Asymptotic analysis of singular problems in perforated cylinders

Abstract

In this paper, we deal with elliptic problems having terms singular in the variable $u$ which represents the solution. The problems are posed in cylinders $\Omega_n^\varepsilon$ of height $2n$ and perforated according to a parameter $\varepsilon$. We study existence, uniqueness and asymptotic behavior of the solutions $u_n^\varepsilon$ as the cylinders become infinite ($n\rightarrow +\infty$) and the size of the holes decreases while the number of the holes increases ($\varepsilon\rightarrow 0$).