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Existence of three solutions for perturbed nonlinear difference equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Using critical point theory, we study the existence of at least three solutions for perturbed nonlinear difference equations with discrete boundary-value condition depending on two positive parameters.
Rocznik
Strony
747--761
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
  • Razi University Faculty of Sciences Department of Mathematics 67149 Kermanshah, Iran
  • Agricultural and Natural Source University Department of Basic Science Sari, Iran
Bibliografia
  • [1] R.P. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker, New York, Basel, 2000.
  • [2] R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic, Dordrecht, 1999.
  • [3] R.P. Agarwal, K. Perera, D. O’Regan, Multiple positive solutions of singular and nonsingular discrete problems via variational methods, Nonlinear Anal. TMA 58 (2004), 69–73.
  • [4] G. Bonanno, P. Candito, Infinitely many solutions for a class of discrete nonlinear boundary value problems, Appl. Anal. 884 (2009), 605–616.
  • [5] G. Bonanno, P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differ. Eqs 244 (2008), 3031–3059.
  • [6] G. Bonanno, P. Candito, Nonlinear difference equations investigated via critical point methods, Nonlinear Anal. TMA 70 (2009), 3180–3186.
  • [7] G. Bonanno, S.A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal. 89 (2010), 1–10.
  • [8] A. Cabada, A. Iannizzotto, S. Tersian, Multiple solutions for discrete boundary value problem, J. Math. Anal. Appl. 356 (2009), 418–428.
  • [9] P. Candito, G. D’Aguì, Three solutions for a discrete nonlinear Neumann problem involving the p-Laplacian, Adv. Difference Equ. 2010, Art. ID 862016, 11 pp.
  • [10] P. Candito, G. D’Aguì, Three solutions to a perturbed nonlinear discrete Dirichlet problem, J. Math. Anal. Appl. 375 (2011), 594–601.
  • [11] P. Candito, N. Giovannelli, Multiple solutions for a discrete boundary value problem, Comput. Math. Appl. 56 (2008), 959–964.
  • [12] J. Chu, D. Jiang, Eigenvalues and discrete boundary value problems for the one-dimensional p-Laplacian, J. Math. Anal. Appl. 305 (2005), 452–465.
  • [13] M. Galewski, S. Głab, On the discrete boundary value problem for anisotropic equation, J. Math. Anal. Appl. 386 (2012), 956–965.
  • [14] J. Henderson, H.B. Thompson, Existence of multiple solutions for second order discrete boundary value problems, Comput. Math. Appl. 43 (2002), 1239–1248.
  • [15] D. Jiang, J. Chu, D. O’Regan, R.P. Agarwal, Positive solutions for continuous and discrete boundary value problems to the one-dimensional p-Laplacian, Math. Inequal. Appl. 7 (2004), 523–534.
  • [16] L. Jiang, Z. Zhou, Three solutions to Dirichlet boundary value problems for p-Laplacian difference equations, Adv. Diff. Equ. 2008 (2008), 1–10.
  • [17] W.G. Kelly, A.C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, San Diego, New York, Basel, 1991.
  • [18] A. Kristály, M. Mihailescu, V. Radulescu, Discrete boundary value problems involving oscillatory nonlinearities: small and large solutions, J. Difference Equ. Appl.,doi:10.1080/10236190903555245 (to appear).
  • [19] N. Marcu, G. Molica Bisci, Existence and multiplicity results for nonlinear discrete inclusions, Electron. J. Differential Equations 2012 (2012), 1–13.
  • [20] M. Mihailescu, V. Radulescu, S. Tersian, Eigenvalue problems for anisotropic discrete boundary value problems, J. Difference Equ. Appl. 15 (2009), 557–567.
  • [21] G. Molica Bisci, D. Repovs, Nonlinear algebraic systems with discontinuous terms, J. Math. Anal. Appl. 398 (2013), 846–856.
  • [22] G. Molica Bisci, D. Repovs, On sequences of solutions for discrete anisotropic equations, Expositiones Mathematicae (to appear).
  • [23] G. Molica Bisci, D. Repovs, On some variational algebraic problems, Adv. Nonlinear Analysis 2 (2013), 127–146.
  • [24] B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. TMA 70 (2009), 3084–3089.
  • [25] D.B. Wang, W. Guan, Three positive solutions of boundary value problems for p-Laplacian difference equations, Comput. Math. Appl. 55 (2008), 1943–1949.
  • [26] P.J.Y.Wong, L. Xie, Three symmetric solutions of Lidstone boundary value problems for difference and partial difference equations, Comput. Math. Appl. 45 (2003), 1445–1460.
  • [27] J.S. Yu, Z.M. Guo, On boundary value problems for a discrete generalized Emden-Fowler equation, J. Differential Equations 231 (2006), 18–31.
  • [28] G. Zhang, Z.L. Yang, Positive solutions of a general discrete boundary value problem, J. Math. Anal. Appl. 339 (2008), 469–481.
  • [29] G. Zhang, W. Zhang, S. Liu, Multiplicity result for a discrete eigenvalue problem with discontinuous nonlinearities, J. Math. Anal. Appl. 328 (2007), 1068–1074.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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