MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 531-545, 2002

Localization of nonsmooth lower and upper functions for periodic boundary value problems

Irena Rachunkova, Milan Tvrdy

Irena Rachunkova, 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)$, $u'(0)=u'(2\pi)$, $k\in\R$, $k\ne0.$ 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 (MSC 2000): 34B15, 34C25

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