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	1. Ground state solution for Schr\"{o}dinger-KdV system with asymptotically periodic potential
	Liang Fei-Fei,Wu Xing-Ping,Tang Chun-Lei
	Mathematics 08 March 2021
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	Abstract:In this paper, we study the coupled nonlinear Schr\"{o}dinger-Korteweg-de Vries system with asymptotically periodic potential. By using the variational method and Nehari manifold, we obtain the existence of non-trivial ground state solution in dimensions $N\leq3$.
	TO cite this article:Liang Fei-Fei,Wu Xing-Ping,Tang Chun-Lei. Ground state solution for Schr\"{o}dinger-KdV system with asymptotically periodic potential[OL].[ 8 March 2021] http://en.paper.edu.cn/en_releasepaper/content/4753986


	2. Infinitely many high energy radial solutions for Chern-Simons-Schr\"{o}dinger systems
	YuYanyan,Tang Chunlei
	Mathematics 03 April 2020
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	Abstract:In this paper, we investigate the following Chern-Simons-Schr\"{o}dinger system\begin{equation}\label{css}\begin{cases} -\Delta u+ u+A_{0}u+A_{1}^{2}u+A_{2}^{2}u=f(u), \\ \partial_{1}A_{2}-\partial_{2}A_{1}=-\frac{1}{2}u^{2},\qquad\partial_{1}A_{1}+\partial_{2}A_{2}=0,\\ \partial_{1}A_{0}=A_{2}u^{2}, \qquad \partial_{2}A_{0}=-A_{1}u^{2},\end{cases}\end{equation}where $\partial_{1}=\frac{\partial}{\partial x_{1}}, \partial_{2}=\frac{\partial}{\partial x_{2}}$ for $x=\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2}$, $A_{j} : \mathbb{R}^{2} \rightarrow \mathbb{R}$ is the gauge field $(j=0,1,2)$. If $f$ satisfies the suitable subcritical conditions.By using variational methods, we prove that Chern-Simons-Schr\"{o}dinger system has infinitely many high energy radial solutions.
	TO cite this article:YuYanyan,Tang Chunlei. Infinitely many high energy radial solutions for Chern-Simons-Schr\"{o}dinger systems[OL].[ 3 April 2020] http://en.paper.edu.cn/en_releasepaper/content/4751383

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	3. Stochastic Near-optimal Controls in Infinite Dimensional Spaces
	Tang Chao,Zhang Shiqing
	Mathematics 26 July 2017
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	Abstract:A general stochastic near-maximum principle in some integral sense is proved for near-optimal control of an stochastic evolution system,where both the drift and diffusion terms are allowed to depend on controls, and also the control domain need not be convex. Error bounds for thenear-optimal controls and the near-maximum condition in infinite dimensional spaces are obtained. Finally, an example isgiven to illustrate our results.
	TO cite this article:Tang Chao,Zhang Shiqing. Stochastic Near-optimal Controls in Infinite Dimensional Spaces[OL].[26 July 2017] http://en.paper.edu.cn/en_releasepaper/content/4739545


	4. On the Classical Solutions of Infinite-dimensional Linear Systemswith State and Input Delays
	MEI Zhandong,MAO Hefeng
	Mathematics 27 April 2017
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	Abstract:This paper is concerned with infinite-dimensional linear systems with state and input delays. It is proved that the classical solution of such delayed system is also associated to the classical solution of abstract linear control system. Moreover, a weaker sufficient conditions is introduced for the existence of classical solution.
	TO cite this article:MEI Zhandong,MAO Hefeng. On the Classical Solutions of Infinite-dimensional Linear Systemswith State and Input Delays[OL].[27 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4727712


	5. On super weak compactness of subsets and its equivalences in Banach spaces
	CHENG Li-Xin,CHENG Qing-Jin,TU Kun,ZHANG Ji-Chao
	Mathematics 26 April 2017
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	Abstract:Analogous to weak compactness of subsets of Banach spaces and to property of subsets in super reflexive spaces, the purpose of this paper is to discuss super weak compactness of both convex and nonconvex subsets in Banach spaces. As a result, this paper gives two characterizations of super weakly compact sets: The first one is Grothendiek's type theorem; the second one is James' type characterization. These are done by localizing some basic properties of ultrapowers and using some geometric procedures of Banach spaces.
	TO cite this article:CHENG Li-Xin,CHENG Qing-Jin,TU Kun, et al. On super weak compactness of subsets and its equivalences in Banach spaces[OL].[26 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4729884


	6. A new approach to measure of non-compactness of Banach spaces
	CHENG Li-Xin,CHENG Qing-Jin,SHEN Qin-Rui,TU Kun,ZHANG Wen
	Mathematics 26 April 2017
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	Abstract:This paper aims to deal with measures of noncompactness of a Banach space $X$ in a new way: Assume that $mathfrak C$ is the collection of all nonempty bounded closed convex sets of $X$, $mathfrak Ksubsetmathfrak C$ consisting of all compact convex sets and $Omega$ is the closed unit ball of the dual $X^*$. Then (1); $mathfrak C$ is a normed semigroup endowed with the set addition $Aoplus B=overline{A+B}$, the usual scaler multiplication of sets and endowed with the norm $\|\|cdot\|\|$ defined for $Cinmathfrak C$ by $\|\|C\|\|=sup_{cin C}\|c\|$; (2); $J: mathfrak C ightarrow C_b(Omega)$ defined by $JC=sup_{cin C}langlecdot,c angle$ is a positively linear order isometry; further (3); both $E_mathfrak C=overline{Jmathfrak C-Jmathfrak C}$ and $E_mathfrak K=overline{Jmathfrak K-Jmathfrak K}$ are Banach sublattices and $E_mathfrak K$ is a lattice ideal of $E_mathfrak C$;(4) the quotient space $Q(E_mathfrak C)equiv E_mathfrak C/E_mathfrak K$ is an abstract $M$ space; consequently, it is order isometric to a sublattice $T(E_mathfrak C/E_mathfrak K)$ of a $C(K)$ space for some compact Hausdorff space $K$.
	TO cite this article:CHENG Li-Xin,CHENG Qing-Jin,SHEN Qin-Rui, et al. A new approach to measure of non-compactness of Banach spaces[OL].[26 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4729878


	7. 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


	8. Fixed points of operators without increasing property with applications to nonlinear integral equations
	ZHAO Zengqin,LIN Xiuli
	Mathematics 20 April 2017
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	Abstract:By using the cone theory, it is studied that existence of fixed points of operator $A$ without increasing property. The operator $A$ lies between operators $B_1$ and $B_2$, where $B_1, B_2$ have some increasing property. We obtain the existence of fixed points of the operator $A$ and the interval containing the fixed points. Lastly, the results are applied to a class of nonlinear integral equations.
	TO cite this article:ZHAO Zengqin,LIN Xiuli. Fixed points of operators without increasing property with applications to nonlinear integral equations[OL].[20 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4727227


	9. Existence and multiplicity of positive solutions for a class of fractional boundaryvalue problem
	WANG Yongqing,LIU Lishan
	Mathematics 13 October 2016
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	Abstract:The aim of this paper is to consider the following fractionaldifferential equation$$left{ligned & D^{lpha}_{0+}u(t)+a(t) f(t,u(t))=0 , 0<t<1,\& u(0)=u'(0)=u''(0)=u''(1)=0,endaligned ight.$$where $3 < lpha leq 4$ is a real number, $D^{lpha}_{0+}$ isthe standard Riemann-Liouville derivative, $f:[0,1] imes[0,+infty) ightarrow [0,+infty)$ is continuous, $a(t)inC((0,1),[0,+infty))$ may be singular at $t=0,1$. Bymeans of the fixed point index theory, a number of theorems on theexistence and multiplicity of positive solutions are obtained andsome previous results are improved. Finally one example is workedout to demonstrate our main results.
	TO cite this article:WANG Yongqing,LIU Lishan. Existence and multiplicity of positive solutions for a class of fractional boundaryvalue problem[OL].[13 October 2016] http://en.paper.edu.cn/en_releasepaper/content/4707079


	10. Positive solutions for a class of fractional 3-point boundaryvalue problems at resonance
	WANG Yongqing,LIU Lishan
	Mathematics 12 October 2016
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	Abstract:The aim ofthis paper is to study the fractional nonlocal resonant boundary valueproblems$$left{ligned & D^{lpha}_{0+}u(t)+f(t,u(t))=0 , 0<t<1,\&u(0)=0, u(1)=eta u(xi),endaligned ight.$$where $1 < lpha < 2$, $0 < xi < 1$, $eta xi^{lpha-1}= 1$,$D^{lpha}_{0+}$ is the standard Riemann-Liouville derivative,$f:[0,1] imes [0,+infty) ightarrow mathbb{R}$ is continuous.The existence and uniqueness of positive solutions are obtained bymeans of the fixed point index theory and iterative technique.
	TO cite this article:WANG Yongqing,LIU Lishan. Positive solutions for a class of fractional 3-point boundaryvalue problems at resonance[OL].[12 October 2016] http://en.paper.edu.cn/en_releasepaper/content/4707005

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