The Convexity of a Fully Nonlinear Operator and Its Related Eigenvalue Problem (Journal of Mathematical Study, 2019)
We first get an existence and uniqueness result for a nonlinear eigenvalueproblem. Then, we establish the constant rank theorem for the problem and use it toget a convexity property of the solution.
Keywords: Hessian operator; eigenvalue problem; constant rank theorem; strict convexity.