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.
Downloads
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
Issue
Section
Science Journal of University of Zakho
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-SA 4.0] that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work, with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online.
