Positive entire solutions of the equation \(\Delta{}u+f(x,u)=0\)
The author considers equations of the form \(\Delta u+K(x)u^ p=0\), \(x\in R^ n\), \(n>2\), where \(\Delta\) is the \(n\)-dimensional Laplacian and \(p=(n+2)/(n-2)\). He gives and proves conditions for there to be infinitely many positive entire solutions without any pair of them intersecting and develops an asymptotic approximation to \(u(x)\) for \(| x|\) large. He uses these theorems to obtain bounds and asymptotic relations for the solutions of equations of the form \(\Delta u+f(x,u)=0\). He also points out a possible application to Riemannian geometry.
scientific article; zbMATH DE number 93317
scientific article