Periodic solutions for some second order differential equations with singularity

被引：0
作者：
Xiong Li
Ziheng Zhang
机构：
[1] Beijing Normal University,School of Mathematical Sciences
来源：
Zeitschrift für angewandte Mathematik und Physik | 2008年 / 59卷
关键词：
34C15; 34C25; Periodic solutions; singularity; generalized Poincaré–Birkhoff Theorem;
D O I：
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学科分类号：
摘要：
In this paper, we will prove the existence of infinitely many harmonic and subharmonic solutions for the second order differential equation ẍ + g(x) = f(t, x) using the phase plane analysis methods and Poincaré–Birkhoff Theorem, where the nonlinear restoring field g exhibits superlinear conditions near the infinity and strong singularity at the origin, and f(t, x) = a(t)xγ + b(t, x) where 0 ≤ γ ≤ 1 and b(t, x) is bounded.
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页码：400 / 415
页数：15
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