I would like to ask if anybody knows something about the methods of solving infinite linear autonomous systems of first-order differential (or possibly difference) equations. There is a well-known method for solving finite-dimensional systems based on the computation of eigenvalues of the system matrix. I wonder if something similar can be done also for infinite-dimensional systems. Perhaps there is a method based on spectral theory... I am mainly looking for references to literature. I have found a reference to a Russian book: K.G. Valeev, O.A. Zhautykov, "Infinite systems of differential equations". (this is an English translation of the title) However, I am quite unable to find this book in local libraries, nor to find out what matters are dealt with in it. If anyone knows this book, I would be grateful for any alternative references dealing with similar matters. As well as for any other references.