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1. Infinitely many high energy solutions for Schr\"{o}dinger-Poisson system | |||
XIONG Biao,TANG Chun-lei | |||
Mathematics 15 February 2023 | |||
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Abstract:In this arcitle, we investigate the following Schr\"{o}dinger-Poisson system\begin{equation*} \begin{cases} -\Delta u+V(x)u+\phi u=f(u), & \text{ in }\R,\\ -\Delta \phi= u^2, & \text{ in }\R, \end{cases}\end{equation*}where $V(x)$ is coercive, $f$ satisfies that $\frac{1}{3}f(t)t\geq F(t)>0$ for every $t\in\RRR\setminus\{0\}$. Under certain assumptions about the above terms, we obtain infinitely many high energy solutions for the system by Symmetric mountain pass theorem. | |||
TO cite this article:XIONG Biao,TANG Chun-lei. Infinitely many high energy solutions for Schr\"{o}dinger-Poisson system[OL].[15 February 2023] http://en.paper.edu.cn/en_releasepaper/content/4759083 |
2. On Riemann-Liouville Abstract Fractional Relaxation Equations | |||
MEI Zhandong,JIN Rui | |||
Mathematics 25 April 2017 | |||
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Abstract:This paper is concerned with abstractfractional relaxation equations. The notion of Riemann-Liouville fractional $(lpha,eta)$ resolvent and some of its propertiesare studied. Moreover, by means of such properties and the properties of general Mittag-Leffler functions, the existence and uniqueness of the strong solution of the homogeneous and inhomogeneous abstract fractional relaxation equations are derived. | |||
TO cite this article:MEI Zhandong,JIN Rui. On Riemann-Liouville Abstract Fractional Relaxation Equations[OL].[25 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4727567 |
3. Thompson's group $F$ and Linear group $GL_{infty}(ZZ)$ | |||
Wu Yan,Chen Xiaoman | |||
Mathematics 21 February 2011 | |||
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Abstract:Thepaper proves that there is an injective Lipschitz map $arphi:(F, d_{S})longrightarrow(H,d)$,where $F$ is the Thompson's group, $d_{S}$ is the word-metric of $F$ with respect to the finite generating set $S={x_{0}, x_{1}}$, $H$ is a subgroup of the linear group $GL_{infty}(ZZ)$ and $d$ is a metric of $H$. | |||
TO cite this article:Wu Yan,Chen Xiaoman. Thompson's group $F$ and Linear group $GL_{infty}(ZZ)$[OL].[21 February 2011] http://en.paper.edu.cn/en_releasepaper/content/4410900 |
4. Commuting Toeplitz Operators with Harmonic Symbols on A^2(overline{mathbb{D}},dmu)$ | |||
Ji You Qing,Wang Chunmei | |||
Mathematics 06 January 2009 | |||
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Abstract:For any given symmetric measure u on the closed unit disk $overline{mathbb{D}}$, by characterizingthe relationship between the Berezin transform and harmonic functions, we obtain that if both $f$ and $g$ are bounded harmonic on $mathbb{D}$, then the Toeplitz operator $T_f$ commutes with $T_g$ on $A^2(overline{mathbb{D}},dmu)$ if and only if at least one of the following conditions holds: (1) both $f$ and $g$ are analytic on $mathbb{D}$; (2) both $overline{f}$ and $overline{g}$ are analytic on $mathbb{D}$;(3) there exist constants $a,binmathbb{C}$, not both 0, such that $af+bg$ is constant on $mathbb{D}$. | |||
TO cite this article:Ji You Qing,Wang Chunmei. Commuting Toeplitz Operators with Harmonic Symbols on A^2(overline{mathbb{D}},dmu)$ [OL].[ 6 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27386 |
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