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Articles

Infinitely many solutions for perturbed difference equations

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Pages 1055-1068 | Received 24 Oct 2013, Accepted 12 Jan 2014, Published online: 20 Feb 2014

References

  • R.P.Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker, New York, Basel, 2000.
  • R.P.Agarwal, D.O'Regan, and P.J.Y.Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic, Dordrecht, 1999.
  • R.P.Agarwal, K.Perera, and D.O'Regan, Multiple positive solutions of singular and nonsingular discrete problems via variational methods, Nonlinear Anal.58 (2004), pp. 69–73.
  • G.Bonanno and P.Candito, Infinitely many solutions for a class of discrete non-linear boundary value problems, Appl. Anal.884 (2009), pp. 605–616.
  • G.Bonanno and P.Candito, Nonlinear difference equations investigated via critical point methods, Nonlinear Anal. TMA.70 (2009), pp. 3180–3186.
  • G.Bonanno and G.Molica Bisci, Infnitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. Value Probl.2009 (2009), 20 pp.
  • A.Cabada, A.Iannizzotto, and S.Tersian, Multiple solutions for discrete boundary value problem, J. Math. Anal. Appl.356 (2009), pp. 418–428.
  • P.Candito and G.D'Aguì, Three solutions for a discrete nonlinear Neumann problem involving the p-Laplacian, Adv. Differ. Equ.2010 (2010), 11 pp., Art. ID 862016.
  • P.Candito and G.D'Aguì, Three solutions to a perturbed nonlinear discrete Dirichlet problem, J. Math. Anal. Appl.375 (2011), pp. 594–601.
  • P.Candito and N.Giovannelli, Multiple solutions for a discrete boundary value problem, Comput. Math. Appl.56 (2008), pp. 959–964.
  • J.Chu and D.Jiang, Eigenvalues and discrete boundary value problems for the one-dimensional p-Laplacian, J. Math. Anal. Appl.305 (2005), pp. 452–465.
  • J.Henderson and H.B.Thompson, Existence of multiple solutions for second order discrete boundary value problems, Comput. Math. Appl.43 (2002), pp. 1239–1248.
  • D.Jiang, J.Chu, D.O'Regan, and R.P.Agarwal, Positive solutions for continuous and discrete boundary value problems to the one-dimensional p-Laplacian, Math. Inequal. Appl.7 (2004), pp. 523–534.
  • L.Jiang and Z.Zhou, Three solutions to Dirichlet boundary value problems for p-Laplacian difference equations, Adv. Differ. Equ.2008 (2008), pp. 1–10.
  • W.G.Kelly and A.C.Peterson, Difference Equations: An Introduction with Applications, Academic Press, San Diego, New York, Basel, 1991.
  • A.Kristály, M.Mihailescu, and V.Rădulescu, Discrete boundary value problems involving oscillatory nonlinearities: Small and large solutions, J. Differ. Equ. Appl. (in press), 10.1080/10236190903555245.
  • A.Marano, G.Molica Bisci, and D.Motreanu, Multiple solutions for a class of elliptic hemivariational inequalities, J. Math. Anal. Appl.337 (2008), pp. 85–97.
  • M.Mihailescu, V.Rădulescu, and S.Tersian, Eigenvalue problems for anisotropic discrete boundary value problems, J. Differ. Equ. Appl.15 (2009), pp. 557–567.
  • G. Molica Bisci and D. Repovs, Nonlinear algebraic systems with discontinuous terms, J. Math. Anal. Appl. 398 (2013), pp. 846-856.
  • G. Molica Bisci and D. Repovs, On sequences of solutions for discrete anisotropic equations, Expo. Math. (in press).
  • B.Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math.113 (2000), pp. 401–410.
  • D.B.Wang and W.Guan, Three positive solutions of boundary value problems for p-Laplacian difference equations, Comput. Math. Appl.55 (2008), pp. 1943–1949.
  • P.J.Y.Wong and L.Xie, Three symmetric solutions of Lidstone boundary value problems for difference and partial difference equations, Comput. Math. Appl.45 (2003), pp. 1445–1460.
  • G.Zhang and Z.L.Yang, Positive solutions of a general discrete boundary value problem, J. Math. Anal. Appl.339 (2008), pp. 469–481.

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