Infinitely Many Solutions for Second-Order Impulsive Differential Inclusions with Relativistic Operator

• Shang, Suiming ^[1] ; Tian, Yu ^[2] ; Bai, ZhanBing ^[1] ; Yue, Yue ^[2]
  1. [1] Shandong University of Science and Technology

     Shandong University of Science and Technology

     China

     
  2. [2] Beijing University of Posts and Telecommunications

     Beijing University of Posts and Telecommunications

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
• Idioma: inglés
• DOI: 10.1007/s12346-021-00481-x
• Enlaces
  • Texto completo
• Resumen

  • In this paper, the boundary value problem of second-order impulsive differential inclusion involving relativistic operator is studied. Infinitely many nonnegative solutions are obtained by using non-smooth critical point theorem for locally Lipschitz functionals.

• Referencias bibliográficas
  • 1. Aubin, J.P., Lygeros, J., Quincampoix, M., Sastry, S.: Impulse differential inclusions: a viability approach to hybrid systems. IEEE Trans....
  • 2. Baskakov, A., Obukhovskii, V., Zecca, P.: Almost periodic solutions at infinity of differential equations and inclusions. J. Math. Anal....
  • 3. Bereanu, C., Jebelean, P., Mawhin, J.: Multiple solutions for Neumann and periodic problems with singular φ-Laplacian. J. Funct. Anal....
  • 4. Bonanno, G., Molica Bisci, G.: Infinitely many solutions for a boundary value problem with discontinuous nonlinearities. Bound. Value Probl....
  • 5. Breckner, B.E., Varga, C.: Infinitely many solutions for a class of systems of differential inclusions. Proc. Edinb. Math. Soc. 54(1),...
  • 6. Brezis, H., Mawhin, J.: Periodic solutions of the forced relativistic pendulum. Differ. Integral Equ. 23(9), 801–810 (2010)
  • 7. Hadjian, A., Heidarkhani, S.: Existence of one non-trivial anti-periodic solution for second-order impulsive differential inclusions. Math....
  • 8. Heidarkhani, S., Afrouzi, G.A., Hadjian, A., Henderson, J.: Existence of infinitely many anti-periodic solutions for second-order impulsive...
  • 9. Heidarkhani, S., Moradi, S., Caristi, G.: Variational approaches for a p-Laplacian boundary-value problem with impulsive effects. B. Iran....
  • 10. Jebelean, P., Mawhin, J., Serban, C.: Multiple periodic solutions for perturbed relativistic pendulum systems. Proc. Am. Math. Soc. 143(7),...
  • 11. Jebelean, P.,Mawhin, J., Serban, C.: Periodic solutions for discontinuous perturbations of the relativistic operator. B. Sci. Math. 140(1),...
  • 12. Kamenskii, M., Obukhovskii, V., Petrosyan, G., Yao, J.C.: Boundary value problems for semilinear differential inclusions of fractional...
  • 13. Kristly, A.: On singular elliptic equations involving oscillatory terms. Nonlinear Anal. 72, 1561–1569 (2010)
  • 14. Lannizzotto, A.: Three periodic solutions for an ordinary differential inclusion with two parameters. Ann. Pol. Math. 103(1), 89–100 (2012)
  • 15. Liang, J., Liu, J.H., Xiao, T.J., Xu, H.K.: Periodicity of solutions to the Cauchy problem for nonautonomous impulsive delay evolution...
  • 16. Liu, J., Zhao, Z.Q.: Multiple solutions for impulsive problems with non-autonomous perturbations. Appl. Math. Lett. 64, 143–149 (2017)
  • 17. Mahmudov, E.N.: Optimization of Mayer problem with Sturm-Liouville-type differential inclusions. J. Optim. Theory. Appl. 177(2), 345–375...
  • 18. Marano, S.A., Motreanu, D.: Infinitely many critical points of non-differentiable functions and applications to a Neumann-type problem...
  • 19. Mawhin, J.: Multiplicity of solutions of relativistic-type systems with periodic nonlinearities: a survey. Electron. J. Differ. Equ. 23,...
  • 20. Mawhin, J., Willem, M.: Critical Point Theory and Hamiltonian Systems. Springer, New York (1989)
  • 21. Shang, S.M., Bai, Z.B., Tian, Y., Yue, Y.: Periodic solution for second-order impulsive differential inclusions with relativistic operator....
  • 22. Tian, Y., Henderson, J.: Three anti-periodic solutions for second-order impulsive differential inclusions via nonsmooth critical point...
  • 23. Tian, Y., Nieto, J.J.: The applications of critical-point theory to discontinuous fractional-order differential equations. Proc. Edinb....
  • 24. Vijayakumar, V., Henriquez, H.R.: Existence of global solutions for a class of abstract second-order nonlocal Cauchy problem with impulsive...
  • 25. Xie, J.L., Luo, Z.G.: Solutions to a boundary value problem of a fourth-order impulsive differential equation. Bound. Value Probl. 1(154),...
  • 26. Yue, Y., Tian, Y., Bai, Z.B.: Infinitely many nonnegative solutions for a fractional differential inclusion with oscillatory potential....