Multiplicity of solutions for the Kirchhoff equation with critical nonlinearity in high dimension

Tang, BiYun; Lan, Yong-Yi

doi:10.1002/mma.7614

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…From then on, many kinds of elliptic equations involving critical or supercritical exponents over bounded domains or in the whole space have been extensively considered. For example, we refer to [13,18,25,10] for the setting of bounded domains, and see also [3,23,8,4] for the setting of whole space. To nonlocal aspect of the tension arising from nonlocal measurements of the fractional length of string, Fiscella and Valdinoci in [11] proposed a stationary Kirchhoff type equation.…”

Section: Introductionmentioning

confidence: 99%

Schr\”{o}dinger-Kirchhoff equations of fractional $p$-Laplacian involving logarithmic and critical nonlinearity

Lv,

Zheng

2024

Preprint

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For $00$, we consider a class of Schr\”{o}dinger-Kirchhoff equations of fractional $p$-Laplacian involving logarithmic nonlinearity and critical exponential growth: \begin{equation*} m\left( \left\Vert u\right\Vert ^{p}\right) \left( \left( -\Delta \right) _{p}^{s}u+\lambda V\left( x\right) \left\vert u\right\vert ^{p-2}u\right) =\lambda h\left( x\right) \left\vert u\right\vert ^{\theta p-2}u\ln \left\vert u\right\vert +\sigma \left\vert u\right\vert ^{p_{s}^{\ast }-2}u\quad \mbox{in}\ \mathbb{R}^{n} \end{equation*}% with \begin{equation*} \left\Vert u\right\Vert =\left( \int_{\mathbb{R}^{2n}}\frac{\left\vert u\left( x\right) -u\left( y\right) \right\vert ^{p}}{\left\vert x-y\right\vert ^{n+sp}}dxdy+\lambda \int_{\mathbb{R}^{n}}V\left( x\right) \left\vert u\right\vert ^{p}dx\right) ^{1/p}, \end{equation*}% where $p_{s}^{\ast }=np/\left( n-sp\right) $, $1\leq \theta

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Section: Introductionmentioning

confidence: 99%

Schr\”{o}dinger-Kirchhoff equations of fractional $p$-Laplacian involving logarithmic and critical nonlinearity

Lv,

Zheng

2024

Preprint

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Existence and multiplicity for fractional p-Kirchhoff problem with competitive nonlinearities and critical growth

Zheng

2022

Anal.Math.Phys.

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Multiplicity of solutions for the Kirchhoff equation with critical nonlinearity in high dimension

Abstract: This paper is devoted to the following Kirchhoff type of problems:whereUnder some suitable assumptions on V(x), we will prove the multiplicity of solutions for the Kirchhoff-type equation by the variational method.

Cited by 2 publications

References 28 publications

Schr\”{o}dinger-Kirchhoff equations of fractional $p$-Laplacian involving logarithmic and critical nonlinearity

Schr\”{o}dinger-Kirchhoff equations of fractional $p$-Laplacian involving logarithmic and critical nonlinearity

Existence and multiplicity for fractional p-Kirchhoff problem with competitive nonlinearities and critical growth

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