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

Annales Polonici Mathematici (1997)

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

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topDaqing 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

top- [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] 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] 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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