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Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

100%

Wang M.-X., Cabada A., Nieto J.

Annales Polonici Mathematici

1993

tom 58

nr 3

221-235

The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.

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Some remarks on Carathéodory conditions

100%

Shragin I. V.

Commentationes Mathematicae

2005

tom 45

nr 1

Let $(T,\mathcal{T})$ be a measurable space, $X$ and $Y$ be metric spaces. For the maps from $T\times X$ into $Y$ the notions of supmeasurability, standardness and Carathéodory conditions are considered, and the logical relations between these notions are discussed.

A generalized periodic boundary value problem for the one-dimensional p-Laplacian

88%

Jiang D., Wang J.

Annales Polonici Mathematici

1996-1997

tom 65

nr 3

265-270

The generalized periodic boundary value problem -[g(u')]' = f(t,u,u'), a < t < b, with u(a) = ξu(b) + c and u'(b) = ηu'(a) is studied by using the generalized method of upper and lower solutions, where ξ,η ≥ 0, a, b, c are given real numbers, $g(s) = |s|^{p-2} s$, p > 1, and f is a Carathéodory function satisfying a Nagumo condition. The problem has a solution if and only if there exists a lower solution α and an upper solution β with α(t) ≤ β(t) for a ≤ t ≤ b.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Commentationes Mathematicae

1 Cabada A.

1 Jiang D.

1 Nieto J.

1 Shragin I. V.

1 Wang J.

1 Wang M.-X.

1 2005

1 1997

1 1993

Wyniki wyszukiwania

Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

Some remarks on Carathéodory conditions

A generalized periodic boundary value problem for the one-dimensional p-Laplacian