Recent Issues
Volume 17, 4 issues
Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182
Volume 16, 5 issues
Volume 16
Issue 5, 727–903
Issue 4, 547–726
Issue 3, 365–546
Issue 2, 183–364
Issue 1, 1–182
Volume 15, 5 issues
Volume 15
Issue 5, 727–906
Issue 4, 547–726
Issue 3, 367–546
Issue 2, 185–365
Issue 1, 1–184
Volume 14, 5 issues
Volume 14
Issue 5, 723–905
Issue 4, 541–721
Issue 3, 361–540
Issue 2, 181–360
Issue 1, 1–179
Volume 13, 5 issues
Volume 13
Issue 5, 721–900
Issue 4, 541–719
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180
Volume 12, 8 issues
Volume 12
Issue 8, 1261–1439
Issue 7, 1081–1260
Issue 6, 901–1080
Issue 5, 721–899
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180
Volume 11, 5 issues
Volume 11
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–540
Issue 2, 181–359
Issue 1, 1–179
Volume 10, 5 issues
Volume 10
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180
Volume 9, 5 issues
Volume 9
Issue 5, 721–899
Issue 4, 541–720
Issue 3, 361–540
Issue 2, 181–359
Issue 1, 1–180
Volume 8, 5 issues
Volume 8
Issue 5, 721–900
Issue 4, 541–719
Issue 3, 361–540
Issue 2, 181–359
Issue 1, 1–179
Volume 7, 6 issues
Volume 7
Issue 6, 713–822
Issue 5, 585–712
Issue 4, 431–583
Issue 3, 245–430
Issue 2, 125–244
Issue 1, 1–124
Volume 6, 4 issues
Volume 6
Issue 4, 383–510
Issue 3, 261–381
Issue 2, 127–260
Issue 1, 1–126
Volume 5, 4 issues
Volume 5
Issue 4, 379–504
Issue 3, 237–378
Issue 2, 115–236
Issue 1, 1–113
Volume 4, 4 issues
Volume 4
Issue 4, 307–416
Issue 3, 203–305
Issue 2, 103–202
Issue 1, 1–102
Volume 3, 4 issues
Volume 3
Issue 4, 349–474
Issue 3, 241–347
Issue 2, 129–240
Issue 1, 1–127
Volume 2, 5 issues
Volume 2
Issue 5, 495–628
Issue 4, 371–494
Issue 3, 249–370
Issue 2, 121–247
Issue 1, 1–120
Volume 1, 2 issues
Volume 1
Issue 2, 123–233
Issue 1, 1–121
Abstract
We study singular discrete third-order boundary value problems with mixed
boundary conditions of the form
− u Δ Δ Δ ( t
i − 2 )
+
f ( t i , u ( t i ) , u Δ ( t
i − 1 ) , u Δ Δ ( t
i − 2 ) )
= 0 ,
u Δ Δ ( t
0 )
= u Δ ( t
n + 1 )
=
u ( t n + 2 )
= 0 ,
over a finite discrete interval
{ t 0 , t 1 , … , t n , t n + 1 , t n + 2 } .
We prove the existence of a positive solution by means of the lower and upper
solutions method and the Brouwer fixed point theorem in conjunction with
perturbation methods to approximate regular problems.
Keywords
singular discrete boundary value problem, mixed conditions,
lower and upper solutions, Brouwer fixed point theorem,
approximate regular problems
Mathematical Subject Classification 2010
Primary: 39A10, 34B16, 34B18
Milestones
Received: 13 June 2012
Revised: 23 July 2012
Accepted: 23 July 2012
Published: 23 June 2013
Communicated by Johnny Henderson