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A discrete problem involving the $p(k)-$ Laplacian operator with three variable exponents | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 40، دوره 12، شماره 1، مرداد 2021، صفحه 521-532 اصل مقاله (409.76 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4834 | ||
نویسندگان | ||
Mohamed Ousbika* ؛ Zakaria El Allali | ||
Oriental applied mathematics laboratory, FS Oujda, Team of Modeling and Scientific Computing, FP Nador, University Mohammed 1, Morocco. | ||
تاریخ دریافت: 10 تیر 1399، تاریخ بازنگری: 18 بهمن 1399، تاریخ پذیرش: 01 شهریور 1399 | ||
چکیده | ||
In this paper, we determine the different intervals of a positive parameters $\lambda$, for which we prove the existence and non existence of a non trivial solutions for the discrete problem (1.1). Our technical approach is based on the variational principle and the critical point theory. | ||
کلیدواژهها | ||
Discrete boundary value problem؛ Anisotropic problem؛ Critical point theory؛ Eigenvalue | ||
مراجع | ||
[1] 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) 69–73. [2] R.P. Agarwal, K. Perera and D. O’Regan, Multiple positive Solutions of singular p-Laplacian discrete problems via variational methods, Adv. Differ. Equ. 2 (2009) 93–99. [3] A. Cabada, A. Iannizzotto and S. Tersssain, Multiple Solutions for discrete boundary value problems, J. Math. Anal. Appl. 356(2009) 418–428. [4] G. Bonanno and P. Candito, Infinitely many solutions for a class of discrete non-linear boundary value problems, Appl. Anal. 884 (2009) 605–616. [5] G. Bonanno, P. Candito and G. DAgui, Variational methods on finite-dimensional Banach spaces and discrete problems, Adv. Nonlinear Stud. 14 (2014) 915–939. [6] G. Bonanno and G. DAgui, Two non-zero solutions for elliptic Dirichlet problems, Z. Anal. Anwend. 35 (2016) 449–464. [7] J. Chu and D. Jiang, Eigenvalues and discrete boundary value problems for the one-dimensional p-Laplacian, J. Math. Anal. Appl. 305 (2005) 452–465. [8] M. Galewski and R. Wieteska, Existence and multiplicity results for boundary value problems connected with the discrete p(.)-Laplacian on weighted finite graphs, Appl. Math. Comput. 290 (2016) 376–391. [9] M. Galewski and R. Wieteska, On the system of anisotropic discrete BVPs, J. Difference Equ. Appl. 19(7) (2013) 1065–1081. [10] M. Galewski and R. Wieteska, Existence and multiplicity of positive solutions for discrete anisotropic equations. Turk. J. Math. 38 (2014) 297–310. [11] M. Galewski and R. Wieteska, Positive solutions for anisotropic discrete boundary-value problems. Electron. J. Differ. Equ. Appl. 2013(32) (2013) 1–9. [12] M. Galewski and Sz. Glab, On the discrete boundary value problem for anisotropic equation, J. Math. Anal. Appl. 386 (2012) 956–965. [13] M. Galewski, G. Molica Bisci and R. Wieteska, Existence and multiplicity of solutions to discrete inclusions with the p(k)-Laplacian problem, J. Difference Equ. Appl. 21(10) (2015) 887–903. [14] J. Henderson and H.B. Thompson, Existence of multiple solutions for second order discrete boundary value problems, Comput. Math. Appl. 43 (2002) 1239–1248. [15] B. Kone and S. Ouaro, Weak solutions for anisotropic discrete boundary value problems, J. Differ. Equ. Appl. 16(2) (2010) 1–11. [16] M. Khaleghi Moghadam and J. Henderson, Triple solutions for a Dirichlet boundary value problem involving a perturbed discrete p(k)-Laplacian operator, Open Math. 15 (2017) 1075–1089. [17] M. Khaleghi Moghadam and M. Avci, Existence results to a nonlinear p(k)-Laplacian difference equation, J. Difference Equ. Appl. 23(10) (2017), 1652 – 1669. [18] B. Kone and S. Ouaro, Weak solutions for anisotropic discrete boundary value problems, J. Differ. Equ. Appl. 17(10) (2011) 1537–1547. [19] A. Kristaly, M. Mihailescu, V. Radulescu and S. Tersian, Spectral estimates for a nonhomogeneous difference problem. Commun. Contemp. Math. 12 (2010) 1015–1029. [20] G. Molica Bisci and D. Repovs, Existence of solutions for p-Laplacian discrete equations, Appl. Math. Comput. 242 (2014) 454–461. [21] G. Molica Bisci and D. Repovs, On sequences of solutions for discrete anisotropic equations, Expo. Math. 32 (2014) 284–295. [22] M. Mihailescu, V. Radulescu and S. Tersian, Eigenvalue problems for anisotropic discrete boundary value problems, J. Difference Equ. Appl. 15 (2009) 557–567. [23] M. Mihailescu and V. Radulescu, Spectrum in an unbounded interval for a class of nonhomogeneous differential operators, Bull. London Math. Soc. 40 (2008) 972–984. [24] J. Smejda and R. Wieteska, On the dependence on parameters for second-order discrete boundary value problems with the p(k)-Laplacian, Opuscula Math. 344 (2014) 851–870. [25] M. Struwe, Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, Berlin, 1986. | ||
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