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Zbl 1157.34310
Minhós, F.; l Gyulov, T.; Santos, A.I.
Existence and location result for a fourth order boundary value problem. (English)
[J] Discrete Contin. Dyn. Syst. 2005, Suppl., 662-671 (2005). ISSN 1078-0947; ISSN 1553-5231/e

Summary: We prove an existence and location result for the fourth order nonlinear equation $$u^{(i \upsilon)} = f(t, u, u', u'', u'''),\quad 0 < t < 1,$$ with the Lidstone boundary conditions $$u(0) = u''(0) = u(1) = u''(1) = 0,$$ where $f: [0,1] \times \Bbb{R}^{4} \to \Bbb R$ is a continuous function satisfying a Nagumo type condition. The existence of at least one solution lying between a pair of well ordered lower and upper solutions is obtained by using an a priori estimate, lower and upper solutions method and degree theory.

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE

Keywords: fourth order boundary value problem; Nagumo condition; a priori estimate; a pair of lower and upper solutions; degree theory

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