当前位置: X-MOL 学术J. Differ. Equ. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Linearization and Hölder continuity for nonautonomous systems
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-07-01 , DOI: 10.1016/j.jde.2021.06.035
Lucas Backes , Davor Dragičević , Kenneth J. Palmer

We consider a nonautonomous systemx˙=A(t)x+f(t,x,y),y˙=g(t,y) and give conditions under which there is a transformation of the form H(t,x,y)=(x+h(t,x,y),y) taking its solutions onto the solutions of the partially linearized systemx˙=A(t)x,y˙=g(t,y). Shi and Xiong [28] proved a special case where g(t,y) was a linear function of y and x˙=A(t)x had an exponential dichotomy. Our assumptions on A and f are of the general form considered by Reinfelds and Steinberga [25], which include many of the generalizations of Palmer's theorem proved by other authors. Inspired by the work of Shi and Xiong, we also prove Hölder continuity of H and its inverse in x and y. Again the proofs are given in the context of Reinfelds and Steinberga but we show what the results reduce to when x˙=A(t)x is assumed to have an exponential dichotomy. The paper is concluded with the discrete version of the results.



中文翻译:

非自治系统的线性化和 Hölder 连续性

我们考虑一个非自治系统X˙=一种()X+F(,X,),˙=G(,) 并给出形式发生转变的条件 H(,X,)=(X+H(,X,),) 将其解带到部分线性化系统的解上X˙=一种()X,˙=G(,). Shi and Xiong [28] 证明了一个特例,其中 G(,)y的线性函数,并且X˙=一种()X有指数二分法。我们对Af 的假设是 Reinfelds 和 Steinberga [25] 考虑的一般形式,其中包括其他作者证明的 Palmer 定理的许多推广。受 Shi 和 Xiong 工作的启发,我们还证明了H及其在xy 上的逆的Hölder 连续性。再次证明是在 Reinfelds 和 Steinberga 的上下文中给出的,但我们展示了结果减少到什么时候X˙=一种()X假定具有指数二分法。论文以结果的离散版本结束。

更新日期:2021-07-01
down
wechat
bug