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Volumn 74, Issue 5, 2011, Pages 1926-1936

Existence of a positive solution to a first-order p-Laplacian BVP on a time scale

Author keywords

Cone; Delta dynamic equation; First order boundary value problem; One dimensional p Laplacian; Time scales

Indexed keywords

CONTINUOUS FUNCTIONS; DELTA DYNAMIC EQUATION; DYNAMIC BOUNDARY; FIRST-ORDER; NUMERICAL EXAMPLE; ONE-DIMENSIONAL P-LAPLACIAN; P-LAPLACIAN; POSITIVE SOLUTION; TIME-SCALES;

EID: 78651379292     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2010.10.062     Document Type: Article
Times cited : (30)

References (49)
  • 1
    • 21344475243 scopus 로고
    • On a nonlinear parabolic problem arising in some models related to turbulent flows
    • J. Diaz, and F. de Thelin On a nonlinear parabolic problem arising in some models related to turbulent flows SIAM J. Math. Anal. 25 1994 1085 1111
    • (1994) SIAM J. Math. Anal. , vol.25 , pp. 1085-1111
    • Diaz, J.1    De Thelin, F.2
  • 2
    • 70350734478 scopus 로고    scopus 로고
    • Periodic solutions for a class of reactiondiffusion equations with p-Laplacian
    • P.Y.H. Pang, Y. Wang, and J. Yin Periodic solutions for a class of reactiondiffusion equations with p-Laplacian Nonlinear Anal. RWA 11 2010 323 331
    • (2010) Nonlinear Anal. RWA , vol.11 , pp. 323-331
    • Pang, P.Y.H.1    Wang, Y.2    Yin, J.3
  • 3
    • 55049128075 scopus 로고    scopus 로고
    • Existence of solutions for a first-order p-Laplacian BVP on time scales
    • D.R. Anderson Existence of solutions for a first-order p-Laplacian BVP on time scales Nonlinear Anal. TMA 69 2008 4521 4525
    • (2008) Nonlinear Anal. TMA , vol.69 , pp. 4521-4525
    • Anderson, D.R.1
  • 4
    • 2642576430 scopus 로고    scopus 로고
    • Existence of three positive pseudo-symmetric solutions for a one dimensional discrete p-Laplacian
    • R.I. Avery, and J. Henderson Existence of three positive pseudo-symmetric solutions for a one dimensional discrete p-Laplacian J. Difference Equ. Appl. 10 2004 529 539
    • (2004) J. Difference Equ. Appl. , vol.10 , pp. 529-539
    • Avery, R.I.1    Henderson, J.2
  • 5
    • 53349095644 scopus 로고    scopus 로고
    • Boundary value problems for second-order nonlinear difference equations with discrete φ-Laplacian and singular φ
    • C. Bereanu, and J. Mawhin Boundary value problems for second-order nonlinear difference equations with discrete φ-Laplacian and singular φ J. Difference Equ. Appl. 14 2008 1099 1118
    • (2008) J. Difference Equ. Appl. , vol.14 , pp. 1099-1118
    • Bereanu, C.1    Mawhin, J.2
  • 6
    • 46249126941 scopus 로고    scopus 로고
    • Multiple solutions for a discrete boundary value problem involving the p-Laplacian
    • P. Candito, and N. Giovannelli Multiple solutions for a discrete boundary value problem involving the p-Laplacian Comput. Math. Appl. 56 2008 959 964
    • (2008) Comput. Math. Appl. , vol.56 , pp. 959-964
    • Candito, P.1    Giovannelli, N.2
  • 7
    • 64749108515 scopus 로고    scopus 로고
    • A two-phase obstacle-type problem for the p-Laplacian
    • A. Edquist, and E. Lindgren A two-phase obstacle-type problem for the p-Laplacian Calc. Var. 35 2009 421 433
    • (2009) Calc. Var. , vol.35 , pp. 421-433
    • Edquist, A.1    Lindgren, E.2
  • 8
    • 35448944368 scopus 로고    scopus 로고
    • Multiple results of p-Laplacian dynamic equations on time scales
    • F. Geng, and D. Zhu Multiple results of p-Laplacian dynamic equations on time scales Appl. Math. Comput. 193 2007 311 320
    • (2007) Appl. Math. Comput. , vol.193 , pp. 311-320
    • Geng, F.1    Zhu, D.2
  • 9
    • 40849139500 scopus 로고    scopus 로고
    • Singular second order boundary value problems on purely discrete time scales
    • C.J. Kunkel Singular second order boundary value problems on purely discrete time scales J. Difference Equ. Appl. 14 2008 411 420
    • (2008) J. Difference Equ. Appl. , vol.14 , pp. 411-420
    • Kunkel, C.J.1
  • 10
    • 0038405055 scopus 로고    scopus 로고
    • Twin positive solutions of boundary value problems for finite difference equations with p-Laplacian operator
    • Y. Liu, and W. Ge Twin positive solutions of boundary value problems for finite difference equations with p-Laplacian operator J. Math. Anal. Appl. 278 2003 551 561
    • (2003) J. Math. Anal. Appl. , vol.278 , pp. 551-561
    • Liu, Y.1    Ge, W.2
  • 11
    • 58149467649 scopus 로고    scopus 로고
    • Three positive solutions of nonhomogeneous multi-point BVPs for second order p-Laplacian functional difference equations
    • Y. Liu Three positive solutions of nonhomogeneous multi-point BVPs for second order p-Laplacian functional difference equations J. Appl. Math. Comput. 29 2009 437 460
    • (2009) J. Appl. Math. Comput. , vol.29 , pp. 437-460
    • Liu, Y.1
  • 12
    • 67349287531 scopus 로고    scopus 로고
    • Sandwich Pairs for p-Laplacian systems
    • K. Perera, and M. Schechter Sandwich Pairs for p-Laplacian systems J. Math. Anal. Appl. 358 2009 485 490
    • (2009) J. Math. Anal. Appl. , vol.358 , pp. 485-490
    • Perera, K.1    Schechter, M.2
  • 13
    • 60449108066 scopus 로고    scopus 로고
    • A free-boundary problem for the evolution p-Laplacian equation with a combustion boundary condition
    • T. To A free-boundary problem for the evolution p-Laplacian equation with a combustion boundary condition Calc. Var. 35 2009 239 262
    • (2009) Calc. Var. , vol.35 , pp. 239-262
    • To, T.1
  • 14
    • 41049095457 scopus 로고    scopus 로고
    • Three positive solutions of boundary value problems for p-Laplacian difference equations
    • D. Wang, and W. Guan Three positive solutions of boundary value problems for p-Laplacian difference equations Comput. Math. Appl. 55 2008 1943 1949
    • (2008) Comput. Math. Appl. , vol.55 , pp. 1943-1949
    • Wang, D.1    Guan, W.2
  • 15
    • 29544449556 scopus 로고    scopus 로고
    • Existence of multiple positive solutions for one-dimensional p-Laplacian
    • Y. Wang, and C. Hou Existence of multiple positive solutions for one-dimensional p-Laplacian J. Math. Anal. Appl. 315 2006 114 153
    • (2006) J. Math. Anal. Appl. , vol.315 , pp. 114-153
    • Wang, Y.1    Hou, C.2
  • 16
    • 77549085429 scopus 로고    scopus 로고
    • Positive solution for third-order SturmLiouville boundary value problems with p-Laplacian
    • C. Yang, and J. Yan Positive solution for third-order SturmLiouville boundary value problems with p-Laplacian Comput. Math. Appl. 59 2010 2059 2066
    • (2010) Comput. Math. Appl. , vol.59 , pp. 2059-2066
    • Yang, C.1    Yan, J.2
  • 17
    • 68849116996 scopus 로고    scopus 로고
    • Positive solutions for a higher-order four-point boundary value problem with a p-Laplacian
    • J. Zhao, and W. Ge Positive solutions for a higher-order four-point boundary value problem with a p-Laplacian Comput. Math. Appl. 58 2009 1103 1112
    • (2009) Comput. Math. Appl. , vol.58 , pp. 1103-1112
    • Zhao, J.1    Ge, W.2
  • 18
    • 84951604495 scopus 로고
    • Analysis on measure chainsa unified approach to continuous and discrete calculus
    • S. Hilger Analysis on measure chainsa unified approach to continuous and discrete calculus Results Math. 18 1990 18 56
    • (1990) Results Math. , vol.18 , pp. 18-56
    • Hilger, S.1
  • 21
    • 38049090651 scopus 로고    scopus 로고
    • Several existence theorems of nonlinear m-point boundary value problem for p-Laplacian dynamic equations on time scales
    • Y. Sang, and H. Su Several existence theorems of nonlinear m-point boundary value problem for p-Laplacian dynamic equations on time scales J. Math. Anal. Appl. 340 2008 1012 1026
    • (2008) J. Math. Anal. Appl. , vol.340 , pp. 1012-1026
    • Sang, Y.1    Su, H.2
  • 22
    • 53949089181 scopus 로고    scopus 로고
    • Triple positive solutions of m-point BVPs for p-Laplacian dynamic equations on time scales
    • Y.H. Su, and W.T. Li Triple positive solutions of m-point BVPs for p-Laplacian dynamic equations on time scales Nonlinear Anal. TMA 69 2008 3811 3820
    • (2008) Nonlinear Anal. TMA , vol.69 , pp. 3811-3820
    • Su, Y.H.1    Li, W.T.2
  • 23
    • 34547675918 scopus 로고    scopus 로고
    • Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales
    • H.R. Sun, and W.T. Li Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales J. Differential Equations 240 2007 217 248
    • (2007) J. Differential Equations , vol.240 , pp. 217-248
    • Sun, H.R.1    Li, W.T.2
  • 24
    • 33745657598 scopus 로고    scopus 로고
    • Positive solution for first-order discrete periodic boundary value problem
    • J.P. Sun Positive solution for first-order discrete periodic boundary value problem Appl. Math. Lett. 19 2006 1244 1248
    • (2006) Appl. Math. Lett. , vol.19 , pp. 1244-1248
    • Sun, J.P.1
  • 25
    • 38349086943 scopus 로고    scopus 로고
    • Twin positive solutions of nonlinear first-order boundary value problem on time scales
    • J.P. Sun Twin positive solutions of nonlinear first-order boundary value problem on time scales Nonlinear Anal. 68 2008 1754 1758
    • (2008) Nonlinear Anal. , vol.68 , pp. 1754-1758
    • Sun, J.P.1
  • 26
    • 34047246665 scopus 로고    scopus 로고
    • Existence of solutions to nonlinear first-order PBVPs on time scales
    • J.P. Sun, and W.T. Li Existence of solutions to nonlinear first-order PBVPs on time scales Nonlinear Anal. TMA 67 2007 883 888
    • (2007) Nonlinear Anal. TMA , vol.67 , pp. 883-888
    • Sun, J.P.1    Li, W.T.2
  • 27
    • 56449120345 scopus 로고    scopus 로고
    • Positive solutions to nonlinear first-order PBVPs with parameter on time scales
    • J.P. Sun, and W.T. Li Positive solutions to nonlinear first-order PBVPs with parameter on time scales Nonlinear Anal. TMA 70 2009 1133 1145
    • (2009) Nonlinear Anal. TMA , vol.70 , pp. 1133-1145
    • Sun, J.P.1    Li, W.T.2
  • 28
    • 50349086966 scopus 로고    scopus 로고
    • Existence and uniqueness results for nonlinear first-order three-point boundary value problems on time scales
    • Y. Tian, and W. Ge Existence and uniqueness results for nonlinear first-order three-point boundary value problems on time scales Nonlinear Anal. TMA 69 2008 2833 2842
    • (2008) Nonlinear Anal. TMA , vol.69 , pp. 2833-2842
    • Tian, Y.1    Ge, W.2
  • 29
    • 33846042078 scopus 로고    scopus 로고
    • Positive solutions of nonlocal boundary value problems: A unified approach
    • G. Infante, and J.R.L. Webb Positive solutions of nonlocal boundary value problems: a unified approach J. Lond. Math. Soc. 74 2006 673 693
    • (2006) J. Lond. Math. Soc. , vol.74 , pp. 673-693
    • Infante, G.1    Webb, J.R.L.2
  • 31
    • 70349490327 scopus 로고    scopus 로고
    • Calculus of variations with fractional derivatives and fractional integrals
    • R. Almeida, and D.F.M. Torres Calculus of variations with fractional derivatives and fractional integrals Appl. Math. Lett. 22 2009 1816 1820
    • (2009) Appl. Math. Lett. , vol.22 , pp. 1816-1820
    • Almeida, R.1    Torres, D.F.M.2
  • 32
    • 35748962937 scopus 로고    scopus 로고
    • Fractional q-calculus on a time scale
    • F.M. Atici, and P.W. Eloe Fractional q-calculus on a time scale J. Nonlinear Math. Phys. 14 2007 333 344
    • (2007) J. Nonlinear Math. Phys. , vol.14 , pp. 333-344
    • Atici, F.M.1    Eloe, P.W.2
  • 33
    • 77950548183 scopus 로고    scopus 로고
    • A transform method in discrete fractional calculus
    • F.M. Atici, and P.W. Eloe A transform method in discrete fractional calculus Int. J. Difference Equ. 2 2007 165 176
    • (2007) Int. J. Difference Equ. , vol.2 , pp. 165-176
    • Atici, F.M.1    Eloe, P.W.2
  • 34
    • 74149083825 scopus 로고    scopus 로고
    • Initial value problems in discrete fractional calculus
    • F.M. Atici, and P.W. Eloe Initial value problems in discrete fractional calculus Proc. Amer. Math. Soc. 137 2009 981 989
    • (2009) Proc. Amer. Math. Soc. , vol.137 , pp. 981-989
    • Atici, F.M.1    Eloe, P.W.2
  • 36
    • 79953286192 scopus 로고    scopus 로고
    • Two-point boundary value problems for finite fractional difference equations
    • in press (doi:10.1080/10236190903029241)
    • F.M. Atici, P.W. Eloe, Two-point boundary value problems for finite fractional difference equations, J. Difference Equ. Appl., in press (doi:10.1080/10236190903029241).
    • J. Difference Equ. Appl.
    • Atici, F.M.1    Eloe, P.W.2
  • 37
    • 77952557731 scopus 로고    scopus 로고
    • Modeling with fractional difference equations
    • F.M. Atici, and S. engl Modeling with fractional difference equations J. Math. Anal. Appl. 2010 10.1016/j.jmaa.2010.02.009
    • (2010) J. Math. Anal. Appl.
    • Atici, F.M.1    Engl, S.2
  • 38
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equation
    • Z. Bai, and H. L Positive solutions for boundary value problem of nonlinear fractional differential equation J. Math. Anal. Appl. 311 2005 495 505
    • (2005) J. Math. Anal. Appl. , vol.311 , pp. 495-505
    • Bai, Z.1
  • 39
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • K. Diethelm, and N. Ford Analysis of fractional differential equations J. Math. Anal. Appl. 265 2002 229 248
    • (2002) J. Math. Anal. Appl. , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.2
  • 40
    • 77953136599 scopus 로고    scopus 로고
    • Continuity of solutions to discrete fractional initial value problems
    • C.S. Goodrich Continuity of solutions to discrete fractional initial value problems Comput. Math. Appl. 59 2010 3489 3499
    • (2010) Comput. Math. Appl. , vol.59 , pp. 3489-3499
    • Goodrich, C.S.1
  • 41
    • 77953688007 scopus 로고    scopus 로고
    • Existence of a positive solution to a class of fractional differential equations
    • C.S. Goodrich Existence of a positive solution to a class of fractional differential equations Appl. Math. Lett. 23 2010 1050 1055
    • (2010) Appl. Math. Lett. , vol.23 , pp. 1050-1055
    • Goodrich, C.S.1
  • 42
    • 78650178926 scopus 로고    scopus 로고
    • Solutions to a discrete right-focal fractional boundary value problem
    • (in press)
    • C.S. Goodrich, Solutions to a discrete right-focal fractional boundary value problem, Int. J. Difference. Equ. 5 (2010) (in press).
    • (2010) Int. J. Difference. Equ. , vol.5
    • Goodrich, C.S.1
  • 43
    • 79953294826 scopus 로고    scopus 로고
    • On a discrete fractional three-point boundary value problem
    • C.S. Goodrich On a discrete fractional three-point boundary value problem J. Difference Equ. Appl. 2010 10.1080/10236198.2010.503240
    • (2010) J. Difference Equ. Appl.
    • Goodrich, C.S.1
  • 44
    • 85086419235 scopus 로고    scopus 로고
    • Some new existence results for fractional difference equations
    • (in press)
    • C.S. Goodrich, Some new existence results for fractional difference equations, Int. J. Dyn. Syst. Differ. Equ. (in press).
    • Int. J. Dyn. Syst. Differ. Equ.
    • Goodrich, C.S.1
  • 45
    • 77954461528 scopus 로고    scopus 로고
    • Positive solutions for three-point boundary value problems of nonlinear fractional differential equations with p-Laplacian
    • J. Wang, H. Xiang, and Z. Liu Positive solutions for three-point boundary value problems of nonlinear fractional differential equations with p-Laplacian Far East J. Appl. Math. 37 2009 33 47
    • (2009) Far East J. Appl. Math. , vol.37 , pp. 33-47
    • Wang, J.1    Xiang, H.2    Liu, Z.3
  • 46
    • 67651094005 scopus 로고    scopus 로고
    • Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation
    • X. Xu, D. Jiang, and C. Yuan Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation Nonlinear Anal. TMA 71 2009 4676 4688
    • (2009) Nonlinear Anal. TMA , vol.71 , pp. 4676-4688
    • Xu, X.1    Jiang, D.2    Yuan, C.3
  • 47
    • 78049333168 scopus 로고    scopus 로고
    • Discrete-time fractional variational problems
    • N.R.O. Bastos Discrete-time fractional variational problems Signal Process. 2010 10.1016/j.sigpro.2010.05.001
    • (2010) Signal Process.
    • Bastos, N.R.O.1
  • 48
    • 77953564728 scopus 로고    scopus 로고
    • Foundations of nabla fractional calculus on time scales and inequalities
    • G.A. Anastassiou Foundations of nabla fractional calculus on time scales and inequalities Comput. Math. Appl. 59 2010 3750 3762
    • (2010) Comput. Math. Appl. , vol.59 , pp. 3750-3762
    • Anastassiou, G.A.1
  • 49
    • 77954861707 scopus 로고    scopus 로고
    • Principles of delta fractional calculus on time scales and inequalities
    • G.A. Anastassiou Principles of delta fractional calculus on time scales and inequalities Math. Comput. Modelling 52 2010 556 566
    • (2010) Math. Comput. Modelling , vol.52 , pp. 556-566
    • Anastassiou, G.A.1


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