Multiplicity and asymptotic behavior of normalized solutions for fourth‐order equations of the Kirchhoff type

Tao Han, Hong‐Rui Sun and Zhen‐Feng Jin

Mathematische Nachrichten, 2025, vol. 298, issue 9, 3172-3190

Abstract: In this paper, we study the following fourth‐order equation of the Kirchhoff type Δ2u−(a+b∥∇u∥22)Δu=λu+|u|p−2uinRd$$\begin{equation*} \Delta ^{2}u-(a+b\Vert \nabla u\Vert _{2}^{2})\Delta u=\lambda u+|u|^{p-2}u \quad \text{ in } \mathbb {R}^{d} \end{equation*}$$under the normalized constraint ∥u∥2=m$\Vert u\Vert _{2}=m$, where a,b,m>0$a,b,m>0$ are constants. d≥2$d\ge 2$ and 2

Date: 2025
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