**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.