TY - JOUR
T1 - The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations
AU - Dai , Limei
JO - Analysis in Theory and Applications
VL - 2
SP - 120
EP - 146
PY - 2023
DA - 2023/06
SN - 39
DO - http://doi.org/10.4208/ata.OA-2022-0009
UR - https://global-sci.org/intro/article_detail/ata/21819.html
KW - Hessian equations, exterior Dirichlet problem, asymptotic behavior.
AB - <p style="text-align: justify;">In this paper, we consider the exterior Dirichlet problem of Hessian equations $$σ_k (λ(D^2u)) = g(x)$$ with $g$ being a perturbation of a general positive function at infinity. The existence of the viscosity solutions with generalized asymptotic behavior at infinity is established by the Perron’s method which extends the previous results for Hessian equations. By the solutions of Bernoulli ordinary differential equations, the viscosity subsolutions and supersolutions are constructed.</p>