Abstract
Motivated by the Lazer–Solimini equation and the Brillouin equation, which present a repulsive singularity at the origin, we will develop in this paper some criterion for the (positive) periodic solution to be of twist type. As an application of the criterion, we will give also some quantitative estimates to the region of parameters so that the equations have twist periodic solutions. These, together with the Moser Twist Theorem, imply that the equations have rich dynamics in the neighborhood of the twist periodic solutions.
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