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Periodic solutions of a $2$-dimensional system of neutral difference equations
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 |
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.
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.
|
| [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. Cecchi, Z. 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. 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. |
| [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. 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.
|
| [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. Cecchi, Z. 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. 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. |
| [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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