Advances in Differential Equations
- Adv. Differential Equations
- Volume 13, Number 3-4 (2008), 323-348.
The critical Neumann problem for semilinear elliptic equations with the Hardy potential
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.
Adv. Differential Equations Volume 13, Number 3-4 (2008), 323-348.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly- Laplacian
Secondary: 35B33: Critical exponents 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations 35J75: Singular elliptic equations 47J30: Variational methods [See also 58Exx]
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.