Brézis, Haïm Elliptic equations with limiting Sobolev exponents - The impact of topology. (English) Zbl 0601.35043 Commun. Pure Appl. Math. 39, Suppl., S17-S39 (1986). We discuss a number of recent results concerning the existence of a solution for the problem \(-\Delta u=u^ p+a(x)u\) on \(\Omega\), \(u>0\) on \(\Omega\), and \(u=0\) on \(\partial \Omega\), where \(\Omega \subset {\mathbb{R}}^ n\) is a smooth bounded domain, \(p=(N+2)/(N-2)\) and a(x) is a given function. Cited in 2 ReviewsCited in 43 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:limiting Sobolev exponents; topology; existence PDFBibTeX XMLCite \textit{H. Brézis}, Commun. Pure Appl. Math. 39, S17--S39 (1986; Zbl 0601.35043)