Chunling Tao, Lintao Liu, Kaimin Teng
Abstract:
In this article we study the existence of normalized solutions to the
Kirchhoff-Boussinesq equation under the mass constraint \(\|u\|_{2}=c\).
In the \(L^{2}\)-subcritical regime, we apply Ekeland's variational principle and
concentration compactness method to minimize the energy functional on the
mass-constrained manifold. In the \(L^{2}\)-supercritical regime, we introduce a
Pohozaev-constrained minimization approach, combined with scaling arguments to
recover compactness. To handle the additional difficulties posed by \(q\)-Laplacian,
we treat distinct ranges of \(q\) separately.
Submitted June 24, 2025. Published December 29. 2025.
Math Subject Classifications: 35J35, 35J92, 35J20.
Key Words: Normalized solutions; biharmonic equations; \(q\)-Laplacian; Kirchhoff-Boussinesq equation.
DOI: 10.58997/ejde.2025.121
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Chunling Tao Department of Mathematics Taiyuan University of Technology Taiyuan 030024, Shanxi, China email: taochunling2024@163.com |
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Lintao Liu Department of Mathematics North University of China Taiyuan 030051, Shanxi, China email: liulintao_math@nuc.edu.cn |
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Kaimin Teng Department of Mathematics Taiyuan University of Technology Taiyuan 030024, Shanxi, China email: tengkaimin2013@163.com |
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