Symmetry of solutions to semilinear elliptic equations via Morse index
Symmetry of solutions to semilinear elliptic equations via Morse index
In this paper we prove symmetry results for solutions of semilinear elliptic equations in a ball or in an annulus in $\mathbb R^N$, $N \ge 2$, in the case where the nonlinearity has a convex first derivative. More precisely we prove that solutions having Morse index $j \le N$ are …