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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-LOD6-0004-0005

Czasopismo

Journal of Applied Analysis

Tytuł artykułu

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

Autorzy Weng, S.  Gao, H.  Jiang, D.  Hou, X. 
Treść / Zawartość
Warianty tytułu
Języki publikacji 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.
Słowa kluczowe
PL twierdzenie o istnieniu  
EN periodic boundary value problem   existence   upper and lower solutions method  
Wydawca Walter de Gruyter GmbH & Co. KG
Czasopismo Journal of Applied Analysis
Rocznik 2008
Tom Vol. 14, nr 1
Strony 53--61
Opis fizyczny Bibliogr. 18 poz.
Twórcy
autor Weng, S.
autor Gao, H.
autor Jiang, D.
autor Hou, X.
Bibliografia
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[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.
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[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.
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[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.
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