# Resonance and multiplicity in periodic boundary value problems with singularity

Irena Rachůnková; Milan Tvrdý; Ivo Vrkoč

Mathematica Bohemica (2003)

- Volume: 128, Issue: 1, page 45-70
- ISSN: 0862-7959

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topRachůnková, Irena, Tvrdý, Milan, and Vrkoč, Ivo. "Resonance and multiplicity in periodic boundary value problems with singularity." Mathematica Bohemica 128.1 (2003): 45-70. <http://eudml.org/doc/249216>.

@article{Rachůnková2003,

abstract = {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.},

author = {Rachůnková, Irena, Tvrdý, Milan, Vrkoč, Ivo},

journal = {Mathematica Bohemica},

keywords = {second order nonlinear ordinary differential equation; periodic problem; lower and upper functions; second-order nonlinear ordinary differential equation; periodic problem; lower and upper functions},

language = {eng},

number = {1},

pages = {45-70},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Resonance and multiplicity in periodic boundary value problems with singularity},

url = {http://eudml.org/doc/249216},

volume = {128},

year = {2003},

}

TY - JOUR

AU - Rachůnková, Irena

AU - Tvrdý, Milan

AU - Vrkoč, Ivo

TI - Resonance and multiplicity in periodic boundary value problems with singularity

JO - Mathematica Bohemica

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 128

IS - 1

SP - 45

EP - 70

AB - 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.

LA - eng

KW - second order nonlinear ordinary differential equation; periodic problem; lower and upper functions; second-order nonlinear ordinary differential equation; periodic problem; lower and upper functions

UR - http://eudml.org/doc/249216

ER -

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