# Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

Annales Polonici Mathematici (1998)

- Volume: 69, Issue: 3, page 265-270
- ISSN: 0066-2216

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topLingbin Kong, and Daqing Jiang. "Multiple positive solutions of a nonlinear fourth order periodic boundary value problem." Annales Polonici Mathematici 69.3 (1998): 265-270. <http://eudml.org/doc/270758>.

@article{LingbinKong1998,

abstract = {The fourth order periodic boundary value problem $u^\{(4)\} - m⁴u + F(t,u) = 0$, 0 < t < 2π, with $u^\{(i)\}(0) = u^\{(i)\}(2π)$, i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of $±10^\{-7\}$.},

author = {Lingbin Kong, Daqing Jiang},

journal = {Annales Polonici Mathematici},

keywords = {nonlinear periodic boundary value problem; multiple positive solutions; cone; fixed point index; fourth-order periodic boundary value problem; positive solutions},

language = {eng},

number = {3},

pages = {265-270},

title = {Multiple positive solutions of a nonlinear fourth order periodic boundary value problem},

url = {http://eudml.org/doc/270758},

volume = {69},

year = {1998},

}

TY - JOUR

AU - Lingbin Kong

AU - Daqing Jiang

TI - Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

JO - Annales Polonici Mathematici

PY - 1998

VL - 69

IS - 3

SP - 265

EP - 270

AB - The fourth order periodic boundary value problem $u^{(4)} - m⁴u + F(t,u) = 0$, 0 < t < 2π, with $u^{(i)}(0) = u^{(i)}(2π)$, i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of $±10^{-7}$.

LA - eng

KW - nonlinear periodic boundary value problem; multiple positive solutions; cone; fixed point index; fourth-order periodic boundary value problem; positive solutions

UR - http://eudml.org/doc/270758

ER -

## References

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- [5] D. Q. Jiang and J. Y. Wang, A generalized periodic boundary value problem for the one-dimensional p-Laplacian, Ann. Polon. Math. 65 (1997), 265-270. Zbl0868.34015
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