Liouville theorems for Kirchhoff equations in RN
Liouville theorems for Kirchhoff equations in RN
Source title:
Journal of Mathematical Physics, 60(6): 061506,
2019
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
This paper is devoted to the nonexistence of nontrivial weak solutions for the Kirchhoff equation in
. We prove that the equation has no weak solution if a ≥ 0, b > 0, q ≤ −2, and f is a positive, convex, nondecreasing function. If only b ≠ 0 and f is a non-negative function, we establish the nonexistence of weak solutions u satisfying
. This implies that the equation has no weak solution when N ≤ 2 and f is a positive function. We also show that the equation has no stable weak solution in dimension
if f(u) = eu, a ≥ 0, and b > 0.