Instability of solutions to Kirchhoff type problems in low dimension
Instability of solutions to Kirchhoff type problems in low dimension
Source title:
Annales Polonici Mathematici, 124: 75-91,
2020
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
We study the Kirchhoff type problem
where p ≥ 2, Ω is a C1 domain of , 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.