Existence of positive solutions for a class of singular elliptic problems with convection term and critical exponential growth

Abstract

Abstract This paper uses the Galerkin method to investigate the existence of positive solution to a class of singular elliptic problems given by { − Δ u = λ 0 u β 0 + Λ 0 | ∇ u | γ 0 + f 0 ( u ) | x | α 0 + h 0 ( x ) , u > 0 in Ω , u = 0 on ∂ Ω , $$\begin{aligned} \textstyle\begin{cases} -\Delta u= \displaystyle \frac {\lambda _{0}}{u^{\beta _{0}}} + \Lambda _{0} |\nabla u|^{\gamma _{0}}+ \frac{f_{0}(u)}{|x|^{\alpha _{0}}}+ h_{0}(x), \ \ u>0 \ \ \text{in} \ \Omega , \\ u=0 \ \text{on} \ \ \partial \Omega , \end{cases}\displaystyle \end{aligned}$$ where Ω ⊂ R 2 $\Omega \subset \mathbb{R}^{2}$ is a bounded smooth domain, 0 0 $\overline{\Upsilon}>0$ .

Keywords

• Galerkin method
• Exponential growth
• Trudinger-Moser inequality
• Hardy-Sobolev inequality