摘要
针对摆型振动模型中的数学问题,分别采用上下解方法、单调迭代法及Schauder不动点定理研究了摆型振动模型的二阶半线性微分方程奇调和解的存在性。证明结果和实例表明,该奇调和解问题中至少存在一个奇性解。
Aimed at the mathematic problem in the model of the pendulum oscillation, the paper introduces the study on the existence of odd-harmonic solutions to second order semi-linear differential equation which describes the model of the pendulum oscillation by using upper and lower solution method monotone iterative technique and the Schauder fixed point theorem respectively. The results and the practical example show the existence of at least one odd solution to the odd-harmonic problem.
出处
《黑龙江科技学院学报》
CAS
2007年第5期389-393,共5页
Journal of Heilongjiang Institute of Science and Technology
关键词
摆型振动方程
奇调和解
上下解方法
单调迭代法
SCHAUDER不动点定理
pendulum oscillation equation
odd-harmonic solution
upper and lower solution method
monotone iterative technique
Schauder fixed point theorem
