In this paper, we consider the following Kirchhoff-type equation:
$ -\left(a+b\int_{ \mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+u = |u|^{p-1}u,\quad {\rm{in }}\; \mathbb{R}^3, $
where $ a $, $ b > 0 $, $ p \in (1, 5) $. By considering a minimization problem on a special constraint set, we prove that the above problem has at least one sign-changing solution for any $ p \in (1, 5) $. Our results (especially $ p \in (1, 3] $) can be regarded as an improvement on the existing results.
Citation: Ting Xiao, Yaolan Tang, Qiongfen Zhang. The existence of sign-changing solutions for Schrödinger-Kirchhoff problems in $ \mathbb{R}^3 $[J]. AIMS Mathematics, 2021, 6(7): 6726-6733. doi: 10.3934/math.2021395
In this paper, we consider the following Kirchhoff-type equation:
$ -\left(a+b\int_{ \mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+u = |u|^{p-1}u,\quad {\rm{in }}\; \mathbb{R}^3, $
where $ a $, $ b > 0 $, $ p \in (1, 5) $. By considering a minimization problem on a special constraint set, we prove that the above problem has at least one sign-changing solution for any $ p \in (1, 5) $. Our results (especially $ p \in (1, 3] $) can be regarded as an improvement on the existing results.
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Ting Xiao, Yaolan Tang, Qiongfen Zhang. The existence of sign-changing solutions for Schrödinger-Kirchhoff problems in $ \mathbb{R}^3 $[J]. AIMS Mathematics, 2021, 6(7): 6726-6733. doi: 10.3934/math.2021395
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