Abstract
We study local and global properties of positive solutions of \(-\Delta u=u^p+M\left| \nabla u\right| ^q\) in a domain \(\Omega \) of \(\mathbb {R}^N\), in the range \(\min \{p,q\}>1\) and \(M\in \mathbb {R}\). We prove a priori estimates and existence or non-existence of ground states for the same equation.
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This article has been prepared with the support of the collaboration programs ECOS C14E08 and FONDECYT Grant 1160540 for the three authors.
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Communicated by Y. Giga.
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Bidaut-Véron, MF., Garcia-Huidobro, M. & Véron, L. A priori estimates for elliptic equations with reaction terms involving the function and its gradient. Math. Ann. 378, 13–56 (2020). https://doi.org/10.1007/s00208-019-01872-x
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DOI: https://doi.org/10.1007/s00208-019-01872-x