The existence of periodic solutions of the quasilinear ordinary differential equation egin{equation} -Big(rac{ u'}{sqrt{1-u'^2}}Big)'=f(t,u,u'), end{equation} which models an oscillator with relativistic acceleration, is proven in the presence of a couple of lower and upper solutions satisfying or not satisfying the standard ordering condition. The proof is based on a simple trick which allows to reduce the quasilinear singular equation to a semilinear one.
A remark on the lower and upper solution method for quasilinear equations modeling relativistic oscillators
omari, pierpaolo
2013-01-01
Abstract
The existence of periodic solutions of the quasilinear ordinary differential equation egin{equation} -Big(rac{ u'}{sqrt{1-u'^2}}Big)'=f(t,u,u'), end{equation} which models an oscillator with relativistic acceleration, is proven in the presence of a couple of lower and upper solutions satisfying or not satisfying the standard ordering condition. The proof is based on a simple trick which allows to reduce the quasilinear singular equation to a semilinear one.File in questo prodotto:
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