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<p>This paper is concerned with the existence of normalized solutions to a coupled Kirchhoff system under prescribed <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-norm constraints. In the mass-mixed setting, we employ a constrained variational approach on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-balls and prove the existence of two distinct positive normalized solutions: a local minimizer with negative energy and a mountain-pass solution with positive energy. Our results extend and complement earlier existence theorems in the literature.</p>

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Multiple Normalized Solutions for Kirchhoff Systems in Mass-Mixed Regimes

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Liu Gao

摘要

This paper is concerned with the existence of normalized solutions to a coupled Kirchhoff system under prescribed \(L^2\) L 2 -norm constraints. In the mass-mixed setting, we employ a constrained variational approach on \(L^2\) L 2 -balls and prove the existence of two distinct positive normalized solutions: a local minimizer with negative energy and a mountain-pass solution with positive energy. Our results extend and complement earlier existence theorems in the literature.