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In this paper, we study the Kirchhoff-type equation: −a+b∫℠3  ∇u2dxI”u+Vxu=Qxfu,in ℠3, where a, b>0, f∈C1â„ 3,â„ , and V,Q∈C1â„ 3,â„ +. Vx and Qx are vanishing at infinity. With the… Click to show full abstract
In this paper, we study the Kirchhoff-type equation: −a+b∫℠3  ∇u2dxI”u+Vxu=Qxfu,in ℠3, where a, b>0, f∈C1â„ 3,â„ , and V,Q∈C1â„ 3,â„ +. 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.
Keywords:
sign changing;
vanishing infinity;
changing solution;
kirchhoff type
Journal Title: Advances in Mathematical Physics
Year Published: 2021
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Journal Title: Advances in Mathematical Physics
Year Published: 2021
Link to full text (if available)
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recommendations!