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Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete p-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.
Rocznik
Strony
683--690
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • University of Reggio Calabria Department DICEAM Via Graziella (Feo Di Vito) 89122 Reggio Calabria, Italy
autor
  • University of Messina Department of Civil, Computer, Construction, Environmental Engineering and Applied Mathematics 98166 - Messina, Italy
Bibliografia
  • [1] R.P. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker, New York, Basel, 2000.
  • [2] R.P. Agarwal, K. Perera, D. O’Regan, Multiple positive solutions of singular and nonsingular discrete problems via variational methods, Nonlinear Anal. 58 (2004), 69–73.
  • [3] R.P. Agarwal, K. Perera, D. O’Regan, Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Diff. Equ. 2 (2005), 93–99.
  • [4] R.P. Agarwal, On multipoint boundary value problems for discrete equations, J. Math. Anal. Appl. 96 (1983) 2, 520-534.
  • [5] D.R. Anderson, I. Rachunková, C.C. Tisdell, Solvability of discrete Neumann boundary value probles, Adv. Diff. Equ. 2 (2005), 93–99.
  • [6] C. Bereanu, J. Mawhin, Boundary value problems for second-order nonlinear difference equations with discrete ‑-Laplacian and singular ‑, J. Difference Equ. Appl. 14 (2008), 1099–1118.
  • [7] C. Bereanu, P. Jebelean, C. Serban, Ground state and mountain pass solutions for discrete p(·)-Laplacian, Bound. Value Probl. 2012 (2012) 104.
  • [8] G. Bonanno, P. Candito, Nonlinear difference equations investigated via critical point methods, Nonlinear Anal. 70 (2009), 3180–3186.
  • [9] G. Bonanno, P. Candito, Infinitely many solutions for a class of discrete nonlinear boundary value problems, Appl. Anal. 88 (2009), 605–616.
  • [10] G. Bonanno, P. Candito, Nonlinear difference equations through variational methods, Handbook on Nonconvex Analysis, Int. Press, Somerville, MA, 2010, pp. 1–44.
  • [11] G. Bonanno, P. Candito, G. D’Aguí, Variational methods on finite dimensional Banach spaces and discrete problems, Adv. Nonlinear Stud. 14 (2014), 915–939.
  • [12] G. Bonanno, P. Candito, G. D’Aguí, Existence of positive solutions for a nonlinear parameter-depending algebraic system, preprint.
  • [13] P. Candito, G. D’Aguí, Three solutions for a discrete nonlinear Neumann problem involving the p-Laplacian, Adv. Difference Equ. 2010, 862016, 11 pp.
  • [14] P. Candito, G. D’Aguí, Three solutions to a perturbed nonlinear discrete Dirichlet problem, J. Math. Anal. Appl. 375 (2011), 594–601.
  • [15] P. Candito, G. D’Aguí, Constant sign solutions for a parameter-dependent superlinear second order difference equation (submitted).
  • [16] P. Candito, N. Giovannelli, Multiple solutions for a discrete boundary value problem involving the p-Laplacian, Comput. Math. Appl. 56 (2008), 959–964.
  • [17] M. Galewski, S. Głab, On the discrete boundary value problem for anisotropic equation, J. Math. Anal. Appl. 386 (2012), 956–965.
  • [18] A. Guiro, I. Nyanquini, S. Ouaro, On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian, Adv. Difference Equ. 2011 (2011) 32.
  • [19] M. Khaleghi, S. Heidarkhani, J. Henderson, Infinitely many solutions for perturbed difference equations, J. Difference Equ. Appl. (to appear).
  • [20] L. Jiang, Z. Zhou, Three solutions to Dirichlet boundary value problems for p-Laplacian difference equations, Adv. Difference Equ. (2008), 345916, 10 pp.
  • [21] W.G. Kelly, A.C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, San Diego, New York, Basel, 1991.
  • [22] I. Rachunková, C.C. Tisdell, Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions, Nonlinear Anal. 67 (2007), 1236–1245.
  • [23] C. Serban, Existence of solutions for discrete p-Laplacian with potential boundary conditions, J. Difference Equ. Appl. 19 (2013), 527–537.
  • [24] M. Struwe, Variational Methods, Springer, Berlin, 1996.
  • [25] Y. Tian, W. Ge, The existence of solutions for a second-order discrete Neumann problem with p-Laplacian, J. Appl. Math. Comput. 26 (2008), 333–340.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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