Where to find Periodic Sobolev spaces?

Question

I am interested in periodic travelling waves for the Gross-Pitaevskii equation... so I need to manage with periodic sobolev spaces. Can anyone give me some good references for this?

I have tried with the classical book by H. Brezis but it does not Work with periodic sobolev spaces.

Thanks in advance.

Answer 1

One good reference for periodic Sobolev spaces (and more generally periodic distributions) and their applications to PDEs is the book Fourier Analysis and Partial Differential Equations by Rafael José Iorio, Jr and Valéria de Magalhães Iorio found here.