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.