A priori estimates for an elliptic equation with exponential nonlinearity
Daniele Bartolucci · Asymptotic Analysis · 2003
We establish compactness and existence results for the following class of nonlinear elliptic problems: −Δu=K(x) e u in Ω, with ∫ Ω K(x) e u =λ, where Ω is a smooth two‐dimensional bounded domain with nontrivial topology and K(x)= $\prod_{j=1}^{m}$ |x−x j | 2α j e σ(x) is a nonnegative function which admits a zero at the point x j ∈Ω with multiplicity α j ∈(0,1), for j=1,…,m. We consider the case where λ∈(8π,min j=1,…,m 4π(3−α j ))\{8π(1+α j )} j=1,…,m and extend the work of Struwe and Tarantello [34] and Ding et al. [12].