Classification of positive solutions of quasilinear elliptic equations
This is a very substantial and beautiful survey on the classification and properties of positive solutions of the equation \[ \Delta u + f \bigl( | x |, u, | \nabla u | \bigr) = 0 \quad \bigl( x \in \mathbb{R}^ n \backslash \{0\} \bigr), \] with a particular emphasis on the cases \(f(r,u,v) = u^ p\), \(f(r,u,v) = u^ p + u^ q\), and \(f(r,u,v) = u^ p - v^ q\). In the case \(f(r,u,v) = u^ p + v^ q\), for example, the number and behaviour of solutions depend in a very sensitive way on the range of the exponents \(p\) and \(q\) below or above the ``critical'' values \(n/(n-2)\) and \((n+2)/(n-2)\). Many illuminating examples are given.
classification and properties of positive solutions
scientific article; zbMATH DE number 640267