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<p>This paper focuses on the existence of normalized solutions for a class of nonlinear Kirchhoff equations with potential <i>V</i> on a bounded smooth domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \subset \mathbb {R}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. By using monotonicity trick and other analytical methods, we prove the existence of two solutions, one being a global minimizer and the other of mountain-pass type, under explicit conditions on mass <i>m</i> and potential <i>V</i>. This study fills a gap in the case <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(10/3&lt;p&lt;14/3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>10</mn> <mo stretchy="false">/</mo> <mn>3</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mn>14</mn> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, which is both interesting and special whether in the entire space or in bounded domains.</p>

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Normalized Solutions of Mass-Subcritical Kirchhoff Equations with Potential on Bounded Domains

  • 期刊论文

  • 发表日期：

    2025年11月22日

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  • Rui Wang,
  • Shuai Yao,
  • Juntao Sun

摘要

This paper focuses on the existence of normalized solutions for a class of nonlinear Kirchhoff equations with potential V on a bounded smooth domain \(\Omega \subset \mathbb {R}^{3}\) Ω ⊂ R 3 . By using monotonicity trick and other analytical methods, we prove the existence of two solutions, one being a global minimizer and the other of mountain-pass type, under explicit conditions on mass m and potential V. This study fills a gap in the case \(10/3<p<14/3\) 10 / 3 < p < 14 / 3 , which is both interesting and special whether in the entire space or in bounded domains.