The Existence of Least Energy Sign-Changing Solution for Kirchhoff-Type Problem with Potential Vanishing at Infinity
In this paper, we study the Kirchhoff-type equation: −a+b∫ℝ3 ∇u2dxΔu+Vxu=Qxfu,in ℝ3, where a, b>0, f∈C1ℝ3,ℝ, and V,Q∈C1ℝ3,ℝ+. Vx and Qx are vanishing at infinity. With the aid of the quantitative deformation lemma and constraint variational method, we prove the existence of a sign-changing solut...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6690204 |
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| Summary: | In this paper, we study the Kirchhoff-type equation: −a+b∫ℝ3 ∇u2dxΔu+Vxu=Qxfu,in ℝ3, where a, b>0, f∈C1ℝ3,ℝ, and V,Q∈C1ℝ3,ℝ+. Vx and Qx 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. |
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| ISSN: | 1687-9120 1687-9139 |