Banach空间中二阶非线性混合型脉冲微分-积分方程的解

利用一个比较结果和M(o)nch不动点定理,研究了Banach空间中二阶非线性混合型脉冲微分-积分方程初值问题解的存在性,推广了某些现有结果.     

ε- 扩展锥和多目标规划的 ε- 恰当有效性

本文引进Banach空间中的ε-扩展集和ε-扩展锥概念．借助ε-扩展锥,定义了多目标规划问题的ε-恰当有效解和局部ε-恰当有效解,并且研究了这些解的性质．此外还讨论了ε-恰当有效解与某些其它恰当有效解的关系．     

Banach空间不连续脉冲微分-积分方程的周期边值问题

本文讨论了Banach空间含间断项的一阶混合型脉冲微分-积分方程的周期边值问题,通过建立一个比较定理,应用不动点定理与上、下解方法证明了最大解、最小解及迭代解的存在性,推广改进了某些文献中的相应结果。     

Banach空间二阶非线性混合型脉冲微分-积分方程边值问题的解

在较弱的条件下,利用MSnch不动点定理,研究了Banach空间中二阶非线性混合型脉冲微分-积分方程边值问题解的存在性,推广和改进了某些已有的结果.     

两类复微分-差分方程组的整函数解

利用Nevanlinna值分布理论以及复差分和复微分理论,讨论了两类复微分-差分方程组的有限级超越整函数解问题,得到了两个结果,并将涉及微分或差分方程的某些结果推广至复微分-差分方程组中.     

一类奇异边值问题正解的存在性

借助上下解方法和锥拉伸与锥压缩不动点定理研究了二阶非线性奇异边值问题u″ λf(t,u(t))=0,0相似文献   

一类具有Holling-Ⅱ型功能性反应的捕食者-食饵系统全局周期解的存在性

利用重合度理论中的延拓定理讨论了一类具有Ｈｏｌｌｉｎｇ Ⅱ 型功能性反应的捕食者-食饵系统（即Ｒｏｓｅｎｚｗｅｉｇ ＭａｃＡｒｔｈｕｒ模型）全局周期解的存在性,得到了保证周期解存在的充分条件,推广了某些已知的相关结果．     

一类含非线性边界条件的高阶微分方程解的存在性(英文)

将上下解方法和Leray-Shauder度应用到一类含有非线性边界条件的n阶微分方程,得到了至少存在一个解的结果,并且改进和推广了文献中的某些结果.     

Banach空间二阶非线性脉冲积分-微分方程初值问题

该文在较宽松的条件下,利用不动点理论,得到了Banach空间中二阶非线性脉冲积分-微分方程初值问题解的存在性定理.作者去掉了脉冲项的紧性和增长性限制, 因而本质上改进和推广了某些现有的结果.     

在非古典变分场中关于SOLITON的某些性质

本文系应用非古典变分法,讨论了孤粒子解的某些性质:一、讨论了孤粒子解的短程线问题;二、讨论了KdV方程孤粒子解的稳定性质,得到了相应的结果,这些结果在正文中由定理1和定理2表示。     

Exact solution of a boundary value problem describing the uniform cylindrical or spherical piston motion

In this paper, we construct the exact solution for fluid motion caused by the uniform expansion of a cylindrical or spherical piston into still air. Following Lighthill [1], we introduce velocity potential into the analysis and seek a similarity form of the solution. We find both numerical and analytic solutions of the second order nonlinear differential equation, with the boundary conditions at the shock and at the piston. The results obtained from the analytic solutions justify numerical solution and the approximate solution of Lighthill [1]. We find that although the approximate solution of Lighthill [1] gives remarkably good numerical results, the analytic form of that solution is not mathematically satisfactory. We also find that in case of spherical piston motion Lighthill’s [1] solution differs significantly from that of our analytic and numerical solutions. We use Pade′ approximation to extend the radius of convergence of the series solution. We also carry out some local analysis at the boundary to obtain some singular solutions.     

Concave solutions of a general self-similar boundary layer problem for power-law fluids

In this paper, we give a rigorous mathematical analysis for a third order nonlinear boundary value problem. The boundary value problem can be applied to steady free convection around a vertical impermeable flat plate in a fluid-saturated porous medium, or steady flow of a power-law fluid induced by impermeable stretching walls in the frame of boundary layer approximation. We establish the uniqueness, existence and nonexistence of (normal) concave solutions or generalized concave solutions to the problem, and obtain some results about boundedness and asymptotic behavior of the (normal) concave solution or the generalized concave solution.     

Stability of the numerical solution of the periodic reaction- diffusion systems

In this paper we study the behavior of the numerical solution of nonlinear reaction-diffusion systems, with periodic in time nonlinear term, obtained via the known θ-method. In particular we are interested to the existence and asymptotic stability of the numerical periodic solutions in order to simulate the behaviour of the theoretical solution. To this end, by imposing the positivity of the numerical scheme, we can use some results about M-matrices.So, by means of particular over and upper solutions, we study some conditions for the stability and instability of the trivial solution.Finally we show when a positive numerical periodic solution exists and when it is unique and asymptotically stable.     

Fractional order iterative functional differential equations with parameter

In this paper, we study a fractional order iterative functional differential equation with parameter. Some theorems to prove existence of the iterative series solutions are presented under some natural conditions. Unfortunately, uniqueness results can not be obtained since the solution operator is not Lipschitz continuous but only Hölder continuous. Meanwhile, data dependence results of solutions and parameters provide possible way to describe the error estimates between explicit and approximative solutions for such problems. We also make some examples to illustrate our results. Finally, we conclude with some possible extensions to general parametrized iterative fractional functional differential equations.     

三阶柯西差分方程在几类群上的解

在几类群上讨论了三阶柯西差分方程解的存在性问题,将二阶柯西差分方程的已有结论进一步推广到三阶的情况,并给出在不同群上的一般解.     

Existence of solutions for impulsive Dirichlet problems with the parameter inequality reverse

In this paper, we consider the existence and multiplicity for second‐order nonlinear impulsive differential equations with Dirichlet boundary condition and a parameter. By using critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution or infinitely many solutions, assuming that the impulsive functions satisfy the superlinear growth condition and the parameter inequality is reverse. Our results extend and improve some recent results. Copyright © 2013 John Wiley & Sons, Ltd.     

Existence and multiplicity of solutions to even order ordinary differential equations via variational methods

In this paper, we study the existence and multiplicity of solutions for two-point boundary value problems for even order ordinary differential equation. By using the critical point theory and the property of projective operator, we establish some conditions on the nonlinearity which guarantee that the nonlinear Hammerstein integral equation with quasi-positive definite kernel has at least one solution, two nontrivial solutions and finite pairs of solutions, respectively. As an application, we get the corresponding results for two-point boundary value problems for even order ordinary differential equation. Moreover, an example is presented to illustrate our main results.     

中立型泛函微分方程周期解问题

利用Fourier级数理论研究了一类k－阶线性中立型泛函微分方程周期解问题，给出了周期解存在唯一性的充要条件。利用此结果并结合Schauder不动点原理，进一步研究了一类k-阶非线性中立型泛函微分方程，得到了存在周期解的新的结果。这些结果改进和推广了近期文献中的已有结论。     

Smooth Compactly Supported Solutions of Some Underdetermined Elliptic PDE,with Gluing Applications

We give sufficient conditions for some underdetermined elliptic PDE of any order to construct smooth compactly supported solutions. In particular we show that two smooth elements in the kernel of certain underdetermined linear elliptic operators P can be glued in a chosen region in order to obtain a new smooth solution. This new solution is exactly equal to the initial elements outside the gluing region. This result completely contrasts with the usual unique continuation for determined or overdetermined elliptic operators. As a corollary we obtain compactly supported solutions in the kernel of P and also solutions vanishing in a chosen relatively compact open region. We apply the result for natural geometric and physics contexts such as divergence free fields or TT-tensors.     

Positive solution for four‐point nonlocal boundary value problems of fractional order

In this paper, we consider the existence of positive solution for four‐point nonlocal boundary value problems of fractional order. By means of some fixed point theorems, some results on the existence and multiplicity of positive solutions are obtained. Furthermore, we provide a representative example to illustrate a possible application of the established results. Copyright © 2013 John Wiley & Sons, Ltd.