Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales

Bouchelaghem, Faycal; Ardjouni, Abdelouaheb; Djoudi, Ahcene

doi:10.2478/mjpaa-2021-0003

Abstract

In this article we study the existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales. The main tool employed here is Schauder’s fixed point theorem. The results obtained here extend the work of Culakova, Hanustiakova and Olach [12]. Two examples are also given to illustrate this work.

References

[1] M. Adivar and Y. N. Raffoul, Existence of periodic solutions in totally nonlinear delay dynamic equations, Electronic Journal of Qualitative Theory of Differential Equations 2009(1) (2009), 1–20.10.14232/ejqtde.2009.4.1
Search in Google Scholar Back to article
[2] A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale, Malaya Journal of Matematik 2(1) (2013), 60–67.
Search in Google Scholar Back to article
[3] A. Ardjouni, A. Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with functional delay on a time scale, Acta Univ. Palacki. Olomnc., Fac. rer. nat., Mathematica 52(1) (2013), 5–19.10.26637/mjm102/008
Search in Google Scholar Back to article
[4] A. Ardjouni, A. Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale, Commun Nonlinear Sci Numer Simulat 17 (2012), 3061–3069.10.1016/j.cnsns.2011.11.026
Search in Google Scholar Back to article
[5] A. Ardjouni, A. Djoudi, Periodic solutions in totally nonlinear dynamic equations with functional delay on a time scale, Rend. Sem. Mat. Univ. Politec. Torino Vol. 68, 4(2010), 349-359.
Search in Google Scholar Back to article
[6] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkh¨auser, Boston, 2001.10.1007/978-1-4612-0201-1
Search in Google Scholar Back to article
[7] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäauser, Boston, 2003.10.1007/978-0-8176-8230-9
Search in Google Scholar Back to article
[8] F. Bouchelaghem, A. Ardjouni, A. Djoudi, Existence and exponential stability of positive periodic solutions for second-order dynamic equations, Ural Math. J. 6(1) (2020), 42–53.10.15826/umj.2020.1.004
Search in Google Scholar Back to article
[9] F. Bouchelaghem, A. Ardjouni, A. Djoudi, Existence and stability of positive periodic solutions for delay nonlinear dynamic equations, Nonlinear Studies 25(1) (2018), 191–202.
Search in Google Scholar Back to article
[10] F. Bouchelaghem, A. Ardjouni, A. Djoudi, Existence of positive solutions of delay dynamic equations, Positivity 21(4) (2017), 1483–1493.10.1007/s11117-017-0480-2
Search in Google Scholar Back to article
[11] F. Bouchelaghem, A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for delay dynamic equations, Proyecciones (Antofagasta) 36(3) (2017), 449–460.10.4067/S0716-09172017000300449
Search in Google Scholar Back to article
[12] I. Culakova, L. Hanustiakova, R. Olach, Existence for positive solutions of second-ordre neutral nonlinear differential equations, Applied Mathematics Letters 22 (2009), 1007–1010.10.1016/j.aml.2009.01.009
Search in Google Scholar Back to article
[13] M. Gouasmia, A. Ardjouni, A. Djoudi, Periodic and nonnegative periodic solutions of nonlinear neutral dynamic equations on a time scale, International Journal of Analysis and Applications 16(2) (2018), 162–177.
Search in Google Scholar Back to article
[14] S. Hilger, Ein Masskettenkalkül mit Anwendung auf Zentrumsmanningfaltigkeiten. PhD thesis, Universit¨at Würzburg, 1988.
Search in Google Scholar Back to article
[15] V. Lakshmikantham, S. Sivasundaram, B. Kaymarkcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996.10.1007/978-1-4757-2449-3
Search in Google Scholar Back to article
[16] D. R. Smart, Fixed Points Theorems, Cambridge Univ. Press, Cambridge, UK, 1980.
Search in Google Scholar Back to article

Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales

Abstract

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