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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