Positive Periodic Solutions for a First Order Singular Ordinary Differential Equation Generated by Impulses

Referencias bibliográficas

• 1. Agarwal, R.P., Franco, D., O’Regan, D.: Singular boundary value problems for first and second order impulsive differential equations. Aequ. Math. 69(1–2), 83–96 (2005). https://doi.org/10.1007/s00010-004-2735-9
• 2. Agarwal, R.P., O’Regan, D.: Existence criteria for singular boundary value problems with sign changing nonlinearities. J. Differ. Equ. 183(2), 409–433 (2002). https://doi.org/10.1006/jdeq.2001.4127
• 3. Agarwal, R.P., O’Regan, D.: Singular Differential and Integral Equations with Applications. Kluwer Academic Publishers, Dordrecht (2003). https://doi.org/10.1007/978-94-017-3004-4
• 4. Agarwal, R.P., Perera, K., O’Regan, D.: Multiple positive solutions of singular problems by variational methods. Proc. Am. Math. Soc. 134(3), 817–824 (2006). https://doi.org/10.1090/S0002-9939-05-07992-X
• 5. Ambrosetti, A., Coti Zelati, Periodic Solutions of Singular Lagrangian Systems. Birkhäuser, Boston Inc., Boston (1993). https://doi.org/10.1007/978-1-4612-0319-3
• 6. Bai, L., Nieto, J.J.: Variational approach to differential equations with not instantaneous impulses. Appl. Math. Lett. 73, 44–48 (2017). https://doi.org/10.1016/j.aml.2017.02.019
• 7. Bainov, D., Simeonov, P.: Impulsive Differential Equations: Periodic Solutions and Applications. Longman, Harlow (1993)
• 8. Bonanno, G., Rodríguez-López, R., Tersian, S.: Existence of solutions to boundary value problem for impulsive fractional differential equations. Fract. Calc. Appl. Anal. 17(3), 717–744 (2014). https://doi. org/10.2478/s13540-014-0196-y
• 9. Chen, X., Du, Z.: Existence of positive periodic solutions for a neutral delay predator-prey model with hassell-varley type functional response and impulse. Qual. Theory Dyn. Syst. (2017). https://doi.org/ 10.1007/s12346-017-0223-6
• 10. Chu, J., Nieto, J.J.: Impulsive periodic solutions of first-order singular differential equations. Bull. Lond. Math. Soc. 40(1), 143–150 (2008). https://doi.org/10.1112/blms/bdm110
• 11. Chu, J., Torres, P.J., Zhang, M.: Periodic solutions of second order non-autonomous singular dynamical systems. J. Differ. Equ. 239(1), 196–212 (2007). https://doi.org/10.1016/j.jde.2007.05.007
• 12. Dai, B., Bao, L.: Positive periodic solutions generated by impulses for the delay Nicholson’s blowflies model. Electron. J. Qual. Theory Differ. Equ. (2016). https://doi.org/10.14232/ejqtde.2016.1.4 (pp. Paper No. 4, 11)
• 13. Dong, L., Takeuchi, Y.: Impulsive control of multiple Lotka–Volterra systems. Nonlinear Anal. Real World Appl. 14(2), 1144–1154 (2013). https://doi.org/10.1016/j.nonrwa.2012.09.006
• 14. Gaines, R.E., Mawhin, J.L.: Coincidence Degree and Nonlinear Differential Equations. Springer, Berlin (1977). https://doi.org/10.1007/BFb0089537
• 15. Kong, F., Luo, Z.: Positive periodic solutions for a kind of first-order singular differential equation induced by impulses. Qual. Theory Dyn. Syst. (2017). https://doi.org/10.1007/s12346-017-0239-y
• 16. Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations, vol. 6. World Scientific, Singapore (1989). https://doi.org/10.1142/0906
• 17. Nie, L.F., Teng, Z.D., Nieto, J.J., Jung, I.H.: State impulsive control strategies for a two-languages competitive model with bilingualism and interlinguistic similarity. Physica A 430, 136–147 (2015). https://doi.org/10.1016/j.physa.2015.02.064
• 18. Nieto, J.J., O’Regan, D.: Variational approach to impulsive differential equations. Nonlinear Anal. Real World Appl. 10(2), 680–690 (2009). https://doi.org/10.1016/j.nonrwa.2007.10.022
• 19. Perestyuk, N.A., Plotnikov, V.A., Samoilenko, A.M., Skripnik, N.V.: Differential Equations with Impulse Effects. Walter de Gruyter & Co, Berlin (2011). https://doi.org/10.1515/9783110218176
• 20. Rach ˚unková, I., Stanˇek, S., Tvrdý, M.: Solvability of Nonlinear Singular Problems for Ordinary Differential Equations. Hindawi Publishing Corporation, New York (2008)
• 21. Rach ˚unková, I., Tomeˇcek, J.: State-Dependent Impulses. Atlantis Press, Paris (2015). https://doi.org/ 10.2991/978-94-6239-127-7
• 22. Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equation. World Scientific Series on Nonlinear Science, vol. 14. World Scientific Publishing Co., Inc., River Edge (1995). https://doi.org/10. 1142/9789812798664
• 23. Stamova, I., Stamov, G.: Applied Impulsive Mathematical Models. Springer, Cham (2016). https://doi. org/10.1007/978-3-319-28061-5
• 24. Stamova, I.M., Stamov, G.T.: Functional and Impulsive Differential Equations of Fractional Order: Qualitative Analysis and Applications. CRC Press, Boca Raton (2017)
• 25. Sun, J., Chu, J., Chen, H.: Periodic solution generated by impulses for singular differential equations. J. Math. Anal. Appl. 404(2), 562–569 (2013). https://doi.org/10.1016/j.jmaa.2013.03.036
• 26. Tian, Y., Ge, W.: Applications of variational methods to boundary-value problem for impulsive differential equations. Proc. Edinb. Math. Soc. (2) 51(2), 509–527 (2008). https://doi.org/10.1017/ S0013091506001532
• 27. Zavalishchin, S.T., Sesekin, A.N.: Dynamic Impulse Systems. Kluwer Academic Publishers Group, Dordrecht (1997). https://doi.org/10.1007/978-94-015-8893-5
• 28. Zhou, H., Wang, W., Yang, L.: Permanence and stability of solutions for almost periodic prey-predator model with impulsive effects. Qual. Theory Dyn. Syst. (2017). https://doi.org/10.1007/s12346-017-0247-y