Large solutions of semilinear elliptic equations with nonlinear gradient terms
The authors show that under suitable assumptions on \(\gamma >1\), \(q>0\), and \(p(x)\) large solutions of the equations \[ \Delta u \pm |\nabla u|^q = p(x) u^\gamma \] exist. Moreover, if \(\gamma \leq 1\) or the continuous function \(p(x)\) has compact support in \(\Omega,\) such solutions do not exist.
scientific article; zbMATH DE number 1417985