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

100%

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.

On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

100%

Gao W., Wang J.

Annales Polonici Mathematici

1995

tom 62

nr 3

283-291

The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Wang J.

1 Gao W.

1 Jiang D.

1 1997

1 1995

Wyniki wyszukiwania

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

On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions