Geodesic
A generalized periodic boundary value problem for the one-dimensional p-Laplacian
Annales Polonici Mathematici, Tome 65 (1996) no. 3, pp. 265-270.

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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.
DOI : 10.4064/ap-65-3-265-270
Keywords: generalized periodic boundary value problem, p-Laplacian, upper and lower solutions, Carathéodory function, Nagumo condition

Daqing Jiang 1 ; Junyu Wang 1

1 
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Daqing Jiang; Junyu Wang. A generalized periodic boundary value problem for the one-dimensional p-Laplacian. Annales Polonici Mathematici, Tome 65 (1996) no. 3, pp. 265-270. doi : 10.4064/ap-65-3-265-270. http://geodesic.mathdoc.fr/articles/10.4064/ap-65-3-265-270/

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