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Jiang, Daqing; Gao, Wenjie; Wan, Aying

A monotone method for constructing extremal solutions to fourth-order periodic boundary value problems. (English) Zbl 1036.34020

Appl. Math. Comput. 132, No. 2-3, 411-421 (2002).
The authors describe a constructive method, which yields two monotone sequences, that converge uniformly to extremal solutions to the periodic boundary value problem \[ u^{(4)}(t)= f(t,u(t), u''(t)),\quad t\in [0,2\pi], \]
\[ u(0)= u(2\pi),\;u'(0)= u'(2\pi),\;u''(0)= u''(2\pi),\;u'''(0)= u'''(2\pi), \] in the presence of an upper solution \(\beta\) and a lower solution \(\alpha\).
The function \(f(t,u,v): [0,2\pi]\times \mathbb{R}\times \mathbb{R}\to \mathbb{R}\) is a Carathéodory function.
Reviewer: Anatolij Ivan Kolosov (Khar’kov)

Cited in 17 Documents

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations

Keywords:

periodic boundary value problem; upper and lower solutions; monotone iterative technique
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\textit{D. Jiang} et al., Appl. Math. Comput. 132, No. 2--3, 411--421 (2002; Zbl 1036.34020)
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References:

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