We　establish　quantitative　asymptotic　behavior　of　positive　solutions　of　a　family　of　nonlinear　elliptic　equations　on　the　half　cylinder　near　the　end.　This　unifies　the　study　of　asymptotic　behavior　of　solutions　near　an　isolated　singularity　of　some　semilinear　elliptic　equations,　such　as　the　Yamabe　equation,　Hardy-H　&　eacute;non　equations,　etc.　(c)　2024　Elsevier　Inc.　All　rights　are　reserved,　including　those　for　text　and　data　mining,　AI　training,　and　similar　technologies.