The Lazer-McKenna conjecture for an anisotropic planar exponential nonlinearity with a singular source

Yibin Zhang

Given a bounded smooth domain $\Omega$ in ${\mathbb{R}}^2$, we study the following anisotropic elliptic problem $$ \begin{cases} -\nabla\big(a(x)\nabla \upsilon\big)= a(x)\big[e^{\upsilon…