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Volumn 217, Issue 9, 2011, Pages 4740-4753

Existence of a positive solution to a system of discrete fractional boundary value problems

Author keywords

Cone; Coupled system of boundary value problems; Discrete fractional calculus; Eigenvalues; Positive solution

Indexed keywords

COUPLED SYSTEMS; EIGENVALUES; FRACTIONAL CALCULUS; FUNCTIONALS; NEW RESULTS; NON-LOCAL BOUNDARY CONDITIONS; ORDER BOUNDARIES; POSITIVE SOLUTION; SYSTEM OF EQUATIONS;

EID: 78650170131     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.11.029     Document Type: Article
Times cited : (118)

References (41)
  • 1
    • 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. London Math. Soc. 74 2 2006 673 693
    • (2006) J. London Math. Soc. , vol.74 , Issue.2 , pp. 673-693
    • Infante, G.1    Webb, J.R.L.2
  • 2
    • 70449397020 scopus 로고    scopus 로고
    • Positive solutions for systems of nonlinear discrete boundary value problems
    • J. Henderson, S.K. Ntouyas, and I.K. Purnaras Positive solutions for systems of nonlinear discrete boundary value problems J. Differ. Equat. Appl. 15 2009 895 912
    • (2009) J. Differ. Equat. Appl. , vol.15 , pp. 895-912
    • Henderson, J.1    Ntouyas, S.K.2    Purnaras, I.K.3
  • 3
    • 55649098198 scopus 로고    scopus 로고
    • Boundary value problem for a coupled system of nonlinear fractional differential equations
    • X. Su Boundary value problem for a coupled system of nonlinear fractional differential equations Appl. Math. Lett. 22 2009 64 69
    • (2009) Appl. Math. Lett. , vol.22 , pp. 64-69
    • Su, X.1
  • 4
    • 0036698158 scopus 로고    scopus 로고
    • Solutions to second-order three-point problems on time scales
    • D.R. Anderson Solutions to second-order three-point problems on time scales J. Differ. Equat. Appl. 8 2002 673 688
    • (2002) J. Differ. Equat. Appl. , vol.8 , pp. 673-688
    • Anderson, D.R.1
  • 5
    • 22344455360 scopus 로고    scopus 로고
    • Positive solutions for a nonlinear functional dynamic equation on a time scale
    • E.R. Kaufmann, and Y.N. Raffoul Positive solutions for a nonlinear functional dynamic equation on a time scale Nonlinear Anal. TMA 62 2005 1267 1276
    • (2005) Nonlinear Anal. TMA , vol.62 , pp. 1267-1276
    • Kaufmann, E.R.1    Raffoul, Y.N.2
  • 6
    • 33847653855 scopus 로고    scopus 로고
    • Multiple positive solutions for discrete nonlocal boundary value problems
    • W. Cheung, J. Ren, P.J.Y. Wong, and D. Zhao Multiple positive solutions for discrete nonlocal boundary value problems J. Math. Anal. Appl. 330 2007 900 915
    • (2007) J. Math. Anal. Appl. , vol.330 , pp. 900-915
    • Cheung, W.1    Ren, J.2    Wong, P.J.Y.3    Zhao, D.4
  • 7
    • 0010709267 scopus 로고    scopus 로고
    • A coupled system of difference equations
    • R. Agarwal, and D. O'Regan A coupled system of difference equations Appl. Math. Comput. 114 2000 39 49
    • (2000) Appl. Math. Comput. , vol.114 , pp. 39-49
    • Agarwal, R.1    O'Regan, D.2
  • 8
    • 45949092930 scopus 로고    scopus 로고
    • Existence of solutions for first-order multi-point problems with changing-sign nonlinearity
    • D.R. Anderson Existence of solutions for first-order multi-point problems with changing-sign nonlinearity J. Differ. Equat. Appl. 14 2008 657 666
    • (2008) J. Differ. Equat. Appl. , vol.14 , pp. 657-666
    • Anderson, D.R.1
  • 9
    • 0035426483 scopus 로고    scopus 로고
    • Twin solutions of boundary value problems for ordinary differential equations and finite difference equations
    • R.I. Avery, and J. Henderson Twin solutions of boundary value problems for ordinary differential equations and finite difference equations Comput. Math. Appl. 42 2001 695 704
    • (2001) Comput. Math. Appl. , vol.42 , pp. 695-704
    • Avery, R.I.1    Henderson, J.2
  • 10
    • 0038473454 scopus 로고    scopus 로고
    • Double symmetric solutions for discrete Lidstone boundary value problems
    • J. Henderson, and P.J.Y. Wong Double symmetric solutions for discrete Lidstone boundary value problems J. Differ. Equat. Appl. 7 2001 811 828
    • (2001) J. Differ. Equat. Appl. , vol.7 , pp. 811-828
    • Henderson, J.1    Wong, P.J.Y.2
  • 11
    • 0742306107 scopus 로고    scopus 로고
    • Positive solutions of three-point nonlinear discrete second order boundary value problem
    • R. Ma, and Y.N. Raffoul Positive solutions of three-point nonlinear discrete second order boundary value problem J. Differ. Equat. Appl. 10 2004 129 138
    • (2004) J. Differ. Equat. Appl. , vol.10 , pp. 129-138
    • Ma, R.1    Raffoul, Y.N.2
  • 12
    • 45849088847 scopus 로고    scopus 로고
    • Positive solutions to nonlinear second-order three-point boundary-value problems for difference equation with change of sign
    • C. Wang, X. Han, and C. Li Positive solutions to nonlinear second-order three-point boundary-value problems for difference equation with change of sign Electon. J. Differ. Eqs. 87 2008 10
    • (2008) Electon. J. Differ. Eqs. , Issue.87 , pp. 10
    • Wang, C.1    Han, X.2    Li, C.3
  • 13
    • 36348980591 scopus 로고    scopus 로고
    • Existence of positive solutions for second-order m-point boundary value problems on time scales
    • P. Wang, and Y. Wang Existence of positive solutions for second-order m-point boundary value problems on time scales Acta Mathmeticae Applicatae Sinica, English Series 22 2006 457 468
    • (2006) Acta Mathmeticae Applicatae Sinica, English Series , vol.22 , pp. 457-468
    • Wang, P.1    Wang, Y.2
  • 14
    • 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
  • 15
    • 71649104924 scopus 로고    scopus 로고
    • Fractional order differential equations on an unbounded domain
    • A. Arara Fractional order differential equations on an unbounded domain Nonlinear Anal. TMA 72 2010 580 586
    • (2010) Nonlinear Anal. TMA , vol.72 , pp. 580-586
    • Arara, A.1
  • 16
    • 0038405057 scopus 로고    scopus 로고
    • Existence of positive solutions of nonlinear fractional differential equations
    • A. Babakhani, and V. Daftardar-Gejji Existence of positive solutions of nonlinear fractional differential equations J. Math. Anal. Appl. 278 2003 434 442
    • (2003) J. Math. Anal. Appl. , vol.278 , pp. 434-442
    • Babakhani, A.1    Daftardar-Gejji, V.2
  • 17
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equation
    • Z. Bai, and H. Lü 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    Lü, H.2
  • 18
    • 69549097929 scopus 로고    scopus 로고
    • Generalized monotone method for periodic boundary value problems of Caputo fractional differential equation
    • J.V. Devi Generalized monotone method for periodic boundary value problems of Caputo fractional differential equation Commun. Appl. Anal. 12 2008 399 406
    • (2008) Commun. Appl. Anal. , vol.12 , pp. 399-406
    • Devi, J.V.1
  • 19
    • 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
  • 20
    • 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
  • 21
    • 77950866104 scopus 로고    scopus 로고
    • Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
    • A. Malinowska, and D.F.M. Torres Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative Comput. Math. Appl. 59 2010 3110 3116
    • (2010) Comput. Math. Appl. , vol.59 , pp. 3110-3116
    • Malinowska, A.1    Torres, D.F.M.2
  • 22
    • 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
  • 23
    • 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 3 2007 333 344
    • (2007) J. Nonlinear Math. Phys. , vol.14 , Issue.3 , pp. 333-344
    • Atici, F.M.1    Eloe, P.W.2
  • 24
    • 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. Differ. Equat. 2 2 2007 165 176
    • (2007) Int. J. Differ. Equat. , vol.2 , Issue.2 , pp. 165-176
    • Atici, F.M.1    Eloe, P.W.2
  • 25
    • 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 3 2009 981 989
    • (2009) Proc. Amer. Math. Soc. , vol.137 , Issue.3 , pp. 981-989
    • Atici, F.M.1    Eloe, P.W.2
  • 26
    • 79953286192 scopus 로고    scopus 로고
    • Two-point boundary value problems for finite fractional difference equations
    • in press
    • F.M. Atici, P.W. Eloe, Two-point boundary value problems for finite fractional difference equations, J. Differ. Equat. Appl., in press, doi:10.1080/10236190903029241.
    • J. Differ. Equat. Appl.
    • Atici, F.M.1    Eloe, P.W.2
  • 27
    • 77952557731 scopus 로고    scopus 로고
    • Modeling with fractional difference equations
    • F.M. Atici, S. engül, Modeling with fractional difference equations, J. Math. Anal. Appl., 2010, doi:10.1016/j.jmaa.2010.02.009.
    • (2010) J. Math. Anal. Appl.
    • Atici, F.M.1
  • 28
    • 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
  • 29
    • 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. Differ. Equat. 5 (2010), in press.
    • (2010) Int. J. Differ. Equat. , vol.5
    • Goodrich, C.S.1
  • 30
    • 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. Differ. Equat. Appl., doi:10.1080/10236198.2010.503240.
    • J. Differ. Equat. Appl.
    • Goodrich, C.S.1
  • 31
    • 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. Equat., in press.
    • Int. J. Dyn. Syst. Differ. Equat.
    • Goodrich, C.S.1
  • 32
    • 78651230726 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
    • C.S. Goodrich, Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions, Comput. Math. Appl., doi:10.1016/j.camwa.2010.10.041.
    • Comput. Math. Appl.
    • Goodrich, C.S.1
  • 35
    • 78049333168 scopus 로고    scopus 로고
    • Discrete-time fractional variational problems
    • N.R.O. Bastos, et al., Discrete-time fractional variational problems, Signal Process., 2010, doi:10.1016/j.sigpro.2010.05.001.
    • (2010) Signal Process.
    • Bastos, N.R.O.1
  • 36
    • 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. Model. 52 2010 556 566
    • (2010) Math. Comput. Model. , vol.52 , pp. 556-566
    • Anastassiou, G.A.1
  • 38
    • 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
  • 39
    • 0031281241 scopus 로고    scopus 로고
    • Existence and multiplicity of positive solutions for elliptic systems
    • D. Dunninger, and H. Wang Existence and multiplicity of positive solutions for elliptic systems Nonlinear Anal. TMA 29 1997 1051 1060
    • (1997) Nonlinear Anal. TMA , vol.29 , pp. 1051-1060
    • Dunninger, D.1    Wang, H.2
  • 41
    • 0036567685 scopus 로고    scopus 로고
    • Existence of multiple solutions for second-order discrete boundary value problems
    • J. Henderson, and H.B. Thompson Existence of multiple solutions for second-order discrete boundary value problems Comput. Math. Appl. 43 2002 1239 1248
    • (2002) Comput. Math. Appl. , vol.43 , pp. 1239-1248
    • Henderson, J.1    Thompson, H.B.2


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