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On the existence of positive solutions of a state-dependent neutral functional differential equation with two state-delay functions 一类具有两状态时滞函数的状态相关中立型泛函微分方程正解的存在性
Pub Date : 2020-12-14 DOI: 10.30538/PSRP-OMA2020.0072
E. A. M. A, Hamdallah, E. M. A, Ebead, H. R
In this paper, we study the existence of positive solutions for an initial value problem of a state-dependent neutral functional differential equation with two state-delay functions. The continuous dependence of the unique solution will be proved. Some especial cases and examples will be given.
本文研究了具有两个状态时滞函数的状态相关中立型泛函微分方程初值问题正解的存在性。将证明唯一解的连续依赖性。文中列举了一些特殊情况和实例。
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引用次数: 0
Well-posedness for a modified nonlinear Schrödinger equation modeling the formation of rogue waves 模拟流氓波形成的修正非线性Schrödinger方程的适定性
Pub Date : 2020-10-30 DOI: 10.30538/psrp-oma2021.0088
C. Holliman, L. Hyslop
The Cauchy problem for a higher order modification of the nonlinear Schrödinger equation (MNLS) on the line is shown to be well-posed in Sobolev spaces with exponent (s > frac{1}{4}). This result is achieved by demonstrating that the associated integral operator is a contraction on a Bourgain space that has been adapted to the particular linear symbol present in the equation. The contraction is proved by using microlocal analysis and a trilinear estimate that is shown via the ([k; Z])-multiplier norm method developed by Terence Tao.
证明了非线性Schrödinger方程(MNLS)在线上的高阶修正的Cauchy问题在指数为(s>frac{1}{4})的Sobolev空间中是适定的。这一结果是通过证明相关的积分算子是布尔增益空间上的收缩来实现的,布尔增益空间已经适应于方程中存在的特定线性符号。利用微观局部分析和Terence Tao提出的([k;Z])-乘数范数方法给出的三线性估计证明了收缩性。
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引用次数: 0
Exponentiated transmuted lindley distribution with applications 指数变换林德利分布与应用
Pub Date : 2019-12-31 DOI: 10.30538/PSRP-OMA2019.0035
Emmanuel W. Okereke
In this paper, we study a new distribution called the exponentiated transmuted Lindley distribution. The proposed distribution has three special cases namely Lindley, exponentiated Lindley and transmuted Lindley distributions. Along with the basic properties of the distribution, the maximum likelihood technique of estimating the parameters of the distribution are discussed. Two applications of the distribution are also part of this article.
本文研究了一种新的分布,即指数变换林德利分布。所提出的分布有三种特殊情况,即林德利分布、指数林德利分布和变形林德利分布。结合分布的基本性质,讨论了估计分布参数的极大似然技术。该发行版的两个应用程序也是本文的一部分。
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引用次数: 4
Existence and uniqueness results for Navier problems with degenerated operators 退化算子Navier问题的存在唯一性结果
Pub Date : 2019-12-31 DOI: 10.30538/PSRP-OMA2019.0028
A. C. Cavalheiro
Ω⊂RN is a bounded open set, f ω2 ∈Lp (Ω, ω2), G ν2 ∈ [Ls (Ω, ν2)] , ω1, ω2, ν1 and ν2 are four weight functions (i.e., ωi and νi, i = 1, 2 are locally integrable functions on RN such that 0 < ωi(x), νi(x) < ∞ a.e. x∈RN), ∆ is the Laplacian operator, 1 < q, s < p < ∞, 1/p + 1/p ′ = 1 and 1/s + 1/s ′ = 1. For degenerate partial differential equations, i.e., equations with various types of singularities in the coefficients, it is natural to look for solutions in weighted Sobolev spaces (see [1–8]). The type of a weight depends on the equation type. A class of weights, which is particularly well understood, is the class of Ap weights that was introduced by B.Muckenhoupt in the early 1970’s (see [7]). These classes have found many useful applications in harmonic analysis (see [9] and [10]). Another reason for studying Ap-weights is the fact that powers of the distance to submanifolds of RN often belong to Ap (see [8] and [11]). There are, in fact, many interesting examples of weights (see [6] for p-admissible weights). In the non-degenerate case (i.e. with ω(x) ≡ 1), for all f ∈ Lp(Ω) the Poisson equation associated with the Dirichlet problem { −∆u = f (x), in Ω u(x) = 0, in ∂Ω
Ω⊂RN是一个有界开集,fω2∈Lp(Ω,ω2),GΓ2∈[Ls(Ω,Γ2)],ω1,ω2,Γ1和Γ2是四个权函数(即,ωi和Γi,i=1,2是RN上的局部可积函数,使得0<ωi(x),Γi(x)<∞a.e.x∈RN),∆是拉普拉斯算子,1
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引用次数: 0
Positive solutions for nonlinear Caputo-Hadamard fractional differential equations with integral boundary conditions 具有积分边界条件的非线性Caputo-Hadamard分数阶微分方程的正解
Pub Date : 2019-12-31 DOI: 10.30538/PSRP-OMA2019.0033
A. Ardjouni, A. Djoudi
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引用次数: 10
Small convective motions of a visco-elastic fluid filling completely a container when the fluid is heated from below 粘弹性流体被从下面加热时完全充满容器的小的对流运动
Pub Date : 2019-12-31 DOI: 10.30538/PSRP-OMA2019.0030
H. Essaouini, Fs, Morocco. Tetuan, P. Capodanno
Abstract: In this paper, we study the small oscillations of a visco-elastic fluid that is heated from below and fills completely a rigid container, restricting to the more simple Oldroyd model. We obtain the operatorial equations of the problem by using the Boussinesq hypothesis. We show the existence of the spectrum, prove the stability of the system if the kinematic coefficient of viscosity and the coefficient of temperature conductivity are sufficiently large and the existence of a set of positive real eigenvalues having a point of the real axis as point of accumulation. Then, we prove that the problem can be reduced to the study of a Krein-Langer pencil and obtain new results concerning the spectrum. Finally, we obtain an existence and unicity theorem of the solution of the associated evolution problem by means of the semigroups theory.
摘要:在本文中,我们研究了粘弹性流体从下加热并完全填充刚性容器时的小振动,限制在更简单的Oldroyd模型中。利用Boussinesq假设,得到了该问题的算子方程。我们证明了谱的存在性,证明了系统的稳定性,如果运动粘度系数和温度电导率系数足够大,并且存在一组正实特征值,实轴的一个点为积累点。然后,我们证明了该问题可以简化为克林-兰格铅笔的研究,并得到了有关谱的新结果。最后,利用半群理论得到了关联演化问题解的存在性和唯一性定理。
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引用次数: 0
Global well-posedness and analyticity for generalized porous medium equation in critical Fourier-Besov-Morrey spaces 临界Fourier Besov-Morrey空间中广义多孔介质方程的全局适定性和分析性
Pub Date : 2019-12-31 DOI: 10.30538/psrp-oma2019.0040
Mohamed Toumlilin
In this paper, we study the generalized porous medium equations with Laplacian and abstract pressure term. By using the Fourier localization argument and the Littlewood-Paley theory, we get global well-posedness results of this equation for small initial data u0 belonging to the critical Fourier-Besov-Morrey spaces. In addition, we also give the Gevrey class regularity of the solution.
本文研究了具有拉普拉斯算子和抽象压力项的广义多孔介质方程。利用傅立叶定域论和Littlewood-Paley理论,我们得到了该方程对于属于临界傅立叶Besov-Morrey空间的小初始数据u0的全局适定性结果。此外,我们还给出了解的Gevrey类正则性。
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引用次数: 3
Random attractors for Stochastic strongly damped non-autonomous wave equations with memory and multiplicative noise 具有记忆和乘性噪声的随机强阻尼非自治波动方程的随机吸引子
Pub Date : 2019-12-31 DOI: 10.30538/psrp-oma2019.0039
Abdelmajid Ali Dafallah, Qiaozhen Ma, Ahmed Eshag Mohamed
Abstract: In this paper, we study the dynamical behavior of solutions for the stochastic strongly damped wave equation with linear memory and multiplicative noise defined on Rn. Firstly, we prove the existence and uniqueness of the mild solution of certain initial value for the above-mentioned equations. Secondly, we obtain the bounded absorbing set. Lastly, We investigate the existence of a random attractor for the random dynamical system associated with the equation by using tail estimates and the decomposition technique of solutions.
摘要:本文研究了Rn上定义的具有线性记忆和乘性噪声的随机强阻尼波动方程解的动力学行为。首先,我们证明了上述方程具有一定初值的温和解的存在性和唯一性。其次,我们得到了有界吸收集。最后,我们利用尾估计和解的分解技术研究了与方程相关的随机动力系统的随机吸引子的存在性。
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引用次数: 2
Strong convergence theorems of common fixed points for a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in Hilbert spaces Hilbert空间中一致闭渐近可数拟lipschitz映射族的公共不动点的强收敛定理
Pub Date : 2019-12-31 DOI: 10.30538/PSRP-OMA2019.0027
Afshan Perveen, Samina Kausar, W. Nazeer
In this paper, we present a new non-convex hybrid iteration algorithm for common fixed points of a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in the domains of Hilbert spaces.
本文给出了Hilbert空间上一致闭渐近可数拟lipschitz映射族的公共不动点的一种新的非凸混合迭代算法。
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引用次数: 2
Solutions structures for some systems of fractional difference equations 一类分数阶差分方程组的解结构
Pub Date : 2019-12-31 DOI: 10.30538/PSRP-OMA2019.0032
M. Almatrafi
It is a well-known fact that the majority of rational difference equations cannot be solved theoretically. As a result, some scientific experts use manual iterations to obtain the exact solutions of some of these equations. In this paper, we obtain the fractional solutions of the following systems of difference equations: xn+1 = xn−1yn−3 yn−1 (−1− xn−1yn−3) , yn+1 = yn−1xn−3 xn−1 (±1± yn−1xn−3) , n = 0, 1, ..., where the initial data x−3, x−2, x−1, x0, y−3, y−2, y−1 and y0 are arbitrary non-zero real numbers. All solutions will be depicted under specific initial conditions.
众所周知,大多数有理差分方程都无法从理论上求解。因此,一些科学专家使用手动迭代来获得其中一些方程的精确解。在本文中,我们得到了以下差分方程组的分式解:xn+1=xn−1yn−3 yn−1(−1−xn−1 yn−3),yn+1=yn−1xn−3 xn−3(±1±yn−1xn-3),n=0,1。。。,其中初始数据x−3、x−2、x−1、x0、y−3、y−2、y−1和y0是任意非零实数。所有解决方案将在特定的初始条件下进行描述。
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引用次数: 13
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Open Journal of Mathematical Analysis
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