We study two nonlinear degenerate eigenvalue problems on $\mathbb R^N$.
For the first problem we prove the existence of a positive
eigenvalue while for the second we show the existence of a
continuous family of eigenvalues. Our approach is based on
standard tools in the critical point theory combined with
adequate variational methods. We also apply an idea developed
recently by Szulkin and Willem.
@article{1126195347,
author = {Mih\u ailescu, Mihai},
title = {Nonlinear eigenvalue problems for some degenerate
elliptic operators on $\mathbb R^N$},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {5},
year = {2005},
pages = { 435-448},
language = {en},
url = {http://dml.mathdoc.fr/item/1126195347}
}
Mihăilescu, Mihai. Nonlinear eigenvalue problems for some degenerate
elliptic operators on $\mathbb R^N$. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp. 435-448. http://gdmltest.u-ga.fr/item/1126195347/