Global continuation of branches of nondegenerate solutions
The author discusses an equation \(-u''=u(1-u)(u-\alpha)\) on [0,L] with Robin boundary conditions. He shows that by varying L,\(\alpha\) and a constant in the boundary conditions in a suitable way, one can join the Dirichlet problem to the Neumann problem such that at each stage all solutions are non-degenerate (and thus the number of solutions remains constant during the homotopy). The proofs depend on a careful study of the time map. He uses this result in some of his work on travelling waves [J. Differ. Equations 61, 335-379 (1986)].
scientific article; zbMATH DE number 3955441
scientific article