Quasi-periodic solutions for the general semilinear Dung equations with asymmetric nonlinearity and oscillating potential
Quasi-periodic solutions for the general semilinear Dung equations with asymmetric nonlinearity and oscillating potential
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具有非对称非线性和振荡势的一般半线性Dung方程的准周期解
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通讯作者：
Daxiong Piao
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作者：
Xinli Zhang;Yaqun Peng;Daxiong Piao
本文证明了一般半线性拟周期微分方程x′′ +ax+ bx− = Gx（x; t）+f（t）的拟周期解的存在性和所有解的有界性，其中x+ = maxfx; 0 g，. x − = maxfx; 0 g，a和B是两个不同的正常数，f（t）在t上是C39光滑的，G（x; t）在x和t上是C35光滑的，f（t）和G（x; t）在t中具有丢番图频率的准周期性！= (! 1;！2），且Dix.Dj.tG（x; t）.对于0 6 i + j 6 35是有界的.
In this paper, we prove the existence of quasi-periodic solutions and boundeness of all solutions of the.general semilinear quasi-periodic dierential equation x′′ +ax+ bx− = Gx(x; t)+f(t), where x+ = maxfx; 0g,.x− = maxfx; 0g, a and b are two dierent positive constants, f(t) is C39 smooth in t, G(x; t) is C35 smooth in.x and t, f(t) and G(x; t) are quasi-periodic in t with the Diophantine frequency ! = (!1; !2), and Dix.Dj.tG(x; t).is bounded for 0 6 i + j 6 35.