Global bifurcation problems associated with $k$-Hessian operators

Jon Jacobsen

DOI: http://dx.doi.org/10.12775/TMNA.1999.023

Abstract


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.

Keywords


Global bifurcation; Monge-Ampère equations; $k$-Hessian equations; $k$-convex functions; Krein-Rutman; principal eigenvalue; critical exponents

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