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Fourth Mississippi State Conference on Differential Equations and Computational Simulations
May 21-22, 1999
Mississippi State University and Electronic Journal of Differential Equations
Starkville, MS, USA

Organizers
Ratnasingham Shivaji, Bharat Soni, Jianping Zhu (Program Chair)

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Nonlinear problems associated with k-Hessian operators
by
Jon Jacobsen
University of Utah

In this paper we examine nonlinear problems associated with k-Hessian operators of the form Sk(D2 u) = g(\lambda, u), with Dirichlet boundary conditions, where \Omega is a strictly (k-1)-convex domain in Rn.

Using techniques from global bifurcation theory we demonstrate how existence results may be established for "powerlike" g. In addition, a problem of Liouville-Gelfand type will be discussed.

Applications to the theory of critical exponents and the geometry of k-convex functions will be considered.

Date received: March 24, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacr-24.