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Tytuł artykułu

On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study the existence and the nonexistence of solutions for the boundary value problems of a class of nonlinear second-order discrete equations depending on a parameter. Variational (the mountain pass technique) and non-variational methods are applied.
Rocznik
Strony
851--870
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • Technical University of Lodz Institute of Mathematics Wolczanska 215, 90-924 Lodz, Poland
autor
  • Technical University of Lodz Institute of Mathematics Wolczanska 215, 90-924 Lodz, Poland
Bibliografia
  • [1] R.P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.
  • [2] R.P. Agarwal, K. Perera, D. O’Regan, Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Difference Equ. 2005 (2005) 2, 93–99.
  • [3] C. Bereanu, P. Jebelean, C. Serban, Periodic and Neumann problems for discrete p(·)-Laplacian, J. Math. Anal. Appl. 399 (2013), 75–87.
  • [4] P. Candito, G. D’Aguì, Three solutions for a discrete nonlinear Neumann problem involving the p-Laplacian, Adv. Difference Equ. 2010 (2010), Art. ID 862016.
  • [5] M. Galewski, A note on the dependence on parameters for a nonlinear system via monotonicity theory, J. Difference Equ. Appl. 18 (2012) 7, 1253–1256.
  • [6] M. Galewski, A note on the well posed anisotropic discrete BVP’s, J. Difference Equ. Appl. 9 (2012), 1607–1610.
  • [7] M. Galewski, J. Smejda, On the dependence on parameters for mountain pass solutions of second order discrete BVP’s, Appl. Math. Comput. 19 (2013) 11, 5963–5971.
  • [8] M. Galewski, R. Wieteska, Existence and multiplicity of positive solutions for discrete anisotropic equations, Turk. J. Math. 38 (2014), 297–310.
  • [9] P. Harjulehto, P. Hästö, U.V. Le, M. Nuortio, Overview of differential equations with non-standard growth, Nonlinear Anal. 72 (2010), 4551–4574.
  • [10] X. He, X. Wu, Existence and multiplicity of solutions for nonlinear second order difference boundary value problems, Comput. Math. Appl. 57 (2009), 1–8.
  • [11] S. Huang, Z. Zhou, On the nonexistence and existence of solutions for a fourth-order discrete boundary value problem, Adv. Difference Equ. 2009, Art. ID 389624, 18 pp.
  • [12] W. Jiang, M. Cui, Constructive proof for existence of nonlinear two-point boundary value problems, Appl. Math. Comput. 215 (2009) 5, 1937–1948.
  • [13] U. Ledzewicz, H. Schättler, S. Walczak, Optimal control systems governed by second-order ODEs with Dirichlet boundary data and variable parameters, Ill. J. Math. 47 (2003) 4, 1189–1206.
  • [14] P. Lindqvist, On the equation div(|ru|p−2ru)+ᄃ|u|p−2u = 0, Proc. Amer. Math. Soc. 109 (1990), 157–164.
  • [15] J. Mawhin, Problèmes de Dirichlet Variationnels non Linéaires, Les Presses de l’Université de Montréal, Montréal, 1987.
  • [16] M. Mihˇailescu, V. Rˇadulescu, S. Tersian, Eigenvalue problems for anisotropic discrete boundary value problems, J. Difference Equ. Appl. 15 (2009), 557–567.
  • [17] P. Stehlík, On variational methods for periodic discrete problems, J. Difference Equ. Appl. 14 (2008) 3, 259–273.
  • [18] M. Struwe, Variational Methods, Springer, Berlin, 1996.
  • [19] K. Teng, C. Zhang, Existence of solution to boundary value problem for impulsive differential equations, Nonlinear Anal. Real World Appl. 11 (2010) 5, 4431–4441.
  • [20] M. Willem, Minimax Theorem, Birkhäuser, 1996.
  • [21] Y. Yang, J. Zhang, Existence of solutions for some discrete boundary value problems with a parameter, Appl. Math. Comput. 211 (2009) 2, 293–302.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-332eaaf1-a2e3-4e80-8304-88bfaa46d8e4
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