EXISTENCE OF WEAK SOLUTIONS TO A p-LAPLACIAN PROBLEM INVOLVING DIRICHLET BOUNDARY CONDITION

In this paper, by virtue of Leray-Lions theorem, we are mainly concerned with the existence of weak solutions to a Dirichlet boundary value problem with the p-Laplacian operator.     

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.     

GLOBAL SOLUTIONS TO THE EVOLUTION EQUATION OF SCHRODINGER TYPE WITH NONLOCAL TERM

The existence of weak and smooth solutions for the nonlocal nonlinear Schrodinger equation is solved by parabolic regularization. In addition, the continuous dependence on the initial data of smooth solution is also discussed.     

EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE

We study the existence of solutions to the following parabolic equation{ut-△pu=λ/|x|s|u|q-2u,(x,t)∈Ω×(0,∞),u(x,0)=f(x),x∈Ω,u(x,t)=0,(x,t)∈Ω×(0,∞),(P)}where-△pu ≡-div(|▽u|p-2▽u),1相似文献   

REGULARITY OF SOLUTIONS TO THE DIRICHLET PROBLEM FOR DEGENERATE ELLIPTIC EQUATION

In this paper, the author studies the regularity of Solutions to the Dirichlet problem for equation Lu = f, where L is a second order degenerate elliptic operator in divergence form in Ω, a bounded open subset of Rn (n ≥3).     

BLOW-UP OF SOLUTIONS TO ELLIPTIC EQUATIONS WITH SEMILINEAR DYNAMICAL BOUNDARY CONDITIONS OF HYPERBOLIC TYPE

In this paper,we present some sufficient conditions for blow-up of soluti- ons to elliptic equations under semilinear dynamical boundary conditions of hyperbolic type.     

GLOBAL SOLVABILITY OF NONLINEAR WAVE EQUATION WITH A VISCOELASTIC BOUNDARY CONDITION

The paper deals with the global solvability of nonlinear wave equation with a viscoelastic boundary condition. The problem is a mathematical mode for nonlinare one-dimensional motion of an elastic bar connected with a viscoelastic element at one end of the bar. Under some physically reasonable assumptions, the boundary condition is dissipative and the existence of global smooth solution of the problem is proved for small data.     

POSITIVE SOLUTIONS TO m-POINT BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION WITH p-LAPLACIAN

In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel'skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained.     

PERIODIC SOLUTIONS TO DUFFING TYPE p-LAPLACIAN EQUATION WITH SEVERAL p-LAPLACIAN OPERATORS

Based on Mansevich-Mawhin continuation theorem and some analysis skill, some new sufficient conditions for the existence of periodic solutions to a duffing type p-Laplacian differential equation with several p-Laplacian operators are obtained. Moreover, we construct an example to illustrate the feasibility of our results.     

ON PROPERTIES OF MEROMORPHIC SOLUTIONS FOR COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

In this paper, we present the properties on zeros, fixed points, poles, Borel exceptional value of finite order transcendental meromorphic solutions of complex difference equation of Malmquist typewhere n（∈ N） 〉 2, P（f（z）） and Q（f（z）） are relatively prime polynomials in f（z） with rational coefficients a8 （s = 0, 1,…,p） and bt （t = 0, 1,… ,q） such that aoapbq 7≠ O, and also consider the existence and the forms on rational solutions of this type of difference equations. Some examples are also listed to show that the assumptions of theorems, in certain senses, are the best possible.     

EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS TO p-KIRCHHOFF TYPE EQUATION

In this paper, by applying Fountain theorem, we study the existence of nontrivial solutions to the nonlinear kirchhof nonlocal equation under Ambrosetti-Rabinowitztype growth conditions.     

EXISTENCE AND MULTIPLICITY OF SOLUTIONS TO A CLASS OF DIRICHLET PROBLEMS WITH IMPULSIVE EFFECTS

In this paper, we study the existence and multiplicity of solutions to a class of Dirichlet problems with impulsive effects via variational methods. Under an assumption that the nonlinearity f is superlinear but does not necessarily satisfy the Ambrosetti-Rabinowitz condition, we extend and improve some recent results.     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel'skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.     

具非线性边界条件的奇异扩散方程

本文讨论具非线性第二边界条件的一端无界的奇异扩散方程的初边值间题,利用先验估计方法得到的主要结果是:存在唯一的整体光滑解,且解连续依赖于初值．     

计算立方体上Henon方程多个正解的分歧方法

本文首先应用分歧方法给出计算立方体上Henon方程边值问题D₄(3)对称正解的三种算法, 然后以Henon方程中的参数r为分歧参数, 在D₄(3)对称正解解枝上 用扩张系统方法求出对称破缺分歧点, 进而用解枝转接方法计算出其它具有不同对称性质的正解.     

MULTIPLICITY OF NONNEGATIVE SOLUTIONS TO SECOND-ORDER SINGULAR DIFFERENTIAL EQUATION WITH INTEGRAL BOUNDARY CONDITIONS IN BANACH SPACES

This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].     

用边界积分方程法解平面双调和方程的Dirichlet问题

1.积分方程及变分公式 设Ω是R~2中具有规则边界T的有界开区域,Ω′为Ω=Ω T的补域。考虑如下Dirichlet问题:     

The heat equation in R with anti-periodic boundary condition

1Intr0ducti0nThispaPerdeaIswiththef0llowingproblerns:whereTisanypositivenumberandaisarealnumberwithIal31.In[1],A.Pazydiscussedtheproblelnasfollows:Heobtainedtheexistenceanduniqueness0fthesolutionfor(P3)intl1espaceC[0,1lundersomehypotheses0nf.(P3)isannonlinearheatequati0nwithinitialconditionandperi0dicboundaryc0nditi0n.Recentlysomeauthorshavediscussedsomedtherentialequationswithantiperi0dicboundarycondition8([2],[3]).However,theyonlystudiedtheclassicalsolutionslikewhatA.Pazydidforperiodicb…     

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF VOLTERRA－HAMMERSTEIN TYPE INTEGRODIFFERENTIAL EQUATION

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