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Title: Resonance and multiplicity in periodic boundary value problems with singularity  (English)
Author: Rachůnková, Irena
Author: Tvrdý, Milan
Author: Vrkoč, Ivo
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 128
Issue: 1
Year: 2003
Pages: 45-70
Summary lang: English
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Category: math
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Summary: The paper deals with the boundary value problem \[ u^{\prime \prime }+k\,u=g(u)+e(t),\quad u(0)=u(2\pi ),\,\,u^{\prime }(0)=u^{\prime }(2\pi ), \] where $k\in \mathbb{R}$, $g\:I\mapsto \mathbb{R}$ is continuous, $e\in \mathbb{L}J$ and $\lim _{x\rightarrow 0+}\int _x^1g(s)\,\hspace{0.56905pt}\text{d}s=\infty .$ In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.
Keyword: second order nonlinear ordinary differential equation
Keyword: periodic problem
Keyword: lower and upper functions
MSC: 34B15
MSC: 34C25
idZBL: Zbl 1023.34015
idMR: MR1973424
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Date available: 2009-09-24T22:06:52Z
Last updated: 2012-06-18
Stable URL: http://hdl.handle.net/10338.dmlcz/133937
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