**
MATHEMATICA BOHEMICA, Vol. 128, No. 1, pp. 45-70 (2003)
**

#
Resonance and multiplicity in periodic boundary value problems with singularity

##
Irena Rachunkova, Milan Tvrdy, Ivo Vrkoc

* Irena Rachunkova*, Department of Mathematics, Palacky University, 779 00 Olomouc, Tomkova 40, Czech Republic, e-mail: ` rachunko@risc.upol.cz`; * Milan Tvrdy*, Mathematical Institute, Academy of Sciences of the Czech Republic, 115 67 Praha 1, Zitna 25, Czech Republic, e-mail: ` tvrdy@math.cas.cz`; * Ivo Vrkoc*, Mathematical Institute, Academy of Sciences of the Czech Republic, 115 67 Praha 1, Zitna 25, Czech Republic, e-mail: ` vrkoc@ns.math.cas.cz`

**Abstract:** The paper deals with the boundary value problem

u"+k u=g(u)+e(t),\quad u(0)=u(2\pi), u'(0)=u'(2\pi),

where $k\in\R$, $g \I\mapsto\R$ is continuous, $e\in\LL\J$ and $\lim_{x\to0+}\int_x^1g(s) \dd s=\infty.$ 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.

**Keywords:** second order nonlinear ordinary differential equation, periodic problem, lower and upper functions

**Classification (MSC2000):** 34B15, 34C25

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number] [Journals Homepage]

*
© 2004–2010
FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
*