THE SPECTRUM OF THE PERIODIC p-LAPLACIAN
نویسندگان
چکیده
We consider one dimensional p-Laplacian eigenvalue problems of the form −∆pu = (λ− q)|u|p−1sgnu, on (0, b), together with periodic or separated boundary conditions, where p > 1, ∆p is the p-Laplacian, q ∈ C1[0, b], and b > 0, λ ∈ R. It will be shown that when p 6= 2, the structure of the spectrum in the general periodic case (that is, with q 6= 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 6= 2 and q = 0, and (iii) the general separated case with any p > 1.
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