Boundedness of semilinear Duffing equations with singularity |
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| Authors: | Xiumei Xing Lei Jiao |
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| Institution: | 1. School of Mathematics and Statistics, YiLi Normal University, Yining 835000, China2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China |
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| Abstract: | We prove the boundedness of all solutions for the equation x″ + V′(x) = DxG(x, t), where V(x) is of singular potential, i.e., limx→-1V(x) = +∞, and G(x, t) is bounded and periodic in t. We give sufficient conditions on V(x) and G(x, t) to ensure that all solutions are bounded. |
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| Keywords: | Hamiltonian system repulsive singularity boundedness ofsolutions canonical transformation Moser＇s small twist theorem |
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