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. AgarwalK. Perera and D. O'Regan, Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Difference Equ., 2005 (2005), 93-99.

[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.

[3]

A. Burton, Stability by Fixed Point Theory for Functional Differential Equations Dover Publications, Inc., Mineola, NY, 2006.

[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.

[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.

[6]

M. CecchiZ. Došlá and M. Marini, Intermediate solutions for nonlinear difference equations with p-Laplacian, Adv. Stud. Pure Math., 53 (2009), 33-40.

[7]

C. Costara and D. Popa, Exercises in Functional Analysis Kluwer Academic Publisher Group, Dordrecht, 2003. doi: 10.1007/978-94-017-0223-2.

[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.

[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.

[10]

M. MigdaE. 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.

[11]

E. Schmeidel, Boundedness of solutions of nonlinear three-dimensional difference systems with delays, Fasc. Math., 44 (2010), 107-113.

[12]

E. Schmeidel, Oscillation of nonlinear three-dimensional difference systems with delays, Math. Bohem., 135 (2010), 163-170.

[13]

E. Schmeidel, Properties of solutions of system of difference equations with neutral term, Funct. Differ. Equ., 18 (2011), 293-302.

[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.

show all references

References:
[1]

R. AgarwalK. Perera and D. O'Regan, Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Difference Equ., 2005 (2005), 93-99.

[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.

[3]

A. Burton, Stability by Fixed Point Theory for Functional Differential Equations Dover Publications, Inc., Mineola, NY, 2006.

[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.

[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.

[6]

M. CecchiZ. Došlá and M. Marini, Intermediate solutions for nonlinear difference equations with p-Laplacian, Adv. Stud. Pure Math., 53 (2009), 33-40.

[7]

C. Costara and D. Popa, Exercises in Functional Analysis Kluwer Academic Publisher Group, Dordrecht, 2003. doi: 10.1007/978-94-017-0223-2.

[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.

[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.

[10]

M. MigdaE. 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.

[11]

E. Schmeidel, Boundedness of solutions of nonlinear three-dimensional difference systems with delays, Fasc. Math., 44 (2010), 107-113.

[12]

E. Schmeidel, Oscillation of nonlinear three-dimensional difference systems with delays, Math. Bohem., 135 (2010), 163-170.

[13]

E. Schmeidel, Properties of solutions of system of difference equations with neutral term, Funct. Differ. Equ., 18 (2011), 293-302.

[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.

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