Liouville type theorem for an anisotropic singular model

In this article, we establish a Liouville type theorem for the anisotropic singular problem \sum_{i=1}^{N}\frac{\partial}{\partial x_i}(|\frac{\partial u}{\partial x_i}|^{p_i-2}\frac{\partial u}{\partial x_i})=e^\frac{1}{u}\;\;\mbox{in}\;\;\mathbb{R}^N concerning positive $W^{1,p_i}(\mathbb{R}^N)$ stable solution, provided $N\geq 1$ and $p_i>2$ for all $i=1,2,\dots{N}$.Comment: 7 page

On a class of mixed local and nonlocal semilinear elliptic equation with singular nonlinearity

In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish existence of at least one weak solution for a parameter dependent singular nonlinearity and existence of multiple solution for purturbed singular nonlinearity. Our argument is based on the variational and approximation approach.Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:2112.1329