Existence result of solutions for a class of nonlinear differential systems

Document Type : Research Paper


Department of Mathematics, Faculty of Science, Ferhat Abbas University, Setif, Algeria


In this paper, we will discuss the existence of bounded positive solutions for a class of nonlinear  differential systems. The objective will be achieved by applying some results and techniques of  functional analysis such as Schauder's fixed point theorem and potential theory tools.


[1] M. A. Abdellaoui, Z. Dahmani and N. Bedjaoui, New existence results for a coupled system of nonlinear differential equations of arbitrary order, Int. J. Nonlinear Anal. Appl. 6 (2015) 65–75.
[2] R. P. Agarwal and D. O’Regan, Existence theory for single and multiple solutions to singular positone boundary value problems, J. Differential Equations 175 (2001) 393–414.
[3] R.P. Agarwal and D. O’Regan, Twin solutions to singular Dirichlet problems, J. Math. Anal. Appl. 240 (1999) 433–445.
[4] N. Akhmediev and A. Ankiewicz, Partially coherent solitons on a finite background, Phys. Rev. Lett. 82 (1999) 2661-2664.
[5] D.H. Armitage and S.J. Gardiner, Classical Potential Theory, Springer-Verlag London, 2001.
[6] S. Ben Othman, H. Maˆagli and N. Zeddini, On the existence of positive solutions of nonlinear differential equation, Int. J. Math. Sci. 2007 (2007) Article ID 58658, 12 pages.
[7] J. Damirchi and T. Rahimi, Differential transform method for a nonlinear system of differential equations arising in HIV infection of CD4 +T cell, Int. J. Nonlinear Anal. Appl. 7 (2016) 269–277.
[8] A. Ghanmi, H. Maagli, V. Radulescu and N. Zeddini, Large and bounded solutions for a class of nonlinear Schrodinger stationary systems, Anal. Appl. 7 (2009) 391–404.
[9] S. Gontara, Existence of bounded positive solutions of a nonlinear differential system, Electron. J. Diff. Eq. 2012 (2012) 1–9.
[10] R. Kannan and D. O’Regan, A note on singular boundary value problems with solutions in weighted spaces, Nonlinear Anal. 37 (1999) 791–796.
[11] A. V. Lair and A. W. Wood, Existence of entire large positive solutions of semilinear elliptic systems, J. Diff. Eq. 164 (2000) 380–394.
[12] H. Li and M. Wang, Existence and uniqueness of positive solutions to the boundary blow-up problem for an elliptic system, J. Diff. Eq. 234 (2007) 246–266.
[13] R. Ma, Existence of positive radial solutions for elliptic systems, J. Math. Anal. Appl. 201 (1996) 375–386.
[14] H. Maagli and N. Zeddini, Positive solutions for a singular nonlinear Dirichlet problem, Nonlinear Stud. 10 (2003) 295–306.
[15] H. Maagli, On the solution of a singular nonlinear periodic boundary value problem, Poten. Anal. 14 (2001) 437–447.
[16] H. Maagli and S. Masmoudi, Sur les solutions d’un operateur differentiel singulier semi-lineaire, Poten. Anal. 10 (1999) 289–304.
[17] S. Masmoudi and N. Yazidi, On the existence of positive solutions of a singular nonlinear differential equation, J. Math. Anal. Appl. 268 (2002) 53–66.
[18] C.R. Menyuk, Pulse propagation in an elliptically birefringent Kerr medium, IEEE J. Quantum Elec. 25 (1989) 2674–2682.
[19] Y. Peng and Y. Song, Existence of entire large positive solutions of a semilinear elliptic system, Appl. Math. Comput. 155 (2004) 687–698.
[20] S.D. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979) 897–904.
[21] J. Velin, A criterion for existence of a positive solution of a nonlinear elliptic system, Anal. Appl. (Singap.) 6 (2008) 299–321.
[22] X. Wang and A. W. Wood, Existence and nonexistence of entire positive solutions of semilinear elliptic systems, J. Math. Anal. Appl. 267 (2002) 361–368.
Volume 12, Issue 2
November 2021
Pages 1-10
  • Receive Date: 18 February 2019
  • Revise Date: 06 February 2020
  • Accept Date: 11 February 2020