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 system and give conditions under which there is a transformation of the form taking its solutions onto the solutions of the partially linearized system Shi and Xiong [28] proved a special case where was a linear function of y and 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 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 并给出形式发生转变的条件 将其解带到部分线性化系统的解上 Shi and Xiong [28] 证明了一个特例,其中 是y的线性函数,并且有指数二分法。我们对A和f 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x和y 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假定具有指数二分法。论文以结果的离散版本结束。