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We introduce, in the abstract framework of finite isometry groups on a Hilbert space, a generalization of antiperiodicity called N-cyclicity. The non-existence of N-cyclic solutions of a certain type for the autonomous ODE implies the existence of N different subharmonic solutions for some forced equations of the type where c and ε are some positive constants and f is, for instance, a sinusoidal function. 相似文献
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Rui Wu 《Applied Mathematics Letters》2010,23(9):984-987
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In this paper, we study the existence of periodic solutions of the Liénard equation with a singularity and a deviating argument When has a strong singularity at and satisfies a new small force condition at , we prove that the given equation has at least one positive -periodic solution. 相似文献
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In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form where is a real constant. The results are applicable to well-known Emden–Fowler and Lienard type equations. An illustrative example is also provided. 相似文献
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