含分数阶 $p$-Laplacian 算子基尔霍夫方程解的存在性及其渐近行为

Abstract

Abstract:

In this paper, we are interested in the existence of normalized solutions for some fractional Kirchhoff equations with $p$-Laplacian operator. For the existence and nonexistence of normalized solutions, using the method of energy estimates, we give a complete classification with respect to nonlinear term exponent $q$ and an explicit threshold value of $c$ (with $\int_{\mathbb{R}^N}|u|^p{\rm d}x=c^p$) in the range $q\in (p,p+\frac{2sp^2}{N})$. We also derive some existence of mountain pass type normalized solutions on the $L^2$ manifold in the range $q\geq p+\frac{2sp^2}{N}$. Furthermore, some asymptotic behaviors with respect to $c$ were also given.

Key words: Kirchhoff equation, normalized solutions, existence, asymptotic behavior

CLC Number:

O175.25

Meng Xiaoying,Lu Lu. Existence and Asymptotic Behavior of Solutions for Kirchhoff Equations Involving the Fractional $ p$-Laplacian[J].Acta mathematica scientia,Series A, 2025, 45(2): 434-449.

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References 31

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Existence and Asymptotic Behavior of Solutions for Kirchhoff Equations Involving the Fractional $ p$-Laplacian

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