Classification of the solutions of semilinear elliptic problems in a ball
This paper fully describes the set of the positive and nodal (regular and singular) radial solutions of the superlinear elliptic problem: \[ -\Delta u=\lambda u+|u|^{p-1} u\quad\text{in }B,\qquad u= 0\quad\text{on }\partial B, \] where \(p>1\) and \(B= \{x\in \mathbb{R}^N:|x|< 1\}\). The solutions are of three different types: bounded with a finite number of zeros in \((0,1)\), singular at the origin with a finite number of zeros, and singular with sign changing oscillations at the origin.
scientific article; zbMATH DE number 1545274
scientific article