On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential

Manuela Chaves; Jesús García-Azorero

doi:10.4171/jems/49

JournalsjemsVol. 8, No. 2pp. 229–242

On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential

Manuela Chaves
Universidad Autónoma de Madrid, Spain
Jesús García-Azorero
Universidad Autónoma de Madrid, Spain

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Abstract

We will present some results concerning the problem

{- Δ u = λ \frac{u}{∣ x ∣ ^{2}} + u^{q}, u > 0 in Ω, u ∣_{\partial Ω} = 0,

where $0 < q < \frac{N + 2}{N - 2}$ , $q \neq = 1$ , $λ \geq 0$ and $Ω$ is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.

Cite this article

Manuela Chaves, Jesús García-Azorero, On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 229–242

DOI 10.4171/JEMS/49