In this paper, we study solutions u of fully nonlinear elliptic equations of the form F(D²u)=f in Rⁿ, where f is periodic. We establish the existence and Liouville type results for entire quadratic polynomial growth solutions, that is, the solution is a quadratic polynomial plus a periodic function. As a consequence, we consider applications to k-Hessian equations.
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Li et al. (2024) studied this question.
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