Advances in Differential Equations

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

J. Chabrowski

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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

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

First available in Project Euclid: 18 December 2012

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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.

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