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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. Positive solutions for coupled system of nonlinear fractional differential equations with nonlocal conditions
	QI Chao-Fan,XUE Chun-Yan
	Mathematics 22 February 2021
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	Abstract:In this work, we study the existence of positive solutions for a nonlinear coupled system of Riemann-Liouville derivatives fractional differential equations with integral boundary value problems and a parameter. By means of a new fixed point theory due to Radu Precup, Krasnoselskii's cone fixed point theory of the vector version, we also investigate the localization and multiplicity of the positive solutions.
	TO cite this article:QI Chao-Fan,XUE Chun-Yan. Positive solutions for coupled system of nonlinear fractional differential equations with nonlocal conditions[OL].[22 February 2021] http://en.paper.edu.cn/en_releasepaper/content/4753658

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	3. 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


	4. A two-level method for the Allen-Cahn equation
	LIU Qingfang
	Mathematics 17 April 2017
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	Abstract:We consider the fully implicit treatment for the nonlinear term ofthe Allen-Cahn equation. To solve the nonlinear problem efficiently,the two-level scheme is employed. We obtain the discrete energy lawof the fully implicit scheme and two-level scheme with finiteelement method. Also the convergence of the two-level method ispresented. Finally, some numerical experiments are provided toconfirm the theoretical analysis.
	TO cite this article:LIU Qingfang. A two-level method for the Allen-Cahn equation[OL].[17 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4725276


	5. Traveling wavefronts in a discrete reaction-convection-diffusion equations with nonlocal delay
	TIAN Yue,ZHAO Zhihong,ZHAO Xiangkui
	Mathematics 16 March 2017
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	Abstract:In this paper, we study the existence, uniqueness and asymptotic stability of travelling wavefronts in a class of spatially discrete reaction-convection-diffusion equation with nonlocal delay.
	TO cite this article:TIAN Yue,ZHAO Zhihong,ZHAO Xiangkui. Traveling wavefronts in a discrete reaction-convection-diffusion equations with nonlocal delay[OL].[16 March 2017] http://en.paper.edu.cn/en_releasepaper/content/4722298


	6. 2-extendability of bipartite and cubic non-bipartite vertex-transitive graphs
	LI Qiu-Li,GAO Xing
	Mathematics 02 December 2016
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	Abstract:Chan et al. classified the2-extendable abelian Cayley graphs and posed the problem ofcharacterizing all 2-extendable Cayley graphs. We first show that a connected bipartite Cayley (vertex-transitive) graph is 2-extendable if and only if it is not a cycle. %Thereafter, the 2-extendability of Cayley graphs on specific groups, such as Dihedral group, Dicylic group, Generalized xing{generalized} dihedral group, Quasi-abelian groups and etc, has been investigated. We first show that all $k$-regular ($kgeq 3$) bipartite Cayley graphs are 2-extendable. It is known that a non-bipartite Cayley (vertex-transitive) graph is 2-extendable when it is of minimum degree at least 5. %Hence the 2-extendability of Cayley graphs of minimum degrees 3 and 4 are left.We next characterize all 2-extendable cubic non-bipartite Cayley graphs and obtain that: a cubic non-bipartite Cayley graph with girth $g$ is2-extendable if and only if $ggeq 4$ and it doesn't isomorphic to $Z_{4n}(1,4n-1,2n)$ or $Z_{4n+2}(2,4n,2n+1)$ with $ngeq 2$. Indeed, we prove a more stronger result that a cubic non-bipartite vertex-transitive graph with girth $g$ is2-extendable if and only if $ggeq 4$ and it doesn't isomorphic to $Z_{4n}(1,4n-1,2n)$ or $Z_{4n+2}(2,4n,2n+1)$ with $ngeq 2$ or the Petersen graph.
	TO cite this article:LI Qiu-Li,GAO Xing. 2-extendability of bipartite and cubic non-bipartite vertex-transitive graphs[OL].[ 2 December 2016] http://en.paper.edu.cn/en_releasepaper/content/4712274


	7. Prediction of Stock Price Index with Hidden Markov Model
	HE Fengxia,HUANG Jingfeng
	Mathematics 08 April 2016
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	Abstract:The change law of the stock price which is affected by lots of stochastic interference factors is filled with complex nonlinearity and randomicity. Therefore, predicting the stock price accurately is of great research significance. This paper concerns the closing price of S&P 500 index as the research object and the status quo and characteristics of the S&P 500 index is analyzed. A new prediction method on the basis of continuous hidden Markov model with the combination of K-Means clustering algorithm is established. The proposed prediction method for the stock price index has more certain validity and feasibility compared with the Autoregressive Integrated Moving Average Model(ARIMA) in the time series.
	TO cite this article:HE Fengxia,HUANG Jingfeng. Prediction of Stock Price Index with Hidden Markov Model[OL].[ 8 April 2016] http://en.paper.edu.cn/en_releasepaper/content/4683378


	8. A discontinuous Galerkin finite element method for the Cahn-Hilliard equation
	Liu Lijie, Gong Yurong
	Mathematics 20 February 2016
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	Abstract:In this paper, we develop, analysis and testthe Discontinuous Galerkin (DG) finite element method for the fourth orderCahn-Hilliard equation in one dimension. The method, which isdifferent from the traditional local discontinuous Galerkin (LDG)method, can be applied without introducing any auxiliary variablesor rewriting the original equation into a larger system. we provestability by choosing interface numerical fluxes carefully, finallyfor the linear case, a $O(h^{k-1})$ error estimate can be proved forpiecewise polynomials of degree $k$ when $kgeq 3$.
	TO cite this article:Liu Lijie, Gong Yurong. A discontinuous Galerkin finite element method for the Cahn-Hilliard equation[OL].[20 February 2016] http://en.paper.edu.cn/en_releasepaper/content/4678069


	9. Existence and Uniqueness of the Solution for a Class of Fractional Stochastic Differential Equations
	MingTang,Shiqing Zhang
	Mathematics 23 December 2015
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	Abstract:In this paper we get the following result: (i)When Hurst index 1/n<H<1/(n-1), n>2, we prove the integration by parts of stochastic integral formula about a special class of stochastic process driven by fractional Brown motion (ii)using Picard's iteration method, we study existence and uniqueness of solutions of stochastic differential equations driven by fractional Brown motion(fBm) with Hurst index 1/3<H<1/2. (iii) using same method, for Hurst index 1/n<H<1/(n-1). (iv) and for Hurst index H=1/n.
	TO cite this article:MingTang,Shiqing Zhang. Existence and Uniqueness of the Solution for a Class of Fractional Stochastic Differential Equations[OL].[23 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4673158


	10. Dynamics of a Stochastic Ratio-dependent Predator-prey System
	Wei Zhang-Zhi,Wu Zheng,Hu Ling,Wang Liang-Long
	Mathematics 08 December 2015
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	Abstract:This paper is concerned with a stochastic ratio-dependent predator-preymodel of interacting populations with varible coefficients. By comparison theorem ofstochastic differential equations and It^{o} formula, the globalexistence of a unique positive solution of the ratio-dependentmodel is obtained. The stochastically ultimate boundedness and stochastic permanence for this model also are established.
	TO cite this article:Wei Zhang-Zhi,Wu Zheng,Hu Ling, et al. Dynamics of a Stochastic Ratio-dependent Predator-prey System [OL].[ 8 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4669252

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