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MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 531-545 (2002)
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# Localization of nonsmooth lower and upper functions for periodic boundary value problems

## Irena Rachunkova, Milan Tvrdy

* Irena Rachuu nkova*, Department of Mathematics, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: ` rachunko@risc.upol.cz`

* Milan Tvrdy*, Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: ` tvrdy@math.cas.cz`

**Abstract:**
In this paper we present conditions ensuring the existence and localization of lower and upper functions of the periodic boundary value problem $u"+k u=f(t,u)$, $ u(0)=u(2 \pi )$, $u'(0)=u'(2\pi )$, $k\in \R $, $k\ne 0.$ These functions are constructed as solutions of some related generalized linear problems and can be nonsmooth in general.

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

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

**Full text of the article:**

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