyright (c) 2017 Raad N. Butris, Ava Sh. Rafeeq, Hewa S. Faris
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