Unbounded solutions of second order discrete BVPs on infinite intervals
-
2093
Downloads
-
3805
Views
Authors
Hairong Lian
- School of Science, China University of Geosciences, Beijing 100083, P. R. China.
Jingwu Li
- School of Science, China University of Geosciences, Beijing 100083, P. R. China.
Ravi P Agarwal
- Department of Mathematics, Texas A&M University-Kingsville, Kingsville, Texas 78363, USA.
Abstract
In this paper, we study Sturm-Liouville boundary value problems for second order difference equations on a
half line. By using the discrete upper and lower solutions, the Schäuder fixed point theorem, and the degree
theory, the existence of one and three solutions are investigated. An interesting feature of our existence
theory is that the solutions may be unbounded.
Share and Cite
ISRP Style
Hairong Lian, Jingwu Li, Ravi P Agarwal, Unbounded solutions of second order discrete BVPs on infinite intervals, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 2, 357--369
AMA Style
Lian Hairong, Li Jingwu, Agarwal Ravi P, Unbounded solutions of second order discrete BVPs on infinite intervals. J. Nonlinear Sci. Appl. (2016); 9(2):357--369
Chicago/Turabian Style
Lian, Hairong, Li, Jingwu, Agarwal, Ravi P. "Unbounded solutions of second order discrete BVPs on infinite intervals." Journal of Nonlinear Sciences and Applications, 9, no. 2 (2016): 357--369
Keywords
- Coincidence point
- discrete boundary value problem
- infinite interval
- upper solution
- lower solution
- degree theory common fixed point.
MSC
References
-
[1]
R. P. Agarwal, M. Bohner, D. O'Regan, Time scale boundary value problems on infinite intervals, J. Comput. Appl. Math., 141 (2002), 27-34.
-
[2]
R. P. Agarwal, S. R. Grace, D. O'Regan, Nonoscillatory solutions for discrete equation, Comput. Math. Appl., 45 (2003), 1297-1302.
-
[3]
R. P. Agarwal, D. O'Regan, Boundary value problems for discrete equations, Appl. Math. Lett., 10 (1997), 83-89.
-
[4]
R. P. Agarwal, D. O'Regan , Boundary value problems for general discrete systems on infinite intervals , Comput. Math. Appl., 33 (1997), 85-99.
-
[5]
R. P. Agarwal, D. O'Regan, Discrete systems on infinite intervals, Comput. Math. Appl., 35 (1998), 97-105.
-
[6]
R. P. Agarwal, D. O'Regan , Existence and approximation of solutions of nonlinear discrete systems on infinite intervals, Math. Meth. Appl. Sci., 22 (1999), 91-99.
-
[7]
R. P. Agarwal, D. O'Regan, Continuous and discrete boundary value problems on the infinite interval: existence theory, Mathematika, 48 (2001), 273-292.
-
[8]
R. P. Agarwal, D. O'Regan, Nonlinear Urysohn discrete equations on the infinite interval: a fixed point approach , Comput. Math. Appl., 42 (2001), 273-281.
-
[9]
N. C. Apreutesei, On a class of difference equations of monotone type , J. Math. Anal. Appl., 288 (2003), 833-851.
-
[10]
M. Benchohra, S. K. Ntouyas, A. Ouahab, Upper and lower solutions method for discrete inclusions with nonlinear boundary conditions, J. Pure Appl. Math., 7 (2006), 1-7.
-
[11]
C. Bereanu, J. Mawhin , Existence and multiplicity results for periodic solutions of nonlinear difference equations , J. Difference Equ. Appl., 12 (2006), 677-695.
-
[12]
G. Sh. Guseinov, A boundary value problem for second order nonlinear difference equations on the semi-infinite interval , J. Difference Equ. Appl., 8 (2002), 1019-1032.
-
[13]
J. Henderson, H. B. Thompson , Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations, J. Difference Equ. Appl., 7 (2001), 297-321.
-
[14]
J. Henderson, H. B. Thompson , Existence of multiple solutions for second order discrete boundary value problems, Comput. Math. Appl., 43 (2002), 1239-1248.
-
[15]
D. Jiang, D. O'Regan, R. P. Agarwal, A generalized upper and lower solution method for singular discrete boundary value problems for the one-dimensional p-Laplacian , J. Appl. Anal., 11 (2005), 35-47.
-
[16]
I. Kubiaczyk, P. Majcher, On some continuous and discrete equations in Banach spaces on unbounded intervals, Appl. Math. Comput., 136 (2003), 463-473.
-
[17]
Z. Liu, X. Hou, T. Sh. Ume, Sh. M. Kang, Unbounded positive solutions and Mann iterative schemes of a second order nonlinear neutral delay difference equation, Abstr. Appl. Anal., 2013 (2013), 12 pages.
-
[18]
M. Mohamed, H. B. Thompson, M. S. Jusoh , Solvability of discrete two-point boundary value problems, J. Math. Res., 3 (2011), 15-26.
-
[19]
L. Rachůnek, I. Rachůnková , Homoclinic solutions of non-autonomous difference equations arising in hydrodynamics, Nonlinear Anal. Real World Appl., 12 (2011), 14-23.
-
[20]
I. Rachůnková, L. Rachůnek, Solvability of discrete Dirichlet problem via lower and upper functions method, J. Difference Equ. Appl., 13 (2007), 423-429.
-
[21]
I. Rachůnková, C. C. Tisdell, Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions , Nonlinear Anal., 67 (2007), 1236-1245.
-
[22]
J. Rodriguez, Nonlinear discrete systems with global boundary conditions, J. Math. Anal. Appl., 286 (2003), 782-794.
-
[23]
V. S. Ryaben'kiim, S. V. Tsynkov , An effective numerical technique for solving a special class of ordinary difference equations, Appl. Numer. Math., 18 (1995), 489-501.
-
[24]
H. B. Thompson, C. C. Tisdell, Systems of difference equations associated with boundary value problems for second order systems of ordinary differential equations , J. Math. Anal. Appl., 248 (2000), 333-347.
-
[25]
H. B. Thompson, Topological methods for some boundary value problems, Comput. Math. Appl., 42 (2001), 487-495.
-
[26]
Y. Tian, W. Ge, Multiple positive solutions of boundary value problems for second order discrete equations on the half line, J. Difference Equ. Appl., 12 (2006), 191-208.
-
[27]
Y. Tian, C. C. Tisdell, W. Ge, The method of upper and lower solutions for discrete BVP on infinite intervals, J. Difference Equ. Appl., 17 (2011), 267-278.
-
[28]
Y. M. Wang, Monotone methods of a boundary value problem of second order discrete equation , Comput. Math. Appl., 36 (1998), 77-92.
-
[29]
Y. M. Wang , Accelerated monotone iterative methods for a boundary value problem of second order discrete equations, Comput. Math. Appl., 39 (2000), 85-94.