Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on $ {\Bbb R}^n $

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Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level (2005, background): “Note that L, T = ∅; in particular, T contains any positive solution of (2.1), the first positive eigenfunction of −∆, and suitable functions w ∈ C2 c (Ω); see the proof of [ 30, Theorem 2.5 ].”
Nonexistence of positive weak solutions of elliptic inequalities (2009, methodology): “Then for the quasilinear case we refer to [26], [21], [1], [18], [19], [ 20 ], [15], [11], [10], [12], [13], [14], and the references therein.”