Affiliation:
1. University of Mazandaran Babolsar
2. University of Technology Babol
Abstract
In this paper, using variational method, we study the existence and mutiplicity of the solutions for the following multi-singular critical elliptic problem \begin{eqnarray*}\begin{cases}\begin{array}{cc}-\Delta{u}-\displaystyle\sum_{i=1}^k\frac{\mu_i}{|x-a_i|^2}u=f_\lambda \left( x,u \right)& x \in{\Omega{\backslash}}\{a_1,...,a_k\},\\u(x)>0 & x \in{\Omega}{\backslash}\{a_1,...,a_k \},\\u(x)=0 &x \in{\partial{\Omega}}.\end{array}\end{cases}\end{eqnarray*}where $\Omega{\subset}\mathbb{R}^N(N\geq3)$ is a smooth boundeddomain such that $a_i\in{\Omega},i=1,2,...,k,$ for $k\geq2$ aredifferent points, $0\leq{\mu_i} \in \mathbb{R}$.In this class of nonlinear elliptic Dirichlet boundary value problems the combination effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results.
Publisher
Sociedade Paranaense de Matematica