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Volumn 16, Issue 4, 2007, Pages 743-754

Upper and lower solutions method and a superlinear singular discrete boundary value problem

Author keywords

Singular discrete boundary value problem; Upper and lower solutions

Indexed keywords


EID: 37249048439     PISSN: 10562176     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (6)

References (47)
  • 2
    • 0030595241 scopus 로고    scopus 로고
    • Singular boundary value problems for superlinear second ordinary and delay differential equations
    • R. P. Agarwal and D. O'Regan, Singular boundary value problems for superlinear second ordinary and delay differential equations, J. Differential Equations 130(1996), 335-355.
    • (1996) J. Differential Equations , vol.130 , pp. 335-355
    • Agarwal, R.P.1    O'Regan, D.2
  • 3
    • 0001711641 scopus 로고    scopus 로고
    • Nonlinear superlinear singular and nonsingular second order boundary value problems
    • R. P. Agarwal and D. O'Regan, Nonlinear superlinear singular and nonsingular second order boundary value problems, J. Differential Equations 143(1998), 60-95.
    • (1998) J. Differential Equations , vol.143 , pp. 60-95
    • Agarwal, R.P.1    O'Regan, D.2
  • 4
    • 0038349293 scopus 로고    scopus 로고
    • Singular discrete (n,p) boundary value problems
    • R. P. Agarwal and D. O'Regan, Singular discrete (n,p) boundary value problems, Appl. Math. Lett. 12(1999), 113-119.
    • (1999) Appl. Math. Lett , vol.12 , pp. 113-119
    • Agarwal, R.P.1    O'Regan, D.2
  • 5
    • 0041184915 scopus 로고    scopus 로고
    • Singular discrete boundary value problems
    • R. P. Agarwal and D. O'Regan, Singular discrete boundary value problems, Appl. Math. Lett. 12(1999), 127-131.
    • (1999) Appl. Math. Lett , vol.12 , pp. 127-131
    • Agarwal, R.P.1    O'Regan, D.2
  • 6
    • 0033131620 scopus 로고    scopus 로고
    • Multiple solutions for higher-order difference equations
    • R. P. Agarwal and D. O'Regan, Multiple solutions for higher-order difference equations, Computers Math. Applic. 37(1999), 39-48.
    • (1999) Computers Math. Applic , vol.37 , pp. 39-48
    • Agarwal, R.P.1    O'Regan, D.2
  • 7
    • 0034301909 scopus 로고    scopus 로고
    • Singular initial and boundary value problems with sign changing nonlinearities
    • R. P. Agarwal and D. O'Regan, Singular initial and boundary value problems with sign changing nonlinearities, IMA J. Appl. Math. 65(2000), 173-198.
    • (2000) IMA J. Appl. Math , vol.65 , pp. 173-198
    • Agarwal, R.P.1    O'Regan, D.2
  • 9
    • 0000908808 scopus 로고    scopus 로고
    • Upper and lower solutions method for higher-order discrete boundary value problems
    • R. P. Agarwal and F. Wong, Upper and lower solutions method for higher-order discrete boundary value problems, Math. Inequal. Appl. 1(1998), 551-557.
    • (1998) Math. Inequal. Appl , vol.1 , pp. 551-557
    • Agarwal, R.P.1    Wong, F.2
  • 10
    • 0005247575 scopus 로고    scopus 로고
    • Positive solutions for nonlinear singular boundary value problems
    • R. P. Agarwal, F. Wong and W. Lian, Positive solutions for nonlinear singular boundary value problems, Appl. Math. Lett. 12(1999), 115-120.
    • (1999) Appl. Math. Lett , vol.12 , pp. 115-120
    • Agarwal, R.P.1    Wong, F.2    Lian, W.3
  • 11
    • 0000267528 scopus 로고
    • Solvability of some nonlinear boundary value problems
    • L. E. Bobisud, D. O'Regan and W. D. Royalty, Solvability of some nonlinear boundary value problems, Nonlinear Anal. 12(1988), 855-869.
    • (1988) Nonlinear Anal , vol.12 , pp. 855-869
    • Bobisud, L.E.1    O'Regan, D.2    Royalty, W.D.3
  • 12
    • 0034216263 scopus 로고    scopus 로고
    • Optimal existence results for nth order periodic boundary difference equations
    • A. Cabada and V. Otero-Espinar, Optimal existence results for nth order periodic boundary difference equations, J. Math. Anal. Appl. 247(2000), 67-86.
    • (2000) J. Math. Anal. Appl , vol.247 , pp. 67-86
    • Cabada, A.1    Otero-Espinar, V.2
  • 13
    • 0017982184 scopus 로고
    • Some singular nonlinear differential equations arising in boundary layer theory
    • A. Callegari and A. Nachman, Some singular nonlinear differential equations arising in boundary layer theory, J. Math. Anal. Appl. 64(1978), 96-105.
    • (1978) J. Math. Anal. Appl , vol.64 , pp. 96-105
    • Callegari, A.1    Nachman, A.2
  • 14
    • 0003504382 scopus 로고    scopus 로고
    • An Introduction to Difference Equations
    • Springer-Verlag, New York
    • S. N. Elaydi, An Introduction to Difference Equations, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1996.
    • (1996) Undergraduate Texts in Mathematics
    • Elaydi, S.N.1
  • 15
    • 84974274902 scopus 로고
    • Radially symmetric solutions of a class of singular elliptic equations
    • J. A. Gatica, G. E. Hernandez and P. Waltman, Radially symmetric solutions of a class of singular elliptic equations, Proc. Edinburgh Math. Soc. 33(1990), 168-180.
    • (1990) Proc. Edinburgh Math. Soc , vol.33 , pp. 168-180
    • Gatica, J.A.1    Hernandez, G.E.2    Waltman, P.3
  • 16
    • 0002123175 scopus 로고
    • Singular nonlinear boundary value problems for second order differential equations
    • J. A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary value problems for second order differential equations, J. Differential Equations 79(1989), 62-78.
    • (1989) J. Differential Equations , vol.79 , pp. 62-78
    • Gatica, J.A.1    Oliker, V.2    Waltman, P.3
  • 17
    • 38249018445 scopus 로고
    • Krasonselskii's Theorem on operators compressing a cone: Application to some singular boundary value problems
    • S. M. Gomes and J. Sprekels, Krasonselskii's Theorem on operators compressing a cone: application to some singular boundary value problems, J. Math. Anal. Appl. 153(1990), 443-459.
    • (1990) J. Math. Anal. Appl , vol.153 , pp. 443-459
    • Gomes, S.M.1    Sprekels, J.2
  • 18
    • 0000911571 scopus 로고
    • Upper and lower solutions for a generalized Emden-Fowler equation
    • P. Habets and F. Zanolin, Upper and lower solutions for a generalized Emden-Fowler equation, J. Math. Anal. Appl. 181(1994), 684-700.
    • (1994) J. Math. Anal. Appl , vol.181 , pp. 684-700
    • Habets, P.1    Zanolin, F.2
  • 19
    • 84972525379 scopus 로고
    • Comparison of eigenvalue for focal point problem for nth order difference equations
    • D. Hankerson and A. C. Peterson, Comparison of eigenvalue for focal point problem for nth order difference equations, Diff. Int. Eq. 3(1990), 363-380.
    • (1990) Diff. Int. Eq , vol.3 , pp. 363-380
    • Hankerson, D.1    Peterson, A.C.2
  • 20
    • 0001091334 scopus 로고
    • Singular boundary value problems for difference equations
    • J. Henderson, Singular boundary value problems for difference equations, Dynam. Systems Appl. 1(1992), 271-282.
    • (1992) Dynam. Systems Appl , vol.1 , pp. 271-282
    • Henderson, J.1
  • 21
    • 0000309339 scopus 로고
    • Singular boundary value problems for higher order difference equations
    • V. Lakshmikantham, ed, Walter de Gruyter
    • J. Henderson, Singular boundary value problems for higher order difference equations, in Proceedings of the First World Congress on Nonlinear Analysts, (V. Lakshmikantham, ed.), Walter de Gruyter, 1994, pp 1139-1150.
    • (1994) Proceedings of the First World Congress on Nonlinear Analysts , pp. 1139-1150
    • Henderson, J.1
  • 22
    • 0000336083 scopus 로고
    • A generalized Emden-Fowler equation with a negative exponent
    • J. Janus and J. Myjak, A generalized Emden-Fowler equation with a negative exponent, Non-linear Anal. 23(1994), 953-970.
    • (1994) Non-linear Anal , vol.23 , pp. 953-970
    • Janus, J.1    Myjak, J.2
  • 23
    • 0034818204 scopus 로고    scopus 로고
    • Upper and lower solutions for a superlinear singular boundary value problem
    • D. Jiang, Upper and lower solutions for a superlinear singular boundary value problem, Computers Math. Applic. 41(2001), 563-569.
    • (2001) Computers Math. Applic , vol.41 , pp. 563-569
    • Jiang, D.1
  • 24
    • 0035452140 scopus 로고    scopus 로고
    • Upper and lower solutions method and a superlinear singular boundary value problem for the one-dimension p-Laplacian
    • D. Jiang, Upper and lower solutions method and a superlinear singular boundary value problem for the one-dimension p-Laplacian, Computers Math. Applic. 42(2001), 927-940.
    • (2001) Computers Math. Applic , vol.42 , pp. 927-940
    • Jiang, D.1
  • 25
    • 0034670596 scopus 로고    scopus 로고
    • Upper and lower solution method and a singular boundary value problem for the one-dimension p-Laplacian
    • D. Jiang and W. Gao, Upper and lower solution method and a singular boundary value problem for the one-dimension p-Laplacian, J. Math. Anal. Appl. 252(2000), 631-648.
    • (2000) J. Math. Anal. Appl , vol.252 , pp. 631-648
    • Jiang, D.1    Gao, W.2
  • 26
    • 0002448224 scopus 로고    scopus 로고
    • On the existence of nonnegative radial solutions for the one-dimensional p-Laplacian elliptic systems
    • D. Jiang and H. Liu, On the existence of nonnegative radial solutions for the one-dimensional p-Laplacian elliptic systems, Ann. Polon. Math. 71(1999), 19-29.
    • (1999) Ann. Polon. Math , vol.71 , pp. 19-29
    • Jiang, D.1    Liu, H.2
  • 28
    • 84954810567 scopus 로고
    • Two positive solutions of a boundary value problems for difference equations
    • F. Merdivenci, Two positive solutions of a boundary value problems for difference equations, J. Difference Eq. Appl. 1(1995), 262-270.
    • (1995) J. Difference Eq. Appl , vol.1 , pp. 262-270
    • Merdivenci, F.1
  • 29
    • 0001771783 scopus 로고
    • Green's matrices and positive solution of a discrete boundary value problem
    • F. Merdivenci, Green's matrices and positive solution of a discrete boundary value problem, Panamer. Math. J. 5(1995), 25-42.
    • (1995) Panamer. Math. J , vol.5 , pp. 25-42
    • Merdivenci, F.1
  • 30
    • 0002265474 scopus 로고
    • Positive solutions for focal point problem 2nth order difference equations
    • F. Merdivenci, Positive solutions for focal point problem 2nth order difference equations, Panamer. Math. J. 5(1995), 71-82.
    • (1995) Panamer. Math. J , vol.5 , pp. 71-82
    • Merdivenci, F.1
  • 31
    • 38249025703 scopus 로고
    • Positive solutions to singular and nonsingular second-order boundary value problems
    • D. O'Regan, Positive solutions to singular and nonsingular second-order boundary value problems, J. Math. Anal. Appl. 142(1989), 40-52.
    • (1989) J. Math. Anal. Appl , vol.142 , pp. 40-52
    • O'Regan, D.1
  • 32
    • 0001662218 scopus 로고
    • Some general existence principles and results for [φ(y′)]′ = q(t)f(t, y, y′), (0 < t < 1)
    • D. O'Regan, Some general existence principles and results for [φ(y′)]′ = q(t)f(t, y, y′), (0 < t < 1), SIAM J. Math. Anal. 24(1993), 648-668.
    • (1993) SIAM J. Math. Anal , vol.24 , pp. 648-668
    • O'Regan, D.1
  • 33
    • 0031185491 scopus 로고    scopus 로고
    • Singular Dirichlet boundary value problems I: Superlinear and nonresonant case
    • 291997, 221-245
    • D. O'Regan, Singular Dirichlet boundary value problems I: superlinear and nonresonant case, Nonlinear Anal. 29(1997), 221-245.
    • Nonlinear Anal
    • O'Regan, D.1
  • 34
    • 0034311538 scopus 로고    scopus 로고
    • Singular problems: An upper and lower solution approach
    • D. O'Regan and R. P. Agarwal, Singular problems: an upper and lower solution approach, J. Math. Anal. Appl. 251(2000), 230-250.
    • (2000) J. Math. Anal. Appl , vol.251 , pp. 230-250
    • O'Regan, D.1    Agarwal, R.P.2
  • 35
    • 49249143125 scopus 로고
    • A nonlinear singular boundary value problem
    • S. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3(1979), 897-904.
    • (1979) Nonlinear Anal , vol.3 , pp. 897-904
    • Taliaferro, S.1
  • 36
    • 0000378652 scopus 로고
    • On positive solutions of singular nonlinear two-point boundary problems
    • J. Wang, On positive solutions of singular nonlinear two-point boundary problems, J. Differential Equations 107(1994), 163-174.
    • (1994) J. Differential Equations , vol.107 , pp. 163-174
    • Wang, J.1
  • 37
    • 0030215022 scopus 로고    scopus 로고
    • A singular boundary value problem for the one-dimensional p-Laplacian
    • J. Wang and W. Gao, A singular boundary value problem for the one-dimensional p-Laplacian, J. Math. Anal. Appl. 201(1996), 851-866.
    • (1996) J. Math. Anal. Appl , vol.201 , pp. 851-866
    • Wang, J.1    Gao, W.2
  • 38
    • 84972576250 scopus 로고
    • Boundary value problems for general second order equations and similarity solutions to the Rayleigh problem
    • J. Wang, W. Gao and Z. Lin, Boundary value problems for general second order equations and similarity solutions to the Rayleigh problem, Tohoku Math. J. 47(1995), 327-344.
    • (1995) Tohoku Math. J , vol.47 , pp. 327-344
    • Wang, J.1    Gao, W.2    Lin, Z.3
  • 39
    • 0031172976 scopus 로고    scopus 로고
    • A unified approach to some two-point, three-point and four-point boundary value problems with Caratheodory functions
    • J. Wang and D. Jiang, A unified approach to some two-point, three-point and four-point boundary value problems with Caratheodory functions, J. Math. Anal. Appl. 211(1997). 223-232.
    • (1997) J. Math. Anal. Appl , vol.211 , pp. 223-232
    • Wang, J.1    Jiang, D.2
  • 40
    • 0000090318 scopus 로고
    • The existence of positive solutions to a singular nonlinear boundary value problem
    • J. Wang and J. Jiang, The existence of positive solutions to a singular nonlinear boundary value problem, J. Math. Anal. Appl. 176(1993), 322-329.
    • (1993) J. Math. Anal. Appl , vol.176 , pp. 322-329
    • Wang, J.1    Jiang, J.2
  • 41
    • 0030258083 scopus 로고    scopus 로고
    • Double positive solutions of (n,p) boundary value problems for higher order difference equations
    • P. J. Wong and R. P. Agarwal, Double positive solutions of (n,p) boundary value problems for higher order difference equations, Computers Math. Applic. 32(1996), 1-21.
    • (1996) Computers Math. Applic , vol.32 , pp. 1-21
    • Wong, P.J.1    Agarwal, R.P.2
  • 42
    • 0000737204 scopus 로고    scopus 로고
    • Eigenvalues of boundary value problems for higher order difference equations
    • P. J. Wong and R. P. Agarwal, Eigenvalues of boundary value problems for higher order difference equations, Math. Prob. Engineering 2(1996), 401-434.
    • (1996) Math. Prob. Engineering , vol.2 , pp. 401-434
    • Wong, P.J.1    Agarwal, R.P.2
  • 43
    • 0001395916 scopus 로고    scopus 로고
    • On the existence of positive solutions of higher order difference equations
    • P. J. Wong and R. P. Agarwal, On the existence of positive solutions of higher order difference equations, Topol. Methods Nonlinear Anal. 10(1997), 339-351.
    • (1997) Topol. Methods Nonlinear Anal , vol.10 , pp. 339-351
    • Wong, P.J.1    Agarwal, R.P.2
  • 44
    • 0009459987 scopus 로고    scopus 로고
    • Eigenvalues of an nth order difference equation with (n,p) type conditions
    • P. J. Wong and R. P. Agarwal, Eigenvalues of an nth order difference equation with (n,p) type conditions, Dynam. Contin. Discrete Impuls. Systems 4(1997), 149-172.
    • (1997) Dynam. Contin. Discrete Impuls. Systems , vol.4 , pp. 149-172
    • Wong, P.J.1    Agarwal, R.P.2
  • 45
    • 0030819350 scopus 로고    scopus 로고
    • On the existence of solutions of singular boundary value problems for higher order difference equations
    • P. J. Wong and R. P. Agarwal, On the existence of solutions of singular boundary value problems for higher order difference equations, Nonlinear Anal. 28(1997), 277-287.
    • (1997) Nonlinear Anal , vol.28 , pp. 277-287
    • Wong, P.J.1    Agarwal, R.P.2
  • 46
    • 0032210428 scopus 로고    scopus 로고
    • Extension of continuous and discrete inequalities due to Eloe and Henderson
    • P. J. Wong and R. P. Agarwal, Extension of continuous and discrete inequalities due to Eloe and Henderson, Nonlinear Anal. 34(1998), 479-487.
    • (1998) Nonlinear Anal , vol.34 , pp. 479-487
    • Wong, P.J.1    Agarwal, R.P.2
  • 47
    • 0030380041 scopus 로고    scopus 로고
    • Monotone methods for a discrete boundary value problems
    • W. Zhuang, Y. Chen and S. S. Cheng, Monotone methods for a discrete boundary value problems, Computers Math. Applic. 32(1996), 41-49.
    • (1996) Computers Math. Applic , vol.32 , pp. 41-49
    • Zhuang, W.1    Chen, Y.2    Cheng, S.S.3


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