## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Nonlinear eigenvalue problems for some degenerate elliptic operators on $\mathbb R^N$

Mihai Mihăilescu

#### Abstract

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 information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 3 (2005), 435-448.

Dates
First available in Project Euclid: 8 September 2005

https://projecteuclid.org/euclid.bbms/1126195347

Digital Object Identifier
doi:10.36045/bbms/1126195347

Mathematical Reviews number (MathSciNet)
MR2173705

Zentralblatt MATH identifier
1161.35457

#### Citation

Mihăilescu, Mihai. Nonlinear eigenvalue problems for some degenerate elliptic operators on $\mathbb R^N$. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 3, 435--448. doi:10.36045/bbms/1126195347. https://projecteuclid.org/euclid.bbms/1126195347