Browse > Article
http://dx.doi.org/10.22771/nfaa.2022.27.04.12

AN EXISTENCE OF THREE DIFFERENT NON-TRIVIAL SOLUTIONS FOR DISCRETE ANISOTROPIC EQUATIONS WITH TWO REAL PARAMETERS  

Ahmed A.H., Alkhalidi (Computer Technical Engineering Department, College of Technical Engineering, The Islamic University)
Haiffa Muhsan B., Alrikabi (Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar Nasiriyah)
Mujtaba Zuhair, Ali (Computer Technical Engineering Department, College of Technical Engineering, The Islamic University)
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.4, 2022 , pp. 855-867 More about this Journal
Abstract
This study finds three different solutions (3-Sol's) for the fourth order nonlinear discrete anisotropic equations (DAE) with real parameter. We use the variational method(VM) and 𝜙p-Laplacian operator (𝜙p-LO) to prove the main results. In the following paper, we take the parameters λ, 𝜇 such that λ > 0 and 𝜇 ≥ 0 into consideration.
Keywords
Discrete anisotropic equations; existence solution; three different solutions; variational method; (Lipsz. cond.);
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 R. Ma and C. Gao, Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem, Z. Angew. Math. Phys., 64 (2013), 493-506.   DOI
2 R. Ma, C. Gao and Y. Chang, Existence of solutions of a discrete fourth-order boundary value problem, Discrete Dyn. Nat. Soc., 2010 (2010), 19 pages.
3 A.A. Mebawondu, H.A. Abass, M.O. Aibinu and O.K. Narain, Existence of solution of differential equation via fixed point in complex valued b-metric spaces, Nonlinear Funct. Anal. Appl., 26(2) (2020), 303-322.
4 M.K. Moghadam, S. Heidarkhani and J. Henderson, Infinitely many solutions for perturbed difference equations, J. Diff. Equ. Appl., 20 (2014), 1055-1068.   DOI
5 B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math., 133 (2000), 401-410.   DOI
6 Y. Wang, C. Gao and T. Geng, Multiplicity solutions for discrete fourth-order boundary value problem with multiple parameters, J. Nonlinear Sci., 9 (2016), 3212-3225.   DOI
7 A.H. Alkhalidi, Ghasem A. Afrouzi and Khademloo Somayeh, Variational approaches for Lagrangian discrete nonlinear systems, Mathematics, 276(7) (2019), 1-14.
8 H.M.B. Alrikabi, Ahmed A.H. Alkhalidi and A.K. Yousif, An existence result for three solutions to a Dirichlet problem with real parameter, J. Interdisciplinary Math., 24(6) (2021), 1645-1659.   DOI
9 H.M.B. Alrikabi, A.E. Hashoosh and Ahmed A.H. Alkhalidi, Existence results for nonlocal problems of (p, q)-Kirchhoff form, J. Interdisciplinary Math., 24(4) (2021), 983-993.   DOI
10 G. Bonanno and P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Diff. Equ., 244 (2008), 3031-3059.   DOI
11 G. Bonanno and 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.   DOI
12 G. Bonanno and G. Molica Bisci, Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. Value Prob., (2009), 20 pages.
13 X. Deng, Nonexistence and existence results for a class of fourth-order difference mixed boundary value problems, J. Appl. Math. Comput., 14 (2014), 1-14.   DOI
14 T. He and Y. Su, On discrete fourth-order boundary value problems with three parameters, J. Appl. Math. Comput. 233 (2010), 2506-2520.   DOI
15 Z. He and J. Yu, On the existence of positive solutions of fourth-order difference equations, J. Appl. Math. Comput., 161 (2005), 139-148.   DOI
16 Z. He and J. Yu, Positive solutions for nonlinear difference equations, Nonlinear Stud., 4 (1997), 29-36.
17 S.D. Kadam, R.S. Jain, B.S. Reddy and R. Menon, Existence and controllability of mild solution of impulsive integro-differential inclusions, Nonlinear Funct. Anal. Appl., 25(4) (2020), 657-670.   DOI
18 B. Khaminsou, Ch. Thaiprayoon, W. Sudsutad and S.A. Jose, Qualitative analysis of a proportional Caputo fractional Pantograph differential equation with mixed nonlocal conditions, Nonlinear Funct. Anal. Appl., 26(1) (2021), 197-223.   DOI
19 X. Liu, Y. Zhang, H. Shi and X. Deng, Periodic and subharmonic solutions for fourth-order nonlinear difference equations, J. Appl. Math. Comput., 236 (2014), 613-620.   DOI