Abstract
This paper is devoted to the study of the viscosity solutions of
in the whole space \({\mathbb{R}^{\rm N}}\) , under suitable structural assumptions on \({\mathbb{F}}\) involving the Pucci extremal operators for the leading part and the Keller–Osserman condition on the zeroth order term. By means a kind of Liouville method we prove that uniqueness of solutions holds. Therefore a unique growth at infinity is compatible with the structure of the equations. Furthermore the knowledge of these growth at infinity of solutions is not required a priori. Due to the presence of a strong absorption term, the Liouville Theorem proved is independent on the dimension.
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To Ventura Reyes Prósper, many years later. Partially supported by the projects MTM 2008-06208 of DGISGPI (Spain) and the Research Group MOMAT (Ref. 910480) from Banco Santander and UCM.
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Díaz, G. A note on the Liouville method applied to elliptic eventually degenerate fully nonlinear equations governed by the Pucci operators and the Keller–Osserman condition. Math. Ann. 353, 145–159 (2012). https://doi.org/10.1007/s00208-011-0678-8
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DOI: https://doi.org/10.1007/s00208-011-0678-8