Positive Periodic Solutions for a Kind of First-Order Singular Differential Equation Induced by Impulses

• Kong, Fanchao ^[1] ; Luo, Zhiguo ^[1]
  1. [1] Hunan Normal University

     Hunan Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 2, 2018, págs. 375-386
• Idioma: inglés
• DOI: 10.1007/s12346-017-0239-y
• Enlaces
  • Texto completo
• Resumen

  • By using the continuation theorem due to Mawhin and Gaines, the sufficient conditions ensuring the existence of positive periodic solutions for a kind of first-order singular differential equation induced by impulses. Some recent results in the literature are improved.

• Referencias bibliográficas
  • 1. Agarwal, R.P., Franco, D., O’Regan, D.: Singular boundary value problems for first and second order impulsive differential equations. Aequ....
  • 2. Benchohra, M., Henderson, J., Ntouyas, S.K.: Impulsive Differential Equations and Inclusions, vol. 2. Hindawi Publishing Corporation, New...
  • 3. Bai, L., Dai, B.X.: Three solutions for a p-Laplacian boundary value problem with impulsive effects. Appl. Math. Comput. 217, 9895–9904...
  • 4. Chen, L., Sun, J.: Nonlinear boundary value problem for first order impulsive functional differential equations. J. Math. Anal. Appl. 318,...
  • 5. Chen, L., Tisdell, C.C., Yuan, R.: On the solvability of periodic boundary value problems with impulse. J. Math. Anal. Appl. 331, 233–244...
  • 6. Chen, P., Tang, X.H.: Existence of solutions for a class of second-order p-Laplacian systems with impulsive effectes. Appl. Math. 59, 543–570...
  • 7. Forbat, F., Huaux, A.: Détermination approchée et stabilité locale de la solution périodique d’une équation différentielle non linéaire,...
  • 8. Gaines, R., Mawhin, J.: Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in Math. Springer, Berlin (1977)
  • 9. Huaux, A.: Sur L’existence d’une solution périodique de l’e quation différentielle non linéaire x¨ + (0, 2)x˙ + x 1−x = (0,...
  • 10. Kelevedjiev, P.: Existence of solutions to first-order singular and nonsingular initial value problems. Electron. J. Differ. Eqn. 151,...
  • 11. Kelevedjiev, P., Tersian, S.: Singular and nonsingular first-order initial value problems. J. Math. Anal. Appl. 366(2), 516–524 (2010)
  • 12. Kiguradze, I., Sokhadze, Z.: Positive solutions of periodic type boundary value problems for first order singular functional differential...
  • 13. Kong, F.C., Lu, S.P., Luo, Z.G.: Positive periodic solutions for singular higher order delay differential equations. Results Math (2017)....
  • 14. Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
  • 15. Liu, Y.J.: Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations....
  • 16. Luo, Z.G., Nieto, J.J.: New results for the periodic boundary value problem for impulsive integrodifferential equations. Nonlinear Anal....
  • 17. Luo, Z.G., Shen, J.H.: Stability of impulsive functional differential equations via the Liapunov functional. Appl. Math. Lett. 22, 163–169...
  • 18. Luo, Z.G., Jing, Z.J.: Periodic boundary value problem for first-order impulsive functional differential equations. Comput. Math. Appl....
  • 19. Lu, S.P., Kong, F.C.: Periodic solutions for a kind of prescribed mean curvature Linard equation with a singularity and a deviating argument....
  • 20. Lu, S.P., Zhong, T., Gao, Y.J.: Periodic solutions of p-Laplacian equations with singularities. Adv. Differ. Equ. 146, 1–12 (2016)
  • 21. Lu, S.P., Zhong, T., Chen, L.J.: Periodic solutions for p-Laplacian Rayleigh equations with singularities. Bound. Value Probl. 96, 1–12...
  • 22. Mawhin, J.: Topological degree and boundary value problems for nonlinear differential equations, In: Furi, M., Zecca, P. (eds.) Topologic...
  • 23. Murty, M., Rao, B., Kumar, G.: Three-point boundary value problems for singular system of first order differential equations. Filomat...
  • 24. Nieto, J.J., O’Regan, D.: Variational approach to impulsive differential equations. Nonlinear Anal. Real World Appl. 10, 680–690 (2009)
  • 25. Pishkenari, H., Behzad, M., Meghdari, A.: Nonlinear dynamic analysis of atomic force microscopy under deterministic and random excitation....
  • 26. Qian, D., Li, X.: Periodic solutions for ordinary differential equations with sublinear impulsive effects. J. Math. Anal. Appl. 303, 288–303...
  • 27. Rützel, S., Lee, S., Raman, A.: Nonlinear dynamics of atomic-force-microscope probes driven in Lénard-Jones potentials. Proc. R. Soc....
  • 28. Rachunkovâ, I., Tvrdý, M.: Existence results for impulsive second-order periodic problems. Nonlinear Anal. 59, 133–146 (2004)
  • 29. Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)
  • 30. Tian, Y., Ge, W.G.: Variational methods to SturmCLiouville boundary value problem for impulsive differential equations. Nonlinear Anal....
  • 31. Yang, G., Lu, J., Luo, A.: On the computation of Lyapunov exponents for forced vibration of a LennardJones oscillator. Chaos Solitons...
  • 32. Yang, X.X., Shen, J.H.: Nonlinear boundary value problems for first order impulsive functional differential equations. Appl. Math. Comput....
  • 33. Zavalishchin, S.T., Sesekin, A.N.: Dynamic Impulse Systems: Theory and Applications. Kluwer Academic Publishers, Norwell (1997)
  • 34. Zhang, X., Sun, J.: The existence of positive solution for singular boundary value problems of first order differential equation on unbounded...