Yesterday evening I checked at home, the books were by Tichonov and Samarskij … not Tichonov and Kolmogorov, sorry. I agree with you, Kolmogorov was really a great! There are two books by these authors, one is titled “Equation of Math. Phys” by T. and S., the other “A Collection of Problems in Mathematical Physics” by Budak, S. and T. I found these two extremely useful and nice to read, but I was mainly dealing with wave propagation in that period. I love some chapters of the mathematical work of Smirnov, particularly analysis, complex number, linear algebra and group theory, honestly little less the chapters on special functions and PDEs. Bitsadze came with two books, one of PDE and one on problem with PDEs. Michailov and Bitsadze book sound very good at a first glance, but I bought them more recently and didn’t had yet a working practice with them 🙂 … Extremely well done and useful is the book of Kolmogorov of Functional analysis, best coupled with the Trenoguine book on the same issue, it provides much of the useful general framework important for PDEs too. Concerning ODE, apart from the already mentioned books by Arnold (Geometrical methods/Singularities/ODE) I suggest also L. Esgolts (ODE and calculus of variations). Not Russian, :-), but very well done – I used it a lot – the books of M.K.Keane on PDEs. If you are interested also in numerical methods for PDEs … this is another issue … Ciao