Radial entire solutions for supercritical biharmonic equations

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A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem (2013, background): “(1.7) 16 Solving the corresponding quartic equation, (1.7) holds if and only if p pc(n) where pc(n) > pS(n) is the fourth-order Joseph–Lundgren exponent computed by Gazzola and Grunau [12]: pc(n) = {+∞ if n 12, n+2− √ n2+4−n √ n2−8n+32 n−6− √ n2+4−n √ n2−8n+32 if n 13.”
Eventual local positivity for a biharmonic heat equation in R N (2007, background): “those considered in [5]; for the elliptic counterpart, see [4].”
Liouville theorems for stable solutions of biharmonic problem (2013, background): “Therefore Theorem 1.1 is a first step towards the understanding of stable solutions of fourth order problems.”
Sharp criteria of Liouville type for some nonlinear systems (2013, methodology): “This result was obtained firstly in [15] by the shooting method which was also employed in [49].”
Multiplicity of solutions for a fourth order equation with power-type nonlinearity (2010, methodology): “In the case of positive p and p < pc the authors in [15] showed that the positive entire solutions of (3) oscillate infinitely around the explicit singular solution, see also [20] for positive powers, and [27] in the case N = 3 and p = −2.”