Nonexistence of Positive Solutions for Some Fully Nonlinear Elliptic Equations
نویسندگان
چکیده
denote the kth elementary symmetric function, and let Γk denote the connected component of {λ ∈ R : σk(λ) > 0} containing the positive cone {λ ∈ R : λ1 > 0, · · · , λn > 0}. It is well known that Γk = {λ ∈ R : σl(λ) > 0, 1 ≤ l ≤ k}. Let S denote the set of n× n real symmetric matrices. For any A ∈ S we denote by λ(A) the eigenvalues of A. Throughout this note we will assume that Γ ⊂ R is an open convex symmetric cone with vertex at the origin satisfying Γn ⊂ Γ ⊂ Γ1. Moreover, we also assume that f is a continuous function defined on Γ verifying the following properties:
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