A priori estimates for an elliptic equation with exponential nonlinearity

Article type: Research Article

Authors: Bartolucci, D.

Affiliations: University of Rome “Tor Vergata”, Mathematics Departement, Via della Ricerca Scientifica, 00133 Rome, Italy E‐mail: [email protected]

Abstract: We establish compactness and existence results for the following class of nonlinear elliptic problems: −Δu=K(x) eu in Ω, with ∫ΩK(x) eu=λ, where Ω is a smooth two‐dimensional bounded domain with nontrivial topology and K(x)=$\prod_{j=1}^{m}$|x−xj|2αj eσ(x) is a nonnegative function which admits a zero at the point xj∈Ω with multiplicity αj∈(0,1), for j=1,…,m. We consider the case where λ∈(8π,min j=1,…,m4π(3−αj))\{8π(1+αj)}j=1,…,m and extend the work of Struwe and Tarantello [34] and Ding et al. [12].

Journal: Asymptotic Analysis, vol. 35, no. 3-4, pp. 325-347, 2003