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• W3005970211 abstract "The paper deals with the singular differential equation x′′+g(x)=p(t), where g has a weak singularity at x=0. Sufficient conditions for a coexistence of two types of periodic solutions are presented. The first type is a classical periodic solution which is strictly positive on R and does not reach the singularity. The second type is a bouncing periodic solution which reaches the singularity at isolated points. In particular, we state a constant K>0 such that there exist at least two 2π-periodic bouncing solutions having their maximum less than K and at least one 2π-periodic classical solution having its minimum greater than K. The proofs are based on the ideas of the Poincaré–Birkhoff Twist Map Theorem and approximation principles." @default.
• W3005970211 created "2020-02-24" @default.
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• W3005970211 date "2020-07-01" @default.
• W3005970211 modified "2023-10-16" @default.
• W3005970211 title "Coexistence of bouncing and classical periodic solutions of generalized Lazer–Solimini equation" @default.
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• W3005970211 doi "https://doi.org/10.1016/j.na.2020.111783" @default.
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