On the classification of solutions of the Lane-Emden equation on unbounded domains of Rn

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Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (2010, background): “Lions’ work [11], where the authors dealt with superlinear elliptic equations with regular nonlinearities (see also [53, 64]).”
Partial regularity of finite Morse index solutions to the Lane–Emden equation (2011, background): “4) remains true for stable solutions (see [10]).”
A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem (2013, background): “The above theorem generalizes a similar result of Farina [13] for the classical Lane-Emden equation.”
Saddle-shaped solutions of bistable diffusion equations in all of ℝ2m (2009, background): “Recent works of Dancer and of Farina [ 14 , 15, 11] establish interesting classification results for stable and finite Morse index solutions (general solutions, not only radial, and even unbounded) of supercritical elliptic problems.”
Liouville results for m-Laplace equations of Lane―Emden―Fowler type (2009, methodology): “Exploiting the technique introduced in [14,15], we prove the following Proposition 1.”
Some Liouville theorems for Hénon type elliptic equations (2012, methodology): “The crucial argument is that we can use test function as ζk(u)ψ with ψ ∈ C∞ c (R) as u verifies the Dirichlet boundary condition on ∂R+ , we get all the corresponding estimates since all the boundary terms are zero when doing the integration by parts (see more details in [11]).”