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Instability of solutions to Kirchhoff type problems in low dimension

Authors: 

Nhat Vy Huynh, Phuong Le

Source title: 
Annales Polonici Mathematici, 124: 75-91, 2020 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

We study the Kirchhoff type problem

a

where p ≥ 2, Ω is a C1 domain of  a, w1, w2 are nonnegative functions, m is a positive function and f is an increasing one. Under some assumptions on Ω, w1, w2, m and f, we prove that the problem has no nontrivial stable solution in dimension N < N#. Moreover, additional assumptions on Ω, m or the boundedness of solutions can boost this critical dimension N# to infinity.