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Zbl 0723.65056
Extremal solutions of second order nonlinear periodic boundary value problems.
(English)
[J] Appl. Math. Comput. 40, No.2, 135-145 (1990). ISSN 0096-3003

The authors consider the periodic boundary value problems of the form $- u''(t)=f(t,u(t),u'(t)),\text{ for } a.e.\quad t\in [0,2\pi],\quad u(0)=u(2\pi),$ where f is a Carathéodory function. They develop a monotone method to obtain the existence of extremal solutions between the lower and upper solutions as uniform limit of monotone sequences. This result is a generalization of results earlier obtained by the second author to the case of functions f depending also on $u'$.
MSC 2000:
*65L10 Boundary value problems for ODE (numerical methods)
34B15 Nonlinear boundary value problems of ODE
34C15 Nonlinear oscillations of solutions of ODE

Keywords: monotone iterative method; periodic boundary value problems; extremal solutions; lower and upper solutions

Cited in: Zbl 0866.34037

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