Index bundle, Leray-Schauder reduction and bifurcation of solutions of nonlinear elliptic boundary value problems.
The main result of the paper is the following: A family \(\{F_p:p \in P\}\) of elliptic boundary value problems of index \(0\) parametrized by a compact manifold admits a reduction to a family of compact vector fields parametrized by \(P\) if and only if its index bundle \(\text{Ind}\,F\) vanishes. Next the author describes the restriction on the degree of the map \(F_p\) imposed by non vanishing of the image of \(\text{Ind}\,F\) under the generalized \(J\)-homeomorphism. From this the author obtains a number of corollaries about bifurcation from infinity for solutions of nonlinear elliptic boundary value problems.
nonlinear elliptic boundary value problems
scientific article; zbMATH DE number 1799622