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

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  • Ting Xiao
  • Canlin Gan
  • Qiongfen Zhang

Abstract

In this paper, we study the Kirchhoff-type equation: where , , , and . and 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 to the above equation. Moreover, we obtain that the sign-changing solution has exactly two nodal domains. Our results can be seen as an improvement of the previous literature.

Suggested Citation

  • Ting Xiao & Canlin Gan & Qiongfen Zhang, 2021. "The Existence of Least Energy Sign-Changing Solution for Kirchhoff-Type Problem with Potential Vanishing at Infinity," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-10, January.
    • Handle: RePEc:hin:jnlamp:6690204
    DOI: 10.1155/2021/6690204
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