Abstract
In this paper, we consider the equation |∇u|αℳ a, A (D 2 u) = −f(u) in a bounded smooth domain Ω, with both Dirichlet condition u = 0 and Neumann condition , where c is a constant, α > −1, u is of constant sign and ℳ a, A is one of the Pucci operator. We prove, for different nonlinearities f, that, when a is sufficiently close to A, either u = c = 0 = f(0) or Ω is a ball, u is radial, and c ≠ 0 in Ω.
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