On subharmonic solutions for second order difference equations with relativistic operator

  • Adel Daouas Higher school of sciences and technology, Hammam Sousse, 4011, Hammam Sousse
  • Ameni Guefrej https://orcid.org/0000-0001-9609-7545

Resumo

The purpose of this paper is to investigate the existence of subharmonic solutions of second-order difference equations with relativistic operator. Our approach is variational and based on the use of the critical point theory for convex, lower semi-continuous perturbations of C$^1$-functionals due to A. Szulkin.

Downloads

Não há dados estatísticos.

Referências

Balanov, Z., Garcıa-Azpeitia, C. , Krawcewicz, W, On variational and topological methods in nonlinear difference equations, Communications on pure and applied analysis, Vol. 17, Number 6 ( 2018).

Bereanu, C., Jebelean, P., Mawhin, J., Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities, Calc. Var. Partial Differential Equations 46 (2013), no. 1-2, 113-122.

Bereanu, C., Jebelean, P., Mawhin, J., Variational methods for nonlinear perturbations of singular ϕ-Laplacians, Rendiconti Lincei Matematica e Applicazioni 22 (2011), no. 1, 89-111.

Chang, K. C.: Variational methods for non-differentiable functionals and their applications to partial differential equations, Journal of Mathematical Analysis and Applications, 80(1) (1981), 102-129.

Coelho, I., Corsato, C., Obersnel, F., Omari, P., Positive solutions of the Dirichlet problem for the one dimensional Minkowski-curvature equation, Advances Nonlinear Studies 12 (2012), 621-638.

Coelho, I., Corsato, C., Rivetti, S., Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball, Topological Methods in Nonlinear Analysis, 44(1), pp.23-39 (2014).

Guo, Z. and Yu, J., The existence of periodic and subharmonic solutions of subquadratic second order difference equations, J. London Math. Soc., vol. 68, no. 2(2003), 419-430.

Jebelean, P., Mawhin, J., S¸erban, C., Multiple periodic solutions for perturbed relativistic pendulum systems, Proc. Am. Math. Soc., 143, no. 7 (2015), 3029-3039.

Jebelean, P., Serban, C., Fisher-Kolmogorov type perturbations of the relativistic operator: Differential vs. Difference, Proc. Am. Math. Soc., 146 (2018), 2005-2014.

Kelley, W.G., Peterson, A.C., Difference Equations. An Introduction with Applications, 2nd edn. Elsevier, Amsterdam (2001).

Mawhin, J., A simple proof of multiplicity for periodic solutions of Lagrangian difference systems with relativistic operator and periodic potential, J. Difference Equ. Appl. 22 (2016), no. 2, 306-315.

Mawhin, J., Periodic solutions of second order nonlinear difference systems with ϕ-Laplacian: a variational approach, Nonlinear Anal. 75 (2012), no. 12, 4672-4687.

Merdivenci Atici, F., Guseinov, G. Sh., Positive periodic solutions for nonlinear difference equations with periodic coefficients, J.Math. Anal. 232 (1999) 166-182.

Szulkin, A., Minmax principales for lower semicontinuous functions and applications to nonlinear boundary value problems (English, with French summary), Ann. Inst. H.Poincare Anal. Non Lineaire 3 (1986), no. 2, 77-109. MR837231.

Publicado
2025-08-10
Seção
Artigos