Existence of Solutions for Two-Point Integral Boundary Value Problems with Impulses

• Svetlin G. Georgiev ^[1] ; Sanket Tikare ^[2] ; Vipin Kumar
  1. [1] Sorbonne University
  2. [2] Ramniranjan Jhunjhunwala College
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we investigate the existence of at least one solution and at least two nonnegative solutions of impulsive differential equations with the two-point integral boundary conditions. We employ the recent fixed point theorems for the sum of two operators on Banach spaces. The applicability of the results is illustrated through an example.

• Referencias bibliográficas
  • 1. Ashyralyev, A., Sharifov, Y.A.: Existence and uniqueness of solutions for nonlinear impulsive differential equations with two-point and...
  • 2. Bainov, D.D., Kostadinov, S.I.: Abstract impulsive differential equations. Descartes Press, Peterborough (1996)
  • 3. Bainov, D.D., Simeonov, P.: Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66. CRC Press, Boco Raton (1993)
  • 4. Benchohra, M., Henderson, J., Ntouyas, S.: Impulsive Differential Equations and Inclusions, vol. 2. Hindawi Publishing Corporation, New...
  • 5. Bolojan-Nica, O., Infante, G., Precup, R.: Existence results for systems with coupled nonlocal initial conditions. Nonlinear Anal. Theor....
  • 6. Ding, W., Xing, Y.: Existence of solutions to the first-order nonlinear boundary value problems. Taiwan. J. Math. 14(4), 1577–1589 (2010)
  • 7. Djebali, S., Mebarki, K.: Fixed point index theory for perturbation of expansive mappings by k-set contractions. Topol. Methods Nonlinear...
  • 8. Georgiev, S.G., Zennir, K.: Existence of solutions for a class of nonlinear impulsive wave equations. Ricerche di Matematica 71(1), 211–225...
  • 9. Granas, A., Dugundji, J.: Fixed Point Theory, vol. 14. Springer, Berlin (2003)
  • 10. Herlea, Diana-Raluca.: Existence and localization of positive solutions to first order differential systems with nonlocal conditions....
  • 11. Ilea, V., Novac, A., Otrocol, D., Precup, R.: Solutions with a prescribed interval of positivity for differential systems with nonlocal...
  • 12. Koumla, S., Precup, R.: Integrodifferential evolution systems with nonlocal initial conditions. Stud. Univ. Babes-Bolyai Math. 65, 93–108...
  • 13. Lakshmikantham, V., Bainov, D., Simeonov, P.S.: Theory of Impulsive Differential Equations, vol. 6. World scientific, Singapore (1989)
  • 14. Liu, X., Zhang, K.: Impulsive Systems on Hybrid Time Domains. Springer, Berlin (2019)
  • 15. Mardanov, M.J., Sharifov, Y.A.: Existence results for first order nonlinear impulsive differential equations with nonlocal boundary conditions....
  • 16. Mardanov, M.J., Sharifov, Y.A., Molaei, H.H.: Existence and uniqueness of solutions for first-order nonlinear differential equations with...
  • 17. Mouhous, A., Georgiev, S.G., Mebarki, K.: Existence of solutions for a class of first order boundary value problems. Archivum Mathematicum...
  • 18. Nica, O., Precup, R.: On the nonlocal initial value problem for first order differential systems. Stud. Univ. Babes-Bolyai Math. 56(3),...
  • 19. Pulkina, L.S.: Nonlocal problems for hyperbolic equations with degenerate integral conditions. Electron. J. Differ. Equ. 2016(193), 1–12...
  • 20. Rudd, M., Tisdell, C.C.: On the solvability of two-point, second-order boundary value problems. Appl. Math. Lett. 20(7), 824–828 (2007)
  • 21. Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)
  • 22. Stamov, G.T.: Almost Periodic Solutions of Impulsive Differential Equations, vol. 2047. Springer, Berlin (2012)
  • 23. Stamova, I., Stamov, G.T.: Applied Impulsive Mathematical Models, vol. 318. Springer, Berlin (2016)
  • 24. Tisdell, C.C.: On the solvability of nonlinear first-order boundary-value problems. Electron. J. Differ. Equ. 2006(80), 1–8 (2006)