On non-radially symmetric bifurcation in the annulus
The author considers the equation \(-\Delta u=\lambda e^ u\) on a two- dimensional annulus with Dirichlet boundary conditions. He explicitly finds the radially symmetric solutions and finds the points where non radially symmetric solutions bifurcate from symmetric ones. Reviewer's remark: More recently the reviewer has used the degree in his paper [Ann. Inst. Henri Poincaré, Anal. Nonlineaire 2, 329-370 (1985; Zbl 0579.58022)] to prove that there is a non-radially symmetric solution for each \(\lambda\) in \((0,\lambda^*)\) where \(\lambda^*\) is the largest point of non radially symmetric bifurcation. In fact, there is an unbounded continua of non-radially symmetric solutions.
scientific article; zbMATH DE number 4127679