TY - JOUR AU - Jacobsen, Jon PY - 1999/09/01 Y2 - 2024/03/29 TI - Global bifurcation problems associated with $k$-Hessian operators JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 14 IS - 1 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.1999.023 SP - 81 - 130 AB - In this paper we study global bifurcation phenomena for a class of nonlinear elliptic equations governed by the $h$-Hessian operator. The bifurcation phenomena considered provide new methods for establishing existence results concerning fully nonlinear elliptic equations. Applications to the theory of critical exponents and the geometry of $k$-convex functions are considered.In addition, a related problem of Liouville-Gelfand type is analyzed. ER -