Resonance phenomena for asymmetric weakly nonlinear oscillator  

作　　者：钱定边 

出　　处：《Science China Mathematics》2002年第2期214-222,共9页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 10071055).

摘　　要：We establish the coexistence of periodic solution and unbounded solution, the infinity of largeamplitude subharmonics for asymmetric weakly nonlinear oscillator x' + a2x+ - b2x- + h(x) = p(t) with h(±∞) - 0 and xh(x) → +∞(x →∞), assuming that M(τ ) has zeros which are all simple and M(τ ) 0respectively, where M(τ ) is a function related to the piecewise linear equation x' + a2x+ - b2x- = p(t).We establish the coexistence of periodic solution and unbounded solution, the infinity of large-amplitude subharmonics for asymmetric weakly nonlinear oscillator x″ + a 2 x +— b 2 x - + h(x) = p(t) with h(±∞) = 0 and xh(x) → +∞(x → ∞ ), assuming that M(τ) has zeros which are all simple and M(τ) ≡ 0 respectively, where M(τ) is a function related to the piecewise linear equation x″ + a 2 x +— b 2 x - = p(t).

关 键 词：weakly nonlinearity asymmetric oscillator coexistence of periodic solution and unbounded solution infinity of subharmonic 

分 类 号：O322[理学—一般力学与力学基础]