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Research Article

Existence of infinitely many solutions for a class of difference equations with boundary value conditions involving p(k)-Laplacian operator

| (Reviewing Editor)
Article: 1428030 | Received 21 Aug 2017, Accepted 06 Jan 2018, Published online: 19 Feb 2018

References

  • Avci, M. (2016). Existence results for anisotropic discrete boundary value problems. Electronic Journal of Differential Equations, 2016, 1–11.
  • Avci, M., & Pankov, A. (2015). Nontrivial solutions of discrete nonlinear equations with variable exponent. Journal of Mathematical Analysis and Applications, 431, 22–33.
  • Agarwal, R. P., Perera, K., & O’Regan, D. (2005). Multiple positive solutions of singular discrete p-Laplacian problems via variational methods. Advances in Difference Equations, 2005, 93–99.
  • Bonanno, G. (2012). Critical point theorem via the Ekeland variational principle. Nonlinear Analysis: Theory, Methods \ & Applications, 75, 2992–3007.
  • Bonanno, G., & Candito, P. (2009). Infinitely many solutions for a class of discrete non-linear boundary value problems. Journal of Applied Analysis, 884, 605–616.
  • Bonanno, G., Candito, P., & DAgu‘i, G. (2014). Variational methods on finite dimensional Banach spaces and discrete problems. Advanced Nonlinear Studies, 14, 915–939.
  • Bonanno, G., & Molica Bisci, G. (2009). Infnitely many solutions for a boundary value problem with discontinuous nonlinearities. Boundary Value Problems, 2009, 20.
  • Candito, P., & D’Aguì, G. (2010). Three solutions for a discrete nonlinear Neumann problem involving the -Laplacian. Advances in Difference Equations, 11, Article ID 862016.
  • Candito, P., & Giovannelli, N. (2008). Multiple solutions for a discrete boundary value problem. Computers \ & Mathematics with Applications, 56, 959–964.
  • Chu, J., & Jiang, D. (2005). Eigenvalues and discrete boundary value problems for the one-dimensional-Laplacian. Journal of Mathematical Analysis and Applications, 305, 452–465.
  • Henderson, J., & Thompson, H. B. (2002). Existence of multiple solutions for second order discrete boundary value problems. Computers \ & Mathematics with Applications, 43, 1239–1248.
  • Jiang, L., & Zhou, Z. (2008). Three solutions to Dirichlet boundary value problems for p-Laplacian difference equations. Advances in Difference Equations, 2008, 1–10.
  • Khaleghi Moghadam, M., & Avci, M. (2017). Existence results to a nonlinear p(k)-Laplacian difference equation. Journal of Difference Equations and Applications, 23, 1652–1669.
  • Khaleghi Moghadam, M., Heidarkhani, S., & Henderson, J. (2014). Infinitely many solutions for perturbed difference equations. Journal of Difference Equations and Applications, 207, 1055–1068.
  • Khaleghi Moghadam, M., & Henderson, J. (2017). Triple solutions for a dirichlet boundary value problem involving a perturbed discrete p(k)-Laplacian operator. Open Mathematics Journal, 15, 1075–1089.
  • Khaleghi Moghadam, M., Li, L., & Tersian, S. (2018). Existence of three solutions for a discrete anisotropic boundary value problem. Bulletin of the Iranian Mathematical Society, to appear.
  • Liu, Y. & Ge, W. (2003). Twin positive solutions of boundary value problems for finite difference equations with -Laplacian operator. Journal of Mathematical Analysis and Applications, 278, 551–561.
  • Ricceri, B. (2000). A general variational principle and some of its applications. Journal of Computational and Applied Mathematics, 113, 401–410.
  • Salari, A., Caristi, G., Barilla, D., & Puglisi, A. (2000) A variational approach to perturbed discrete anisotropic equations. Abstract and Applied Analysis, 2016, 12. Article ID 5676138.