Global bifurcation problems associated with $k$-Hessian operators
Keywords
Global bifurcation, Monge-Ampère equations, $k$-Hessian equations, $k$-convex functions, Krein-Rutman, principal eigenvalue, critical exponentsAbstract
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.Downloads
Published
1999-09-01
How to Cite
1.
JACOBSEN, Jon. Global bifurcation problems associated with $k$-Hessian operators. Topological Methods in Nonlinear Analysis. Online. 1 September 1999. Vol. 14, no. 1, pp. 81 - 130. [Accessed 29 March 2024].
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