Invariant criteria for existence of bounded positive solutions
The authors deal with the semilinear elliptic equations \[ \Delta u+\varphi(x,u)=0\quad \text{in }\mathbb{R}^N,\;\mathbb{N}\geq 3 \] and are interested in sufficient conditions on \(\varphi(x,u)\) for the existence of entire bounded positive solutions. Using the standard barrier method; the authors prove the existence of entire bounded positive solutions for (1). Here the authors present many sufficient conditions which are invariant under the isometry group of \(\mathbb{R}^N\).
scientific article; zbMATH DE number 2155029