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8 results on '"Liang, Wenning"'

1. Existence and Uniqueness of Constraint Minimizers for the Planar Schrodinger-Poisson System with Logarithmic Potentials

Author

Guo, Yujin, Liang, Wenning, and Li, Yan

Subjects
Mathematical Physics, Mathematics - Functional Analysis
Abstract

In this paper, we study constraint minimizers $u$ of the planar Schr\"odinger-Poisson system with a logarithmic convolution potential $\ln |x|\ast u^2$ and a logarithmic external potential $V(x)=\ln (1+|x|^2)$, which can be described by the $L^2$-critical constraint minimization problem with a subcritical perturbation. We prove that there is a threshold $\rho ^* \in (0,\infty)$ such that constraint minimizers exist if and only if $0<\rho<\rho^*$. In particular, the local uniqueness of positive constraint minimizers as $\rho\nearrow\rho^*$ is analyzed by overcoming the sign-changing property of the logarithmic convolution potential and the non-invariance under translations of the logarithmic external potential., Comment: 36 pages, all comments are welcome

Published
2022

2. Research on the Requirements Analysis and Key Technologies of Space-Based Information Intelligence Applications

Author

Sun, Lingli, Wei, Xiaofeng, Gong, Jianglei, Liang, Wenning, Angrisani, Leopoldo, Series Editor, Arteaga, Marco, Series Editor, Chakraborty, Samarjit, Series Editor, Chen, Jiming, Series Editor, Chen, Shanben, Series Editor, Chen, Tan Kay, Series Editor, Dillmann, Rüdiger, Series Editor, Duan, Haibin, Series Editor, Ferrari, Gianluigi, Series Editor, Ferre, Manuel, Series Editor, Jabbari, Faryar, Series Editor, Jia, Limin, Series Editor, Kacprzyk, Janusz, Series Editor, Khamis, Alaa, Series Editor, Kroeger, Torsten, Series Editor, Li, Yong, Series Editor, Liang, Qilian, Series Editor, Martín, Ferran, Series Editor, Ming, Tan Cher, Series Editor, Minker, Wolfgang, Series Editor, Misra, Pradeep, Series Editor, Mukhopadhyay, Subhas, Series Editor, Ning, Cun-Zheng, Series Editor, Nishida, Toyoaki, Series Editor, Oneto, Luca, Series Editor, Panigrahi, Bijaya Ketan, Series Editor, Pascucci, Federica, Series Editor, Qin, Yong, Series Editor, Seng, Gan Woon, Series Editor, Speidel, Joachim, Series Editor, Veiga, Germano, Series Editor, Wu, Haitao, Series Editor, Zamboni, Walter, Series Editor, Tan, Kay Chen, Series Editor, Wang, Yue, editor, Zou, Jiaqi, editor, Xu, Lexi, editor, Ling, Zhilei, editor, and Cheng, Xinzhou, editor

Published
2024
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5. Refined spike profiles of constraint minimizers for the planar Schrödinger-Poisson system with logarithmic potentials.

Author

Guo, Yujin, Liang, Wenning, and Li, Yan

Subjects
ASYMPTOTIC expansions
Abstract

This paper is concerned with constraint minimizers of the planar Schrödinger-Poisson system with a logarithmic convolution potential and a logarithmic external potential $ V(x) = \ln(1+|x|^2) $. It is known that minimizers exist if and only if the particle mass $ \rho>0 $ satisfies $ \rho<\rho^* $ for some threshold $ \rho^*\in(0,\infty) $. As a continuation of [22], this paper is devoted to analyzing the refined spike profiles of constraint minimizers as $ \rho\nearrow\rho^* $. [ABSTRACT FROM AUTHOR]

Published
2024
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7. Solutions to a gauged Schrödinger equation with concave–convex nonlinearities without (AR) condition.

Author

Liang, Wenning and Zhai, Chengbo

Subjects
*SCHRODINGER equation, *NONLINEAR Schrodinger equation, *GAGING, *MOUNTAIN pass theorem, *MULTIPLICITY (Mathematics)
Abstract

In this paper, we are concerned with a gauged nonlinear Schrödinger equation − Δ u + V (x) u + λ ( h 2 (| x |) | x | 2 + ∫ | x | ∞ h (s) s u 2 (s) d s) u = μ g (x , u) + ν f (x , u) , i n R 2 , where λ , μ , ν are positive parameters and h (s) = 1 2 ∫ 0 s r u 2 (r) d r. Under appropriate assumptions on the potential V and nonlinear terms g and f, where g has sublinear growth and f has asymptotically linear or superlinear growth without (AR) condition, we acquire the existence and multiplicity of solutions by means of Mountain pass theorem and Fountain theorem. Our results generalize and improve the recent result in the literature. [ABSTRACT FROM AUTHOR]

Published
2021
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