6th Summer Workshop on Operator Theory

9th - 13th July 2018 Kraków

Bruce Watson

The one-dimensional p-Laplacian with indefinite weight
Eigenvalue problems for the one dimensional p-Laplacian on a finite interval,

(|y'(x)|p-1 sgn y'(x))‘=(p-1)(λr(x)-q(x))|y(x)|p-1 sgn y(x),

for 1<p<∞, will be considered.
Here we allow the weight r to be locally integrable and indefinite.
Prüfer angle and variational techniques are used.
The above considerations leads naturally to the definition and study of the complex p-Laplacian, and the exploration of the Jordan structure of the eigenspaces for this non-linear problem.

This talk is based on joint work with Paul Binding and Patrick Browne.

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