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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

Magdalena Nockowska-Rosiak 1, , Piotr Hachuła 2,, and  Ewa Schmeidel 3,

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.

Keywords: p-Laplacian, three-dimensional system of difference equations.
Mathematics Subject Classification: 39A12, 39A22.
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

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