## Differential and Integral Equations

### On the asymptotic behaviour of the eigenvalues of a Robin problem

#### Abstract

We prove that every eigenvalue of a Robin problem with boundary parameter $\alpha$ on a sufficiently smooth domain behaves asymptotically like $-\alpha^2$ as $\alpha \to \infty$. This generalizes an existing result for the first eigenvalue.

#### Article information

Source
Differential Integral Equations, Volume 23, Number 7/8 (2010), 659-669.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019189

Mathematical Reviews number (MathSciNet)
MR2654263

Zentralblatt MATH identifier
1240.35370

Subjects
Primary: 35P15 35B40 35J05

#### Citation

Daners, Daniel; Kennedy, James B. On the asymptotic behaviour of the eigenvalues of a Robin problem. Differential Integral Equations 23 (2010), no. 7/8, 659--669. https://projecteuclid.org/euclid.die/1356019189