]>
2018
11
5
ISSN 2008-1898
142
Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms
Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms
en
en
In this paper, we consider the following nonlinear Schrödinger-Poisson system
\[
\left\{
\renewcommand{\arraystretch}{1.25}
\begin{array}{ll}
-\Delta u + V(x)u+K(x)\phi u= f(x,u), x\in \mathbb{R}^3,\\
-\Delta \phi=K(x)u^{2}, x\in \mathbb{R}^3,
\end{array}
\right.
\]
where~\(V, K\in L^{\infty}(\mathbb{R}^3)\) and \(f:\mathbb{R}^3\times\mathbb{R}\rightarrow\mathbb{R}\) is continuous. We prove that the problem has a nontrivial solution under asymptotically periodic case of \(V, K\), and \(f\) at infinity. Moreover, the nonlinear term \(f\) does not satisfy any monotone condition.
591
601
Da-Bin
Wang
Department of Applied Mathematics
Lanzhou University of Technology
People’s Republic of China
wangdb96@163.com
Lu-Ping
Ma
Department of Applied Mathematics
Lanzhou University of Technology
People’s Republic of China
974531947@qq.com
Wen
Guan
Department of Applied Mathematics
Lanzhou University of Technology
People’s Republic of China
mathguanw@163.com
Hong-Mei
Wu
Department of Applied Mathematics
Lanzhou University of Technology
People’s Republic of China
wuhongmei0610@126.com
Schrödinger-Poisson system
asymptotically periodic
variational method
Article.1.pdf
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]
Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals
Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals
en
en
This paper mainly deals with the stability of delayed neural networks with time-varying impulses, in which both stabilizing and destabilizing impulses are considered. By means of the comparison principle, the average impulsive interval and the Lyapunov function approach, sufficient conditions are obtained to ensure that the considered impulsive delayed neural network is exponentially stable. Different from existing results on stability of impulsive systems with average impulsive approach, it is assumed that impulsive strengths of stabilizing and destabilizing impulses take values from two finite states, and a new definition of impulsive strength-dependent average impulsive interval is proposed to characterize the impulsive sequence. The characteristics of the proposed impulsive strength-dependent average impulsive interval is that each impulsive strength has its own average impulsive interval
and therefore the proposed impulsive strength-dependent average impulsive
interval is more applicable than the average impulsive interval. Simulation examples are given to show the validity and potential advantages of the developed results.
602
612
Huan
Zhang
Department of Mathematics
YangZhou University
China
Wenbing
Zhang
Department of Mathematics
YangZhou University
China
zwb850506@126.com
Zhi
Li
Business School
SiChuan University
China
Neural networks
impulsive strength-dependent average impulsive interval
time-varying impulse
stability
Article.2.pdf
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]
A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\)
A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\)
en
en
In this paper, we obtain solutions to difference equations of the form
\[ x_{n+1}=\frac{ x_{n-5}}{a_n+b_n x_{n-2}x_{n-5}},\]
where \((a_{n})\) and \((b_{n})\) are sequences of real numbers. Consequently, a result of Elsayed is generalized. To achieve this, we use Lie symmetry analysis.
613
623
Mensah
Folly-Gbetoula
School of Mathematics
University of the Witwatersrand
South Africa
Folly-Gbetoula@wits.ac.za
Darlison
Nyirenda
School of Mathematics
University of the Witwatersrand
South Africa
Darlison.Nyirenda@wits.ac.za
Difference equation
symmetry
reduction
group invariant
Article.3.pdf
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Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials
Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials
en
en
Some problems from modern physics and science can be described in terms of
partial differential equations with nonlocal conditions. In this paper, a
numerical method which employs the orthonormal Bernstein polynomials basis
is implemented to give the approximate solution of integro-differential
parabolic equation with purely nonlocal integral conditions. The properties
of orthonormal Bernstein polynomials, and the operational matrices for
integration, differentiation and the product are introduced and are utilized
to reduce the solution of the given integro-differential parabolic equation
to the solution of algebraic equations. An illustrative example is given to
demonstrate the validity and applicability of the new technique.
624
634
Abdelkrim
Bencheikh
Department of Mathematics
University of Ouargla
Algeria
krimbench@yahoo.fr
Lakhdar
Chiter
Department of Mathematics
University of Setif 1
Algeria
lchiter@univ-setif.dz
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Information Science and Engineering
Linyi University
Linyi University
P. R. China
P. R. China
litongx2007@163.com
Integro-differential parabolic equation
purely nonlocal integral conditions
orthonormal Bernstein polynomials
operational matrix
Article.4.pdf
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]
A note on a singular coupled Burgers equation and double Laplace transform method
A note on a singular coupled Burgers equation and double Laplace transform method
en
en
In this paper, modification of double Laplace decomposition method is
proposed for the analytical approximation solution of a coupled system of
Burgers equation with appropriate initial conditions. Some examples are given to support the validity and
applicability of the presented method.
635
643
Hassan
Eltayeb
Mathematics Department, College of Science
King Saud University
Saudi Arabia
hgadain@ksu.edu.sa
Said
Mesloub
Mathematics Department, College of Science
King Saud University
Saudi Arabia
mesloub@ksu.edu.sa
Adem
Kılıçman
Department of Mathematics
University Putra Malaysia
Malaysia
akilic@upm.edu.my
Double Laplace transform
inverse Laplace transform
singular Burgers equation
coupled Burgers equation
single Laplace transform
decomposition methods
Article.5.pdf
[
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Approximation of solutions to a general system of variational inclusions in Banach spaces and applications
Approximation of solutions to a general system of variational inclusions in Banach spaces and applications
en
en
In this paper, a general system of variational inclusions in Banach Spaces is introduced.
An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a \(\lambda\)-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theorems in uniformly convex and 2-uniformly smooth Banach spaces. The results presented in the paper improve and extend various results in the existing literatures. Moreover, some applications to monotone variational inequality problem and convex minimization problem are presented.
644
657
Hongbo
Liu
School of Science
Southwest University of Science and Technology
China
liuhongbo@swust.edu.cn
Qiang
Long
School of Science
Southwest University of Science and Technology
China
longqiang@swust.edu.cn
Yi
Li
School of Science
Southwest University of Science and Technology
China
liyi@swust.edu.cn
General system of variational inclusions
forward-backward splitting method
invex set
resolvent operator
strictly pseudocontractive
Article.6.pdf
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]
New integral inequalities and their applications to convex functions with a continuous Caputo fractional derivative
New integral inequalities and their applications to convex functions with a continuous Caputo fractional derivative
en
en
We say that a function \(f:[a,b]\to \mathbb{R}\) is \((\varphi,\delta)\)-Lipschitzian, where \(\delta\geq 0\) and \(\varphi:[0,\infty)\to [0,\infty)\), if
\[
|f(x)-f(y)|\leq \varphi(|x-y|)+\delta,\quad (x,y)\in [a,b]\times [a,b].
\]
In this work, some Hadamard's type inequalities are established for the class of \((\varphi,\delta)\)-Lipschitzian mappings. Moreover, some
applications to convex functions with a continuous Caputo
fractional derivative are also discussed.
658
671
Bashir
Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
bashirahmad_qau@yahoo.com
Mohamed
Jleli
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
jleli@ksu.edu.sa
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
\((\varphi
\delta)\)-Lipschitzian
Hadamard's type inequalities
convex function
Caputo fractional derivative
fractional mean value theorem
Article.7.pdf
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]
A reduced-order extrapolating Crank-Nicolson finite difference scheme for the Riesz space fractional order equations with a nonlinear source function and delay
A reduced-order extrapolating Crank-Nicolson finite difference scheme for the Riesz space fractional order equations with a nonlinear source function and delay
en
en
This article mainly studies the order-reduction of the classical Crank-Nicolson finite difference (CNFD) scheme for the Riesz space fractional order differential equations (FODEs) with a nonlinear source function and delay on a bounded domain. For this reason, the classical CNFD scheme for the Riesz space FODE and the existence, stability, and convergence of the classical CNFD solutions are first recalled. And then, a reduced-order extrapolating CNFD (ROECNFD) scheme containing very few degrees of freedom but holding the fully second-order accuracy for the Riesz space FODEs is established by means of proper orthogonal decomposition and the existence, stability, and convergence of the ROECNFD solutions are discussed. Finally, some numerical experiments are presented to illustrate that the ROECNFD scheme is far superior to the classical CNFD one and to verify the correctness of theoretical results. This indicates that the ROECNFD scheme is very effective for solving the Riesz space FODEs with a nonlinear source function and delay.
672
682
Yanhua
Cao
School of Sciences
East China Jiaotong University
China
yanhuacao@yeah.net
Zhendong
Luo
School of Mathematics and Physics
North China Electric Power University
China
zhdluo@ncepu.edu.cn
Crank-Nicolson finite difference scheme
Riesz space fractional order differential equation
existence and stability as well as convergence
reduced-order extrapolating Crank-Nicolson finite difference scheme
proper orthogonal decomposition
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]
Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces
Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces
en
en
In this paper, we consider the split monotone variational inclusion problem in Hilbert spaces. By assuming the existence of solutions, we introduce an iterative algorithm, in which the stepsizes does not need any prior information about the operator norm, and show its convergence theorem. Some applications and numerical experiments of the considered problem are also discussed.
683
700
Montira
Suwannaprapa
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
montira.sw@gmail.com
Narin
Petrot
Department of Mathematics, Faculty of Science
Centre of Excellence in Nonlinear Analysis and Optimizations, Faculty of Science
Naresuan University
Naresuan University
Thailand
Thailand
narinp@nu.ac.th
Split monotone variational inclusion problem
maximal monotone operator
inverse strongly monotone operator
convergence theorems
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A topology on lattice-ordered groups
A topology on lattice-ordered groups
en
en
We introduce the concept of the strong-positive cone in a lattice-ordered group \((G,\leq,\cdot)\) and define the continuous lattice-ordered group. We also investigate the \(C\)-topology and bi-\(C\)-topology given on a lattice-ordered group. The main results obtained in this paper are as follows: (1) \((G,\leq,\cdot)\) is a continuous lattice-ordered group if and only if \((G,\leq)\) is a continuous poset; (2) for the bi-\(C\)-topology \(\tau\) in a continuous lattice-ordered group \((G,\leq,\cdot)\), \((G,\cdot,\tau)\) is a topological group and \((G,\leq,\tau)\) is a topological lattice.
701
712
Huanrong
Wu
College of Mathematics and Econometrics
Hunan University
China
xueerzaifei@126.com
Qingguo
Li
College of Mathematics and Econometrics
Hunan University
China
liqingguoli@aliyun.com
Bin
Yu
College of Mathematics and Econometrics
Hunan University
China
yubin20070119@sina.com
Lattice-ordered group
continuous
topology
topological group
topological lattice
Article.10.pdf
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]
Multiple positive almost periodic solutions for some nonlinear integral equations
Multiple positive almost periodic solutions for some nonlinear integral equations
en
en
This paper is concerned with the existence of multiple positive almost periodic solutions for a nonlinear integral equation. By using Avery-Henderson and Leggett-Williams multiple fixed point theorems on cones, the existence theorems of multiple positive almost periodic solutions for the addressed integral equation are established under some sufficient assumptions. An example is given to illustrate our results.
713
722
Hui-Sheng
Ding
College of Mathematics and Information Science
Jiangxi Normal University
People’s Republic of China
dinghs@mail.ustc.edu.cn
Juan J.
Nieto
Departamento de Análisis Matemático, Facultad de Matemáticas
Universidad de Santiago de Compostela 15782
Spain
juanjose.nieto.roig@usc.es
Qiu-Feng
Zou
College of Mathematics and Information Science
Jiangxi Normal University
People’s Republic of China
642074260@qq.com
Almost periodic
multiple solutions
integral equation
Article.11.pdf
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]
On spectral gap for multicolored disordered lattice gas of exclusion processes
On spectral gap for multicolored disordered lattice gas of exclusion processes
en
en
We consider a system of multicolored disordered lattice gas in a volume
\(\Lambda\) of \(\mathbb{Z}^{d}\) driven by a disordered Markov generator
similar to that of Faggionato and Martinelli [A. Faggionato, F. Martinelli,
Probab. Theory Related Fields, \(\textbf{127}\) (2003), 535--608]. The aim of
our work is to give a new and elementary computation of the spectral gap of
multicolored disordered lattice gas which is an important step towards
obtaining the hydrodynamic limit.
723
733
Ali Bey
Touati
LaPS laboratory
Badji-Mokhtar University
Algeria
alibeytouati@gmail.com
Laila
Benaon
LaPS laboratory
Badji-Mokhtar University
Algeria
lbenaoun23@gmail.com
Halim
Zeghdoudi
LaPS laboratory
Badji-Mokhtar University
Algeria
halim.zeghdoudi@univ-annaba.dz
A simple exclusion
Markov generator
spectral gap
Article.12.pdf
[
[1]
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##[2]
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##[3]
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##[4]
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##[5]
A. Dermoune, P. Heinrich, A small step towards the hydrodynamic limit of a colored disordered lattice gas, C. R. Math. Acad. Sci. Paris, 339 (2004), 507-511
##[6]
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##[7]
A. Dermoune, S. Martinez, Around multicolour disordered lattice gas, J. Stat. Phys., 123 (2006), 181-192
##[8]
A. Faggionato, F. Martinelli , Hydrodynamic limit of a disordered lattice gas, Probab. Theory Related Fields, 127 (2003), 535-608
##[9]
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##[10]
M. Mourragui , Large deviations of the empirical current for the boundary driven Kawasaki process with long range interaction, ALEA Lat. Am. J. Probab. Math. Stat., 11 (2014), 643-678
##[11]
H. Zeghdoudi, H. Boutabia , Computation for the Canonical Measures of a Colored Disordered Lattice Gas and Spectral Gap, J. Math. Phys., 2009 (2009), 1-8
##[12]
H. Zeghdoudi, H. Boutabia, Gibbs’s Measures of a Multi-Colored Disordered Lattice Gas, Afr. J. Math. Phys., 10 (2011), 49-54
]