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On the classification of entire solutions to the critical p-Laplace equation
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abstract
Under the assumption of finite energy, positive solutions to the critical p-Laplace equation in $\mathbb{R}^n$ for $1< p<n$ have been classified completely by moving plane method. In this paper, the author provide a new approach to obtain the same classification results for $\frac{n+1}{3}\leq p<n$, without any further assumptions.
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Radial symmetry and sharp asymptotic behaviors of nonnegative solutions to weighted doubly $D^{1,p}$-critical quasi-linear nonlocal elliptic equations with Hardy potential
Every nontrivial nonnegative finite-energy weak solution of the doubly critical quasilinear Hartree equation with Hardy potential is radially symmetric and strictly decreasing, with sharp power-law asymptotics at the ...
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