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Existence, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects Cover

Existence, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects

Open Access
|Dec 2023

References

  1. Bender C.M., Orszag S.A. (1999): Advanced Mathematical Method for Scientists and Engineers Asymptotic Methods and Perturbation. Springer New York, McGraw Hill: 545-551.
  2. Cartwright M.L. (1956): On the Stability of Solution of Certain Differential equation of the Fourth Order Quarter. Journal of Mechanics and Applied Mathematics 9: 185-194.
  3. Chen H., Li Y. (2000): Existence, Uniqueness and Stability of Periodic Solution of an Equation of Duffing type. Journal of American International Mathematical Society 10(10): 10-20.
  4. Daxiong P., Wenling L. (2008): Boundedness of Solution for Reversible System via Moser Twist theorem. Elsevier. Journal of Mathematical Analysis and Applications 341: 1224-1235.
  5. Ding T. (1986): Boundedness of Solutions of Duffing’s Equation. Journal of Differential Equation 61: 178-207.
  6. Eze E.O., Obasi U.E., Agwu E.U. (2019a): Stability Analysis of Periodic Solutions of Some Duffing’s Equation. Open Journal of Applied Sciences 9: 198-24.
  7. Eze E.O., Udaya C.O., Agwu E.U. (2019b): On Existence and Uniqueness of Solutions of Non-Linear First Order Differential Equation Using Implicit Function Theorem in Banach Space. Journal of the Nigerian Association of Mathematical Physics 50: 9-12.
  8. Eze E.O., Obasi U.E., Osu B.O., Oghogho C.P. (2021): Existence and Stability of Periodic Solution of Airy’s Equation with Elastic Coefficients. Nigerian Journal of Pure and Applied Sciences 34 (1): 3631-3640.
  9. Ezeilo J.O.C. (1960): On Existence of Periodic Solutions of a Certain Third Order Differential Equation. Pro Camb. Phi. Soc. 56: 381-387.
  10. Ezeilo J.O.C. (1974): Boundedness theorem for a Certain Third Order Differential Equations. Atti, Accad, Naz. Lincei, Rend Cl. Sci. Fix. Mat. Natur. 55: 194-209.
  11. Ezeilo J.O.C. (1975): Further Result for a System of Third Order Ordinary Differential Equations. Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur. 58: 143-153.
  12. Habets P., Metzen G. (1989): Existence of Periodic Solution of Duffing’s Equation. Journal of Differential Equations78: 1-32.
  13. Li Y., Li Y. (2014): Existence and Global Exponential Stability of Almost Periodic Solution for a Class of Delay Duffing Equation on Time Scale. Journal of Abstract and Applied Analysis, Hindawi Publishing Corporation, ID 857161.
  14. Lim Y.S., Kazda L.F. (1964): Boundedness of Solution for a Second Order Forced Oscillation With Non Linear Damping and Non Linear Resulting Force. Journal of Mathematical Analysis and Application 8: 423-444.
  15. Liu B., Zanolin F. (1998): Boundedness of Solution of Non Linear Differential Equations. Journal of Differential Equations 144: 66-98.
  16. Markus L. (1969): Lecture Notes in Differentiable Dynamics, Amer. Math. Soc., Providence R.I.
  17. Morris G. (1976): Bounds on Solution of Forced Conservative Oscillators. Bull. Austral. Math. Soc. 14: 71-93.
  18. Njoku F.I., Omari P. (2003): Stability properties of periodic solutions of a Duffing’s equation in the presence of a lower and upper solutions, Journal of Mathematics and Computer Application 135: 471-490.
  19. Osisiogu U.A., Eze E.O., Obasi U.E. (2016): Existence and Stability of Periodic Solution for a Class of Second order Nonlinear Differential Equations. Journal of the Nigerian Association of Mathematical Physics 36: 37-42.
  20. Oyesanya M.O. (2008): Duffing Oscillator as a model for predicting earthquake occurrence I, Journal of Nigerian Association of Mathematical Physics 12: 133-142.
  21. Pedro J.T. (2004): Existence and stability of periodic solutions of a Duffing’s Equation by using a new maximum principle, Mediterranean Journal of Mathematics 1: 470-486.
  22. Ressig R. (1972): Periodic Solution of Third Order Non-Linear Differential Equation. Ann. Mat. Pura Appl. 4 (92): 193-198.
  23. Ressig R. (1975): An Extension of Some Results Concerning the Generalized Lienard Equation, Ann. Mat. Pura Appl. 4 (105): 269-281.
  24. Ressig R., Sansone C., Conti R. (1974): Non-Linear Differential Equation of Higher Order Noordho International Publishing Leyden Reuter.
  25. Torres P. (2000): Existence and uniqueness of elliptic periodic solution of the Brillouin electron beam focusing system, Journal of Mathematics, Methods and Applied Sciences 23: 1139-1143.
  26. Torres P.J. (2003): Existence of one-signed periodic solution of some second order differential equations via a Krasnoselskii fixed point theorem, Journal of Differential Equations 190: 643-662.
  27. Voitovich M.V. (2011): Existence of Bounded Solution for a Class of Non Linear Fourth Order Equations. Differential Equations and Applications 3(2): 247-268.
  28. Zeeman E. (1976): Duffing Equation in Brain Modelling, Bull. IMA 12: 207-214.
DOI: https://doi.org/10.2478/bile-2023-0008 | Journal eISSN: 2199-577X | Journal ISSN: 1896-3811
Language: English
Page range: 109 - 124
Published on: Dec 29, 2023
Published by: Polish Biometric Society
In partnership with: Paradigm Publishing Services
Publication frequency: 2 times per year

© 2023 Everestus Obinwanne Eze, Uchenna Emmanuel Obasi, Godwin Ezugorie, Enyiduru Ekwomchi Hannah, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.