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541 results on '"Feng, Zhaosheng"'

3. Normalized solutions for Sobolev critical Schr\'odinger-Bopp-Podolsky systems

Author

Li, Yuxin, Chang, Xiaojun, and Feng, Zhaosheng

Subjects
Mathematics - Analysis of PDEs, 35K92, 35B44, 35B40, 35R02
Abstract

We study the Sobolev critical Schr\"odinger-Bopp-Podolsky system \begin{gather*} -\Delta u+\phi u=\lambda u+\mu|u|^{p-2}u+|u|^4u\quad \text{in }\mathbb{R}^3, -\Delta\phi+\Delta^2\phi=4\pi u^2\quad \text{in } \mathbb{R}^3, \end{gather*} under the mass constraint \[ \int_{\mathbb{R}^3}u^2\,dx=c \] for some prescribed $c>0$, where $20$ is a parameter, and $\lambda\in\mathbb{R}$ is a Lagrange multiplier. By developing a constraint minimizing approach, we show that the above system admits a local minimizer. Furthermore, we establish the existence of normalized ground state solutions., Comment: 19 pages

Published
2023
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6. Optimising the Formulation and Properties of UHPC Material Based on Andreasen’s Model

Author

Feng, Zhaosheng, Huang, Wei, Zheng, Haiao, Liu, Wen, Zheng, Zheng, Editor-in-Chief, Xi, Zhiyu, Associate Editor, Gong, Siqian, Series Editor, Hong, Wei-Chiang, Series Editor, Mellal, Mohamed Arezki, Series Editor, Narayanan, Ramadas, Series Editor, Nguyen, Quang Ngoc, Series Editor, Ong, Hwai Chyuan, Series Editor, Sun, Zaicheng, Series Editor, Ullah, Sharif, Series Editor, Wu, Junwei, Series Editor, Zhang, Baochang, Series Editor, Zhang, Wei, Series Editor, Zhu, Quanxin, Series Editor, Zheng, Wei, Series Editor, Liu, Peng, editor, Bilgin, Hüseyin, editor, Yang, Jialing, editor, and Hu, Bin, editor

Published
2024
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10. Multiple positive solutions for the fractional Schr\'{o}dinger-Poisson systems involving critical nonlinearities with potential

Author

Fan, Haining, Feng, Zhaosheng, and Yan, Xingjie

Subjects
Mathematics - Analysis of PDEs, 35A15, 35B09, 35B33, 35J05
Abstract

In this paper, we study the existence of multiple positive solutions for a class of fractional Schr\"{o}dinger-Poisson systems involving sign-changing potential and critical nonlinearities on an unbounded domain. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we investigate how the coefficient $g(x)$ of the critical nonlinearity affects the number of positive solutions. Moreover, we present a novel relationship between the number of positive solutions and the category of the global maximum set of $g(x)$., Comment: 44pages

Published
2021

11. Positive solutions for the fractional Schr\'{o}dinger equations with logarithmic and critical nonlinearities

Author

Fan, Haining, Feng, Zhaosheng, and Yan, Xingjie

Subjects
Mathematics - Analysis of PDEs, Mathematics - Functional Analysis, 35A15, 35B09, 35B33, 35J60
Abstract

In this paper, we study a class of fractional Schr\"{o}dinger equations involving logarithmic and critical nonlinearities on an unbounded domain, and show that such an equation with positive or sign-changing weight potentials admits at least one positive ground state solution and the associated energy is positive (or negative). By applying the Nehari manifold method and Ljusternik-Schnirelmann category, we deeply investigate how the weight potential affects the multiplicity of positive solutions, and obtain the relationship between the number of positive solutions and the category of some sets related to the weight potential., Comment: 40 pages

Published
2021

17. Multiple solutions of p-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents

Author

Lin Xiaolu, Zheng Shenzhou, and Feng Zhaosheng

Subjects
fractional p-laplacian, multiple solutions, hardy-littlewood-sobolev’s critical exponents, concentration-compactness, genus theory, 35a15, 35j60, 35j20, Mathematics, QA1-939
Abstract

In this article, we are concerned with multiple solutions of Schrödinger-Choquard-Kirchhoff equations involving the fractional pp-Laplacian and Hardy-Littlewood-Sobolev critical exponents in RN{{\mathbb{R}}}^{N}. We classify the multiplicity of the solutions in accordance with the Kirchhoff term M(⋅)M\left(\cdot ) and different ranges of qq shown in the nonlinearity f(x,⋅)f\left(x,\cdot ) by means of the variational methods and Krasnoselskii’s genus theory. As an immediate consequence, some recent related results have been improved and extended.

Published
2023
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38. Global phase portraits of generalized polynomial Liénard system with a unique equilibrium and a periodic annulus.

Author

Chen, Hebai, Dai, Dehong, and Feng, Zhaosheng

Subjects
EQUILIBRIUM, POLYNOMIALS
Abstract

This paper aims to study the sufficient and necessary conditions for a generalized polynomial Liénard system with a unique equilibrium and one periodic annulus. In such a case, there are two types of equilibrium: a centre or a neighbourhood of the equilibrium consisting of a hyperbolic sector and an elliptical sector. The sufficient and necessary conditions for both cases are established and global phase portraits in the Poincaré disc are presented under certain conditions. [ABSTRACT FROM AUTHOR]

Published
2024
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39. Lions-type theorem of the p-Laplacian and applications

Author

Su Yu and Feng Zhaosheng

Subjects
lions theorem, quasilinear elliptic equation, singular potential, critical exponent, ground state solution, 35a15, 35r11, 35j92, Analysis, QA299.6-433
Abstract

In this article, our aim is to establish a generalized version of Lions-type theorem for the p-Laplacian. As an application of this theorem, we consider the existence of ground state solution for the quasilinear elliptic equation with the critical growth.

Published
2021
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50. Well-posedness and stability for non-autonomous stochastic evolution equations of parabolic-type with additive noise.

Author

Zhang, Xuping and Feng, Zhaosheng

Subjects
AUTONOMOUS differential equations, EVOLUTION equations, INITIAL value problems, NOISE
Abstract

We are concerned with the well-posedness and stability for a class of non-autonomous stochastic evolution equations of parabolic-type with additive noise. After proving the local existence of mild solutions of non-autonomous stochastic evolution equations with arbitrarily initial time and initial value, we obtain the blowup alternative property, global existence of mild solutions as well as asymptotic stability of mild solutions in $ p $-th moment for the associated initial value problem when the evolution family is noncompact. [ABSTRACT FROM AUTHOR]

Published
2024
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