#
Liouville theorems for Kirchhoff equations in R^{N}

Liouville theorems for Kirchhoff equations in R^{N}

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) = e^{u}, *a* ≥ 0, and *b* > 0.