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second order nonlinear ordinary differential equation; periodic problem; lower and upper functions; generalized linear differential equation
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.
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