Geodesic
Localization of nonsmooth lower and upper functions for periodic boundary value problems
Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 531-545.

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In this paper we present conditions ensuring the existence and localization of lower and upper functions of the periodic boundary value problem $u^{\prime \prime }+k\,u=f(t,u)$, $ u(0)=u(2\,\pi )$, $u^{\prime }(0)=u^{\prime }(2\pi )$, $k\in \mathbb{R}\hspace{0.56905pt}$, $k\ne 0.$ These functions are constructed as solutions of some related generalized linear problems and can be nonsmooth in general.
DOI : 10.21136/MB.2002.133955
Classification : 34B15, 34C25
Keywords: second order nonlinear ordinary differential equation; periodic problem; lower and upper functions; generalized linear differential equation 
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     title = {Localization of nonsmooth lower and upper functions for periodic boundary value problems},
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Rachůnková, Irena; Tvrdý, Milan. Localization of nonsmooth lower and upper functions for periodic boundary value problems. Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 531-545. doi : 10.21136/MB.2002.133955. http://geodesic.mathdoc.fr/articles/10.21136/MB.2002.133955/

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