Extremal solutions of second order nonlinear periodic boundary value problems. (English) Zbl 0723.65056

Cabada, A.; Nieto, Juan J.

Appl. Math. Comput. 40, No. 2, 135-145 (1990).

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 \(u'\).

Reviewer: H.Weber (Wiesbaden)

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations

Keywords:

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

References:

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