The Existence of Least Energy Sign‐Changing Solution for Kirchhoff‐Type Problem with Potential Vanishing at Infinity

Ting Xiao, Canlin Gan and Qiongfen Zhang

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: In this paper, we study the Kirchhoff‐type equation: −a+b∫ℝ3 ∇u2dxΔu+Vxu=Qxfu,in ℝ3, where a, b > 0, f ∈ C1(ℝ3, ℝ), and V, Q ∈ C1(ℝ3, ℝ+). V(x) and Q(x) are vanishing at infinity. With the aid of the quantitative deformation lemma and constraint variational method, we prove the existence of a sign‐changing solution u to the above equation. Moreover, we obtain that the sign‐changing solution u has exactly two nodal domains. Our results can be seen as an improvement of the previous literature.

Date: 2021
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https://doi.org/10.1155/2021/6690204

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6690204

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