Global bifurcation problems associated with $k$-Hessian operators
KeywordsGlobal bifurcation, Monge-Ampère equations, $k$-Hessian equations, $k$-convex functions, Krein-Rutman, principal eigenvalue, critical exponents
AbstractIn 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.
How to Cite
JACOBSEN, Jon. Global bifurcation problems associated with $k$-Hessian operators. Topological Methods in Nonlinear Analysis [online]. 1 September 1999, T. 14, nr 1, s. 81–130. [accessed 22.1.2022].
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