Testa, Maria Bifurcation for families of nonlinear perturbations of closed Fredholm operators of index zero. (English) Zbl 1026.47008 Differ. Integral Equ. 15, No. 11, 1281-1312 (2002). A bifurcation (at infinity) theorem for some families of \(k\)-set contraction perturbations to closed Fredholm operators of index zero is proved in this paper by using a homotopy invariant (parity) and a degree theory adapted to the situation. An application is given to a class of nonlinear Sturm-Liouville problems on the half-line. Reviewer: Jesus Hernandez (Madrid) MSC: 47A53 (Semi-) Fredholm operators; index theories 58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces 34B40 Boundary value problems on infinite intervals for ordinary differential equations 47H11 Degree theory for nonlinear operators Keywords:Fredholm operator; unbounded domain; boundary value problem; bifurcation at infinity; parity; \(k\)-set contraction; homotopy; degree theory; nonlinear Sturm-Liouville problem PDFBibTeX XMLCite \textit{M. Testa}, Differ. Integral Equ. 15, No. 11, 1281--1312 (2002; Zbl 1026.47008)