Existence of normalized solutions to Kirchhoff-Boussinesq equations in thesubcritical and supercritical regime

作者：Chunling Tao, Lintao Liu, Kaimin Teng · 发表于：Electronic Journal of Differential Equations · 年份：2025 · DOI：10.58997/ejde.2025.121 · 研究领域：Nonlinear Partial Differential Equations、Navier-Stokes equation solutions、Mathematical Biology Tumor Growth

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 Poho\v{z}aev-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. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/121/abstr.html