Nehari-type Oscillation Theorems for Second Order Functional Dynamic Equations

• Autores: Taher S. Hassan, E.M. Elabbasy, Remi-Ahmad El-Nabulsi, Rabie A. Ramadan, H. Saber, A.E. Matouk, Ismoil Odinaev
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper is devoted to studying the half-linear functional dynamic equations of second-order on an unbounded above time scale T. We present some Nehari-type oscillation criteria for a class of second-order dynamic equations. The obtained results show that there is a substantial improvement in the literature on second-order dynamic equations. We include some examples illustrating the significance of our results.

• Referencias bibliográficas
  • 1. Agarwal, R.P., Bohner, M., O’Regan, D., Peterson, A.: Dynamic equations on time scales: A survey. J. Comput. Appl. Math. 141, 1–26 (2002)
  • 2. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: Oscillation criteria for second-order dynamic equations on time scales. Appl. Math. Lett....
  • 3. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: Hille and Nehari type criteria for third order delay dynamic equations. J. Differ. Equ. Appl....
  • 4. Agarwal, R.P., Bohner, M., Li, T.: Oscillatory behavior of second-order half-linear damped dynamic equations. Appl. Math. Comput. 254,...
  • 5. Baculikova, B.: Oscillation of second-order nonlinear noncanonical differential equations with deviating argument. Appl. Math. Lett. 91,...
  • 6. Bazighifan, O., El-Nabulsi, E.M.: Different techniques for studying oscillatory behavior of solution of differential equations. Rocky Mountain...
  • 7. Bohner, M., Li, T.: Oscillation of second-order p−Laplace dynamic equations with a nonpositive neutral coefficient. Appl. Math. Lett. 37,...
  • 8. Bohner, M., Li, T.: Kamenev-type criteria for nonlinear damped dynamic equations. Sci. China Math. 58(7), 1445–1452 (2015)
  • 9. Bohner, M., Peterson, A.: Dynamic equations on time scales: an introduction with applications. Birkhäuser, Boston (2001)
  • 10. Bohner, M., Peterson, A.: Advances in dynamic equations on time scales. Birkhäuser, Boston (2003)
  • 11. Bohner, M., Hassan, T.S.: Oscillation and boundedness of solutions to first and second order forced functional dynamic equations with...
  • 12. Bohner,M., Hassan, T.S., Li, T.: Fite-Hille-Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating...
  • 13. Chatzarakis, G.E., Moaaz, O., Li, T., Qaraad, B.: Oscillation theorems for nonlinear second-order differential equations with an advanced...
  • 14. Džurina, J., Jadlovská, I.: A sharp oscillation result for second-order half-linear noncanonical delay differential equations. Electron....
  • 15. Džurina, J., Jadlovská, I.: A note on oscillation of second-order delay differential equations. Appl. Math. Lett. 69, 126–132 (2017)
  • 16. Elabbasy, E.M., El-Nabulsi, R.A., Moaaz, O., Bazighifan, O.: Oscillatory properties of solutions of even order differential equations....
  • 17. Erbe, L.: Oscillation criteria for second order nonlinear delay equations. Canad. Math. Bull. 16, 49–56 (1973)
  • 18. Erbe, L., Hassan, T.S., Peterson, A.: Oscillation criteria for second order sublinear dynamic equations with damping term. J. Differ....
  • 19. Erbe, L., Hassan, T.S.: New oscillation criteria for second order sublinear dynamic equations. Dynam. Syst. Appl. 22, 49–63 (2013)
  • 20. Erbe, L., Hassan, T.S., Peterson, A., Saker, S.H.: Oscillation criteria for half-linear delay dynamic equations on time scales. Nonlinear...
  • 21. Erbe, L., Hassan, T.S., Peterson, A., Saker, S.H.: Oscillation criteria for sublinear half-linear delay dynamic equations on time scales....
  • 22. Erbe, L., Peterson, A., Saker, S.H.: Hille and Nehari type criteria for third order dynamic equations. J. Math. Anal. Appl. 329, 112–131...
  • 23. Frassu, S., Viglialoro, G.: Boundedness in a chemotaxis system with consumed chemoattractant and produced chemorepellent. Nonlinear Anal....
  • 24. Grace, S.R., Bohner, M., Agarwal, R.P.: On the oscillation of second-order half-linear dynamic equations. J. Differ. Equ. Appl. 15, 451–460...
  • 25. Hilger, S.: Analysis on measure chains – a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)
  • 26. Hille, E.: Non-oscillation theorems. Trans. Amer. Math. Soc. 64, 234–252 (1948)
  • 27. Kac, V.; Chueng, P. Quantum Calculus; Universitext, 2002
  • 28. Leighton, W.: The detection of the oscillation of solutions of asecond order linear differential equation. Duke J. Math. 17, 57–62 (1950)
  • 29. Li, T., Pintus, N., Viglialoro, G.: Properties of solutions to porous medium problems with different sources and boundary conditions....
  • 30. Li, T., Viglialoro, G.: Boundedness for a nonlocal reaction chemotaxis model even in the attractiondominated regime. Differ. Integral...
  • 31. Karpuz, B.: Hille-Nehari theorems for dynamic equations with a time scale independent critical constant. Appl. Math. Comput. 346, 336–351...
  • 32. Nehari, Z.: Oscillation criteria for second-order linear differential equations. Trans. Amer. Math. Soc. 85, 428–445 (1957)
  • 33. Rehak, P.: New results on critical oscillation constants depending on a graininess. Dynam. Syst. Appl. ˇ 19, 271–288 (2010)
  • 34. Sun, S., Han, Z., Zhao, P., Zhang, C.: Oscillation for a class of second-order Emden-Fowler delay dynamic equations on time scales. Adv....
  • 35. Sun, Y., Hassan, T.S.: Oscillation criteria for functional dynamic equations with nonlinearities given by Riemann-Stieltjes integral....
  • 36. Wong, J.S.: Second order oscillation with retarded arguments, In: Ordinary differential equations, 581–596; Washington, 1971. Academic...
  • 37. Zhang, C., Agarwal, R.P., Bohner, M., Li, T.: Oscillation of second-order nonlinear neutral dynamic equations with noncanonical operators....
  • 38. Zhang, Q., Gao, L., Wang, L.: Oscillation of second-order nonlinear delay dynamic equations on time scales. Comput. Math. Appl. 61, 2342–2348...
  • 39. Erbe, L., Higgins, R.: Some Oscillation Results for Second Order Functional Dynamic Equations1. Adv. Dyn. Syst. Appl. 3, 73–88 (2008)