A NONLOCAL NONLINEAR BOUNDARYVALUE PROBLEM FOR THE HEAT EQUATIONS

51.IntroductionandMalnResultsLetflCR"(n=2or3)beaboundedsmoothdomainwithboundaryan=r1ur2,wherer1nr2=Oandr1,r2/O.Weconsiderthefollowingmixedinitial-boundaryvalueproblemfortheheatequation'whereH'DHCR-Risastrict1ydecreasingtunction,ustancnormalvectorattheboundary.Theboundaryconditiononr2appearsinthermistors.Howison,RodriguesandShillorl1]studiedsuchkindofboundaryvalueproblemforellipticequations.HerewesupposethatHisonto'nH=R,andwherea,bdenote,andwillalwaysdenote,varieskindofconstants.Underhy…     

SOME COMPLETELY MONOTONIC FUNCTIONS ASSOCIATED WITH THE q-GAMMA AND THE q-POLYGAMMA FUNCTIONS

In this paper, theq-analogue of the Stirling formula for theq-gamma function(Moak formula) is exploited to prove the complete monotonicity properties of some functions involving theq-gamma and theq-polygamma functions for all real numberq 0. The monotonicity of these functions is used to establish sharp inequalities for theq-gamma and theq-polygamma functions and theq-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].     

具有加权非局部边界条件的多孔介质方程组的临界指标问题

本文研究了具有非局部边界条件和非线性内部源的多孔介质抛物型方程组问题。利用比较原理,获得了权函数和系数对整体解和爆破解的影响,并得到了解的爆破临界指标,推广了先前的研究结果。     

UNIFORM BLOWUP PROFILES FOR DIFFUSION EQUATIONS WITH NONLOCAL SOURCE AND NONLOCAL BOUNDARY

Long time behavior of solutions to semilinear parabolic equations with nonlocal nonlinear source ut - △u = ∫Ω g(u)dx inΩ× (0, T) and with nonlocal boundary condition u(x, t) = ∫Ω f(x, y)u(y, t)dy on(e) Ω× (0, T) is studied. The authors establish local existence, global existence and nonexistence of solutions and discuss the blowup properties of solutions. Moveover, they derive the uniform blowup estimates for g(s) = sp(p ＞ 1) and g(s) = es under the assumption fΩ f(x, y)dy ＜ 1 for x ∈(e)Ω.     

具非局部条件的半线性发展方程的可控性

本文使用Schaefer不动点定理和强连续算子半群理论,建立了抽象空间中具非局部条件的半线性发展方程解的可控性,得到了可控性的充分条件.文末用例子说明了所得结果.     

A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

In this paper,we discuss the existence of solutions for a nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations.Our main result is based on a hybrid fixed point theorem for a sum of three operators due to Dhage,and is well illustrated with the aid of an example.     

由Dziok-Srivastava算子定义的多叶解析函数类的性质

本文研究了由Dziok-Srivastava算子H(a₁,…,a_q;b₁,…,b_s)定义的关于参数b_j ∈ C\Z₀^-(Z₀^-=0,-1,-2,…;j=1,2,…,s)的多叶解析函数类W_p(H(b_j+1);A,B).利用微分从属的方法和卷积的性质,获得了该类函数的特征性质和包含结果,推广了一些已知结果.     

A STUDY OF A FULLY COUPLED TWO-PARAMETER SYSTEM OF SEQUENTIAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL INTEGRO-MULTIPOINT BOUNDARY CONDITIONS

In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.     

具有非局部边界的退化抛物方程组的爆破解

本文研究了具有非局部边界条件和非局部源的退化抛物方程组的弱解问题.利用基于比较原理的上下解的方法,在权函数和初始条件的假设下,获得了该方程组问题的爆破临界指标.此外,还获得了同时爆破解趋于爆破时间时的渐近行为,推广了已有的结果.     

ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.     

EXISTENCE OF SOLUTIONS FOR NONLOCAL BOUNDARY VALUE PROBLEM OF FRACTIONAL DIFFERENTIAL EQUATIONS ON THE INFINITE INTERVAL

In this paper, we study a fractional differential equation ~cD_0~α+u(t) + f(t, u(t)) = 0, t ∈(0, +∞)satisfying the boundary conditions:u′(0) = 0, limt→+∞ ~cD_(0~+)~(α-1)u(t) = g(u),where 1 α 2,~cD_(0~+)~α is the standard Caputo fractional derivative of orderα. The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O'Regan. Under a compactness criterion, the existence of solutions are established.     

CLASSICAL R-MATRIX APPROACH TO THE SYSTEM ASSOCIATED WITH THE THREE-WAVE INTERACTION EQUATIONS

1IntroductionTher-matrixmethodisanimportanttoolforstudyingthefinite--dimensionalintegrablesystems.Fromther-matrixformulathecommutativityofmotionintegralsgeneratedfromtheLaxoperatorcanbeeasilyobtained[1].AnrmatrixalsoallowsonetocanonicallyconstructthematrixMoftheLaxpair[:l.In[3],Y.T.WuandX.G.Gengintroduceda3x3matrixspectralproblemwithsixpotentialsasfollowswherethepotentialvectoru=(u12,u21,u135u31)u23,u,,)',Aisaconstantspectralparameter,allaZanda3arethreedistinctconstants,andproposedacorres…     

SPREADING SPEED IN THE FISHER-KPP EQUATION WITH NONLOCAL DELAY

This paper is concerned with the Fisher-KPP equation with diffusion and non-local delay.Firstly,we establish the global existence and uniform boundedness of sol...     

带非局部边界条件的非线性抛物方程的隐式差分解法

在准静态弹性力学中常遇到求解带有非局部边界条件的抛物方程初边值问题.本文构造了一个数值求解带有非局部边界条件的非线性抛物方程的隐式差分格式,利用离散泛函分析的知识和不动点定理证明了差分解是存在的,且在离散最大模意义下关于时间步长一阶收敛,关于空间步长二阶收敛,并给出了数值算例.     

带跳的耦合正倒向随机微分方程

本文对带跳的耦合正倒向随机微分方程引入了“桥”的概念,证明了如果两个带跳的耦合正倒向随机微分方程被桥连接着,那么它们有相同的唯一可解性.在此基础上,通过桥的构造,得到一些带跳的正倒向随机微分方程的唯一可解性.     

带跳的耦合正倒向随机微分方程

本文对带跳的耦合正倒向随机微分方程引入了"桥"的概念,证明了如果两个带跳的耦合正倒向随机微分方程被桥连接着,那么它们有相同的唯一可解性.在此基础上,通过桥的构造,得到一些带跳的正倒向随机微分方程的唯一可解性.     

具热效应的半导体方程组的初边值问题

证明了热了流模型半导体方程组整体光滑解的存在唯一性。如果区域在某一方向充分窄，则我们证明了平衡解的存在唯一性和解的渐近性。     

CLASSES OF MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS

The object of this article is to introduce new classes of meromorphic functions associated with conic regions.Several properties like the coefficient bounds,growth and distortion theorems,radii of star...     

THE INTERIOR LAYER SOLUTION TO NONLOCAL REACTION DIFFUSION EQUATIONS

An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.