# American Institute of Mathematical Sciences

January  2018, 23(1): 369-375. doi: 10.3934/dcdsb.2018025

## Existence of uncountably many asymptotically constant solutions to discrete nonlinear three-dimensional system with $p$-Laplacian

 1 Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90-924 Lodz, Poland 2 Institute of Logistics and Warehousing, Estkowskiego 6, 61-755 Poznan, Poland 3 Institute of Mathematics, University of Białystok, Ciolkowskiego 1M, 15-245 Bialystok, Poland

* Corresponding author: Piotr Hachuła

Received  July 2016 Revised  December 2016 Published  January 2018

This work is devoted to the study of the existence of uncountably many asymptotically constant solutions to discrete nonlinear three-dimensional system with p-Laplacian.

Citation: Magdalena Nockowska-Rosiak, Piotr Hachuła, Ewa Schmeidel. Existence of uncountably many asymptotically constant solutions to discrete nonlinear three-dimensional system with $p$-Laplacian. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 369-375. doi: 10.3934/dcdsb.2018025
##### References:
 [1] R. Agarwal, K. Perera and D. O'Regan, Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Difference Equ., 2005 (2005), 93-99.   Google Scholar [2] G. Bisci and D. Repovš, Existence of solutions for $p$-{L}aplacian discrete equations, Appl. Math. Comput., 242 (2014), 454-461.  doi: 10.1016/j.amc.2014.05.118.  Google Scholar [3] A. Burton, Stability by Fixed Point Theory for Functional Differential Equations Dover Publications, Inc., Mineola, NY, 2006.  Google Scholar [4] A. Cabada, Extremal solutions for the difference ϕ-laplacian problem with nonlinear functional boundary conditions, Comput. Math. Appl., 42 (2001), 593-601.  doi: 10.1016/S0898-1221(01)00179-1.  Google Scholar [5] A. Cabada and V. Otero-Espinar, Existence and comparison results for difference ϕ-Laplacian boundary value problems with lower and upper solutions in reverse order, J. Math. Anal. Appl., 267 (2002), 501-521.  doi: 10.1006/jmaa.2001.7783.  Google Scholar [6] M. Cecchi, Z. Došlá and M. Marini, Intermediate solutions for nonlinear difference equations with p-Laplacian, Adv. Stud. Pure Math., 53 (2009), 33-40.   Google Scholar [7] C. Costara and D. Popa, Exercises in Functional Analysis Kluwer Academic Publisher Group, Dordrecht, 2003. doi: 10.1007/978-94-017-0223-2.  Google Scholar [8] Z. He, On the existence of positive solutions of $p$-{L}aplacian difference equations, J. Comput. Appl. Math., 161 (2003), 193-201.  doi: 10.1016/j.cam.2003.08.004.  Google Scholar [9] E. Lee and Y. Lee, A result on three solutions theorem and its application to p-Laplacian systems with singular weights, Boundary Value Problems, 2012 (2012), 20pp.  doi: 10.1186/1687-2770-2012-63.  Google Scholar [10] M. Migda, E. Schmeidel and M. Zdanowicz, Existence of nonoscillatory solutions for system of neutral difference equations, Appl. Anal. Discrete Math., 9 (2015), 271-284.  doi: 10.2298/AADM150811016M.  Google Scholar [11] E. Schmeidel, Boundedness of solutions of nonlinear three-dimensional difference systems with delays, Fasc. Math., 44 (2010), 107-113.   Google Scholar [12] E. Schmeidel, Oscillation of nonlinear three-dimensional difference systems with delays, Math. Bohem., 135 (2010), 163-170.   Google Scholar [13] E. Schmeidel, Properties of solutions of system of difference equations with neutral term, Funct. Differ. Equ., 18 (2011), 293-302.   Google Scholar [14] E. Thandapani and B. Ponnammal, Oscillatory properties of solutions of three dimensional difference systems, Math. Comput. Modelling, 42 (2005), 641-650.  doi: 10.1016/j.mcm.2004.04.010.  Google Scholar

show all references

##### References:
 [1] R. Agarwal, K. Perera and D. O'Regan, Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Difference Equ., 2005 (2005), 93-99.   Google Scholar [2] G. Bisci and D. Repovš, Existence of solutions for $p$-{L}aplacian discrete equations, Appl. Math. Comput., 242 (2014), 454-461.  doi: 10.1016/j.amc.2014.05.118.  Google Scholar [3] A. Burton, Stability by Fixed Point Theory for Functional Differential Equations Dover Publications, Inc., Mineola, NY, 2006.  Google Scholar [4] A. Cabada, Extremal solutions for the difference ϕ-laplacian problem with nonlinear functional boundary conditions, Comput. Math. Appl., 42 (2001), 593-601.  doi: 10.1016/S0898-1221(01)00179-1.  Google Scholar [5] A. Cabada and V. Otero-Espinar, Existence and comparison results for difference ϕ-Laplacian boundary value problems with lower and upper solutions in reverse order, J. Math. Anal. Appl., 267 (2002), 501-521.  doi: 10.1006/jmaa.2001.7783.  Google Scholar [6] M. Cecchi, Z. Došlá and M. Marini, Intermediate solutions for nonlinear difference equations with p-Laplacian, Adv. Stud. Pure Math., 53 (2009), 33-40.   Google Scholar [7] C. Costara and D. Popa, Exercises in Functional Analysis Kluwer Academic Publisher Group, Dordrecht, 2003. doi: 10.1007/978-94-017-0223-2.  Google Scholar [8] Z. He, On the existence of positive solutions of $p$-{L}aplacian difference equations, J. Comput. Appl. Math., 161 (2003), 193-201.  doi: 10.1016/j.cam.2003.08.004.  Google Scholar [9] E. Lee and Y. Lee, A result on three solutions theorem and its application to p-Laplacian systems with singular weights, Boundary Value Problems, 2012 (2012), 20pp.  doi: 10.1186/1687-2770-2012-63.  Google Scholar [10] M. Migda, E. Schmeidel and M. Zdanowicz, Existence of nonoscillatory solutions for system of neutral difference equations, Appl. Anal. Discrete Math., 9 (2015), 271-284.  doi: 10.2298/AADM150811016M.  Google Scholar [11] E. Schmeidel, Boundedness of solutions of nonlinear three-dimensional difference systems with delays, Fasc. Math., 44 (2010), 107-113.   Google Scholar [12] E. Schmeidel, Oscillation of nonlinear three-dimensional difference systems with delays, Math. Bohem., 135 (2010), 163-170.   Google Scholar [13] E. Schmeidel, Properties of solutions of system of difference equations with neutral term, Funct. Differ. Equ., 18 (2011), 293-302.   Google Scholar [14] E. Thandapani and B. Ponnammal, Oscillatory properties of solutions of three dimensional difference systems, Math. Comput. Modelling, 42 (2005), 641-650.  doi: 10.1016/j.mcm.2004.04.010.  Google Scholar
 [1] Stanislav Nikolaevich Antontsev, Serik Ersultanovich Aitzhanov, Guzel Rashitkhuzhakyzy Ashurova. An inverse problem for the pseudo-parabolic equation with p-Laplacian. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021005 [2] Shuang Chen, Jinqiao Duan, Ji Li. Effective reduction of a three-dimensional circadian oscillator model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020349 [3] Hua Zhong, Xiaolin Fan, Shuyu Sun. The effect of surface pattern property on the advancing motion of three-dimensional droplets. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020366 [4] Yao Nie, Jia Yuan. The Littlewood-Paley $pth$-order moments in three-dimensional MHD turbulence. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020397 [5] Gui-Qiang Chen, Beixiang Fang. Stability of transonic shock-fronts in three-dimensional conical steady potential flow past a perturbed cone. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 85-114. doi: 10.3934/dcds.2009.23.85 [6] Gang Bao, Mingming Zhang, Bin Hu, Peijun Li. An adaptive finite element DtN method for the three-dimensional acoustic scattering problem. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 61-79. doi: 10.3934/dcdsb.2020351 [7] Yichen Zhang, Meiqiang Feng. A coupled $p$-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075 [8] Guoliang Zhang, Shaoqin Zheng, Tao Xiong. A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations. Electronic Research Archive, 2021, 29 (1) : 1819-1839. doi: 10.3934/era.2020093 [9] Shanding Xu, Longjiang Qu, Xiwang Cao. Three classes of partitioned difference families and their optimal constant composition codes. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020120 [10] Fathalla A. Rihan, Hebatallah J. Alsakaji. Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020468 [11] Anton A. Kutsenko. Isomorphism between one-dimensional and multidimensional finite difference operators. Communications on Pure & Applied Analysis, 2021, 20 (1) : 359-368. doi: 10.3934/cpaa.2020270 [12] Wenqiang Zhao, Yijin Zhang. High-order Wong-Zakai approximations for non-autonomous stochastic $p$-Laplacian equations on $\mathbb{R}^N$. Communications on Pure & Applied Analysis, 2021, 20 (1) : 243-280. doi: 10.3934/cpaa.2020265 [13] Yueh-Cheng Kuo, Huey-Er Lin, Shih-Feng Shieh. Asymptotic dynamics of hermitian Riccati difference equations. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020365 [14] Álvaro Castañeda, Pablo González, Gonzalo Robledo. Topological Equivalence of nonautonomous difference equations with a family of dichotomies on the half line. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020278 [15] Matthieu Alfaro, Isabeau Birindelli. Evolution equations involving nonlinear truncated Laplacian operators. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3057-3073. doi: 10.3934/dcds.2020046 [16] Hongming Ru, Chunming Tang, Yanfeng Qi, Yuxiao Deng. A construction of $p$-ary linear codes with two or three weights. Advances in Mathematics of Communications, 2021, 15 (1) : 9-22. doi: 10.3934/amc.2020039 [17] Lihong Zhang, Wenwen Hou, Bashir Ahmad, Guotao Wang. Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $p$-Laplacian. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020445 [18] Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $p$ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020442 [19] Fuensanta Andrés, Julio Muñoz, Jesús Rosado. Optimal design problems governed by the nonlocal $p$-Laplacian equation. Mathematical Control & Related Fields, 2021, 11 (1) : 119-141. doi: 10.3934/mcrf.2020030 [20] Zaizheng Li, Qidi Zhang. Sub-solutions and a point-wise Hopf's lemma for fractional $p$-Laplacian. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020293

2019 Impact Factor: 1.27