The spectrum of the periodic p-Laplacian

We consider one-dimensional p-Laplacian eigenvalue problems of the form together with periodic or separated boundary conditions, where p>1, Δp is the p-Laplacian, q C1[0,b], and b>0, . It will be shown that when p≠2, the structure of the spectrum in the general periodic case (that is, with q≠0 and periodic boundary conditions), can be completely different from those of the following known cases: (i) the general periodic case with p=2, (ii) the periodic case with p≠2 and q=0, and (iii) the general separated case with any p>1.