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

Volume 65 / 1997

Daqing Jiang, Junyu Wang Annales Polonici Mathematici 65 (1997), 265-270 DOI: 10.4064/ap-65-3-265-270


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.


  • Daqing Jiang
  • Junyu Wang

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