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Upper and lower solutions method for fourth-order periodic boundary value problems

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EN
Abstrakty
EN
The purpose of this paper is to prove the existence of a solution of the following periodic boundary value problem {u(4)(t) = ∫(t, u(t), u" (t), t ∈ [0, 2π] {u(0) = u(2π]), u' (0) = u' (2π), u" (0) = u' (2π), u''' (2π) in the presence of an upper solution β ≤ α, where ∫(t, u, v) satisfies one side Lipschitz condition.
Wydawca
Rocznik
Strony
53--61
Opis fizyczny
Bibliogr. 18 poz.
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Bibliografia
  • [1] Aftabizadeh, A. R., Existence and uniqueness theorems for fourth-order boundary valu problems, J. Math. Anal. Appl. 116 (1986), 415-426.
  • [2] Cabada, A., The method of lower and upper solutions for second, third, fourth, and higher order boundary value problems, J. Math. Anal. Appl. 185 (1994), 302-320.
  • [3] De Coster, C., Sanchez, L., Upper and lower solutions, Ambrosetti-Prodi problems and positwe solutions for fourth order O.D.E., Riv. Mat. Pura Appl. 14 (1994), 1129-1138.
  • [4] Dunninger, D., Existence of positve solutions for fourth-order nonlinear problems, Boli. Un. Mat. Ital. B (7) 1(4) (1987), 1129-1138.
  • [5] Gao, H., Weng, S., Jiang, D., Hou, X., On second order periodic boundary value problems with upper and lower solutions in the reversed order, Electron. J. Differential Equations 2006(25) (2006), 8 pp.
  • [6] Gupta, C. P., Existence and uniqueness results for a bending of an elastic beam equation at resonance, J. Math. Anal. Appl. 135 (1988), 208-225.
  • [7] Gupta, C. P., Existence and uniqueness theorem for a bending of an elastic beam equation, Appl. Anal. 26 (1988), 289-304.
  • [8] Gupta, C. P., Existence and uniqueness results for some fourth order fully quasilinear boundary value problems, Appl. Anal. 36 (1990), 169-175.
  • [9] Jiang, D. Q., Gao, W. J., Wan, A. Y., A monotone method for constructing extremal solutions to fourth-order periodic boundary value problems, Appl. Math. Comput. 132 (2002), 411-421.
  • [10] Korman, P., A maximum principle for fourth-order ordinary differential equations, Appl. Anal. 33 (1989), 267-273.
  • [11] Ladde, G. S., Lakshmikantham, V., Yatsala, A. S., Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman (Advanced Publishing Program), Boston, MA, 1985.
  • [12] Ma, R. Y., Zhang, J. H., Fu, S. M., The method of lower and upper solutions for fourth-order two-point boundary value problems, J. Math. Anal. Appl. 215 (1997), 415-422.
  • [13] Sadyrabaev, F., A two-point boundary value problem for a fourth-order equation (Russian), Latv. Univ. Zinat Raksti 553 (1990), 84-91.
  • [14] Schroder, J., Fourth-order two-point boundary value problems; estimates by two side bounds, Nonlinear Anal. 8 (1984), 107-114.
  • [15] Seda, V., Nieto, J. J., Gera, M., Periodic boundary value problems for nonlinear higher order ordinary differential equations, Appl. Math. Comput. 48 (1992), 71-82.
  • [16] Usmani, R. A., A uniqueness theorem for a boundary value problem, Proc. Amer. Math. Soc. 77 (1979), 327-335.
  • [17] Wang, H.-Z., Periodic solutions of four-order differential equations (Chinese), Acta Sci. Natur. Univ. Jilin. 4 (1993), 415-422.
  • [18] Yang, Y., Fourth-order two-point boundary value problem, Proc. Amer. Math. Soc. 104 (1988), 175-180.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0004-0005
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