带有位势的质量次临界 Kirchhoff 方程的正规化解

Abstract

Abstract:

We study the existence of normalized solution to the following nonlinear mass sub-critical Kirchhoff equation

$-\left(a+b\int_{\mathbb{R}^{N}}|\nabla u|^{2}\right)\triangle u+V(x)u+\lambda u=|u|^{p-2}u \ \ {in} \ {\mathbb{R}^{N}},1\leq N\leq3$

having the normalization constrain $\int_{\mathbb{R}^{N}}|u|^{2}{\rm d}x=c$, for any $a,b,c>0$ prescribed, $2<p<2+\frac{8}{N}$. By a proof of the strict sub-additivity inequality utilizing the iterative framework developed by Zhong $\&$ Zou [Zhong X, Zou W. Diff Inte Equa, 2023, 36(1/2): 133-160], we get the existence of global constraint minimizers when the potential $V(x)$ satisfies some appropriate assumptions and prove the existence of ground state normalized solution.

Key words: normalized solutions, potential, kirchhoff type problems, global minimizers.

CLC Number:

0176.3

Qun Wang, Aixia Qian. Ground State Normalized Solutions to the Kirchhoff Equation with Potential Term: Mass Sub-Critical Case[J].Acta mathematica scientia,Series A, 2026, 46(3): 1292-1303.

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References 31

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Ground State Normalized Solutions to the Kirchhoff Equation with Potential Term: Mass Sub-Critical Case

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