Existence results for fractional Kirchhoff problems with magnetic field and supercritical growth

Gao, Liu; Tan, Zhong

doi:10.1063/5.0127185

Journal of Mathematical Physics

2023

DOI: 10.1063/5.0127185

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Existence results for fractional Kirchhoff problems with magnetic field and supercritical growth

Liu Gao

Zhong Tan

Abstract: In this paper, we investigate a class of fractional Kirchhoff problems with a magnetic field and supercritical growth. By employing a truncation argument and Moser iterative method, we obtain the existence of nontrivial solutions. Our results are new and supplement the previous ones in the literature.

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2024

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Some results for a supercritical Schrödinger-Poisson type system with $ (p, q) $-Laplacian

Liang,

Song,

Yang

2024

MATH

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<abstract>In this work, we focus our attention on the existence of nontrivial solutions to the following supercritical Schrödinger-Poisson type system with $ (p, q) $-Laplacian: <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} -\Delta_{p}u-\Delta_{q}u+\phi|u|^{q-2} u = f\left(x, u\right)+\mu|u|^{s-2} u & \text { in } \Omega, \\ -\Delta \phi = |u|^q & \text { in } \Omega, \\ u = \phi = 0 & \text { on } \partial \Omega, \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula> where $ \Omega \subset \mathbb{R}^N $ is a bounded smooth domain, $ \mu > 0, N > 1 $, and $ -\Delta_{{\wp}}\varphi = div(|\nabla\varphi|^{{\wp}-2} \nabla\varphi) $, with $ {\wp}\in \{p, q\} $, is the homogeneous $ {\wp} $-Laplacian. $ 1 < p < q < \frac{q^*}{2} $, $ q^*: = \frac{Nq}{N-q} < s $, and $ q^* $ is the critical exponent to $ q $. The proof is accomplished by the Moser iterative method, the mountain pass theorem, and the truncation technique. Furthermore, the $ (p, q) $-Laplacian and the supercritical term appear simultaneously, which is the main innovation and difficulty of this paper.</abstract>

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Some results for a supercritical Schrödinger-Poisson type system with $ (p, q) $-Laplacian

Liang,

Song,

Yang

2024

MATH

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Existence results for fractional Kirchhoff problems with magnetic field and supercritical growth

Cited by 1 publication

References 25 publications

Some results for a supercritical Schrödinger-Poisson type system with $ (p, q) $-Laplacian

Some results for a supercritical Schrödinger-Poisson type system with $ (p, q) $-Laplacian

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