Further remarks on the non-degeneracy condition
The author considers positive solutions of the semilinear boundary value problem \[ \Delta u(x)+\lambda f(u(x))= 0\quad \text{in }\Omega,\qquad u= 0\quad \text{on }\partial\Omega, \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\), whose boundary is of class \(C^2\), \(f\in C^1(\overline{\mathbb{R}}_+)\) and \(\lambda> 0\). In contrast to the previous results in this direction (the structure of the set of positive solutions) the author did not assume that \(\Omega\) is either symmetric or convex.
scientific article; zbMATH DE number 2119247