In:
Journal of Mathematical Physics, AIP Publishing, Vol. 60, No. 6 ( 2019-06-01)
Abstract:
This paper is devoted to the nonexistence of nontrivial weak solutions for the Kirchhoff equation −a+b∫RN|∇u|2 dxΔu=|x|qf(u) in RN. We prove that the equation has no weak solution if a ≥ 0, b & gt; 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 lim infR→+∞R1−N2∫BR|x|qf(u) dx & gt;0. 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 N & lt;4q+143 if f(u) = eu, a ≥ 0, and b & gt; 0.
Type of Medium:
Online Resource
ISSN:
0022-2488
,
1089-7658
Language:
English
Publisher:
AIP Publishing
Publication Date:
2019
detail.hit.zdb_id:
1472481-9
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