### The critical Neumann problem for semilinear elliptic equations with the Hardy potential

J. Chabrowski

#### Abstract

We investigate the solvability of the Neumann problem (1.1) involving the critical Sobolev nonlinearity with an indefinite weight function and the Hardy potential. We prove that there exists $\lambda^*>0$ such that for $\lambda \in (0,\lambda^*)$, problem (1.1) admits at least two distinct solutions.

#### Article information

Source
Adv. Differential Equations, Volume 13, Number 3-4 (2008), 323-348.

Dates
First available in Project Euclid: 18 December 2012

Mathematical Reviews number (MathSciNet)
MR2482420

Zentralblatt MATH identifier
1159.35361

#### Citation

Chabrowski, J. The critical Neumann problem for semilinear elliptic equations with the Hardy potential. Adv. Differential Equations 13 (2008), no. 3-4, 323--348. https://projecteuclid.org/euclid.ade/1355867352