Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations
Tóm tắt
In this paper, we consider the exterior Dirichlet problem of Hessian equations
$\sigma _{k}(\lambda (D^{2}u))=g(x)$
with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the solution, we obtain the necessary and sufficient conditions of existence of radial symmetric solutions with asymptotic behavior at infinity.
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