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| A nonlinearity is said to be {\it singular} if it becomes infinite when the state variable approaches a certain point. Beyond the classical gravitational and electrostatic forces, singular nonlinearities arise in a wide variety of mathematical models in the applied sciences, like Celestial Mechanics, molecular dynamics, matter-state Physics, Fluid Mechanics, vortex dynamics, Mechanical Engineering and more.
The purpose of this talk is to present a general review of some recent advances on the study of this relevant family of mathematical models, with a particular emphasis on open problems. Our interest is focused on the existence and stability of periodic oscillations. |
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