Periodic impact behavior of a class of Hamiltonian oscillators with obstacles (Q847750)
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scientific article; zbMATH DE number 5673255
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| English | Periodic impact behavior of a class of Hamiltonian oscillators with obstacles |
scientific article; zbMATH DE number 5673255 |
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Periodic impact behavior of a class of Hamiltonian oscillators with obstacles (English)
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19 February 2010
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The paper proves the existence of infinitely many periodic and subharmonic solutions of the equation \[ -x''=q(x)|x'|^2+g(t)x'+f(t) \] with an elastic impact condition in \(0\). The proof uses a change of variables which transform the equation into a new one with a superlinear nonlinearity, then the Poincaré-Birkhoff twist theorem in the version of Ding can be applied. Previous results by X. Wu are improved.
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non-smooth Hamiltonian oscillators
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periodic bouncing solutions
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Poincaré-Birkhoff twist theorem
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impact behavior
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