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

• Volume: 65, Issue: 3, page 265-270
• ISSN: 0066-2216

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## Abstract

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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, $g\left(s\right)={|s|}^{p-2}s$, 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.

## How to cite

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Daqing Jiang, and Junyu Wang. "A generalized periodic boundary value problem for the one-dimensional p-Laplacian." Annales Polonici Mathematici 65.3 (1997): 265-270. <http://eudml.org/doc/269940>.

@article{DaqingJiang1997,
abstract = {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.},
author = {Daqing Jiang, Junyu Wang},
journal = {Annales Polonici Mathematici},
keywords = {generalized periodic boundary value problem; p-Laplacian; upper and lower solutions; Carathéodory function; Nagumo condition; -Laplacian},
language = {eng},
number = {3},
pages = {265-270},
title = {A generalized periodic boundary value problem for the one-dimensional p-Laplacian},
url = {http://eudml.org/doc/269940},
volume = {65},
year = {1997},
}

TY - JOUR
AU - Daqing Jiang
AU - Junyu Wang
TI - A generalized periodic boundary value problem for the one-dimensional p-Laplacian
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 3
SP - 265
EP - 270
AB - 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.
LA - eng
KW - generalized periodic boundary value problem; p-Laplacian; upper and lower solutions; Carathéodory function; Nagumo condition; -Laplacian
UR - http://eudml.org/doc/269940
ER -

## References

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1. [1] W. J. Gao and J. Y. Wang, On a nonlinear second order periodic boundary value problem with Carathéodory functions, Ann. Polon. Math. 62 (1995), 283-291. Zbl0839.34031
2. [2] J. Y. Wang, W. J. Gao and Z. H. Lin, Boundary value problems for general second order equations and similarity solutions to the Rayleigh problem, Tôhoku Math. J. 47 (1995), 327-344. Zbl0845.34038
3. [3] M. X. Wang, A. Cabada and J. J. Nieto, Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions, Ann. Polon. Math. 58 (1993), 221-235. Zbl0789.34027

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