二阶Sturm-Liouville特征值问题解的存在与非存在性

讨论了二阶Sturm-Liouville特征值边值问题解的存在性与非存在性,得到了边值问题至少有一个正解的特征值λ的存在区间的结论.进一步,给出了边值问题没有正解的特征值存在区间.     

分数阶微分方程m点边值问题正解的存在性

应用凸锥上的不动点定理,讨论了一类分数阶微分方程m点边值问题正解的存在性,得到了这类边值问题至少存在一个正解的充分条件,并给出了一个实例.     

一类边界条件中带有扰动参数的积分边值问题正解的存在性

本文研究边界条件中带有扰动参数的积分边值问题正解的存在性与不存在性及扰动参数对正解存在性的影响.利用不动点指数理论,得出边值问题至少有一个正解、两个正解以及无解的充分条件.     

带p-Laplace算子三点奇异边值问题对称正解的存在性

该文应用不动点指数理论,讨论了一类带p-Laplace算子三点奇异边值问题对称正解的存在性,分别得到了这类边值问题至少存在一个或两个对称正解的充分条件.     

一类具有非线性边值条件的非线性分数阶微分方程正解的存在性（英文）

本文研究一类非线性分数阶边值问题正解的存在唯一性问题.利用混合单调算子的方法,获得至少一个正解的存在性结果,推广了整数阶边值问题的存在唯一性结果.     

含有一阶导数的四阶边值问题正解的存在性

研究了含有一阶导数的四阶边值问题,利用度理论构造出的一个新的不动点定理,由Green函数的性质,给出了一类含有导数的四阶边值问题正解存在的充分条件,得到了边值问题正解存在的一些新结果.     

一类带p-Laplacian算子分数阶微分方程边值问题的正解

本文应用凸锥上的不动点定理,讨论了一类带p-Laplacian算子分数阶微分方程边值问题的正解的存在性,分别得到了这类边值问题至少存在一个正解和多个正解的充分条件.最后,给出了两个具体的例子.     

一类四阶奇异边值问题对称正解的最优存在性

本文研究了一类四阶奇异边值问题.通过建立一个特定的锥,利用Leggett-Williams不动点定理,从而在一定的条件下得到一类四阶奇异边值问题对称正解的最优存在性,推广了奇异边值问题对称正解的最优存在性的结果.     

p-Laplacian分数阶微分方程边值问题正解的存在性北大核心CSCD

在这篇文章,我们讨论了一类p—Laplacian分数阶微分方程边值问题正解的存在性,应用凸锥上的不动点定理,我们得到了这类边值问题至少存在一个和两个正解的充分条件．     

p-Laplacian分数阶微分方程边值问题正解的存在性

在这篇文章,我们讨论了一类p-Laplacian分数阶微分方程边值问题正解的存在性,应用凸锥上的不动点定理,我们得到了这类边值问题至少存在一个和两个正解的充分条件.     

On the stability and spectral radius of a finite set of matrices

This paper studies some problems related to the stability and the spectral radius of a finite set of matrices. A seasonal epidemic model is given to illustrate the use of the obtained results. In this example, the relationship between the obtained results and the stability of a discrete time periodic linear system is obtained.     

Existence of homoclinic solutions for a class of second-order Hamiltonian systems

A new result for existence of homoclinic orbits is obtained for the second-order Hamiltonian systems under a class of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of boundary-value problems which are obtained by the minimax methods.     

稠定闭线性算子的剩余谱刻画及其应用

得到Hilbert空间中的稠定闭线性算子的剩余谱由其点谱及其共轭算子点谱完全刻画,由此给出了其剩余谱为空集的充要条件;从而得到两类稠定闭线性算子的谱结构.     

Existence of even homoclinic orbits for second-order Hamiltonian systems

Some existence theorems for even homoclinic orbits are obtained for a class of second-order nonautonomous Hamiltonian systems with symmetric potentials under a class of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil-boundary-value problems which are obtained by the minimax methods.     

The exact boundaries of the stability domains of linear differential equations with distributed delay

For a differential equation with a distributed varying delay, sufficient criteria for the asymptotic and uniform stability of solutions are obtained. The constructed examples demonstrate exactness of the boundary of the obtained stability domain.     

Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation

Numerical solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a cylindrical vessel are obtained using the hopscotch scheme. We observe that a nonlinear source term in the equation leads to numerical difficulty and hence adjust the scheme to accommodate such a term. Numerical solutions obtained via MATLAB, MATHEMATICA and the Crank-Nicolson implicit scheme are employed as a means of comparison. To gain insight into the accuracy of the hopscotch scheme the solution is compared to a power series solution obtained via the Lie group method. The numerical solution is also observed to converge to a well-known steady state solution. A linear stability analysis is performed to validate the stability of the results obtained.     

Solution of the stationary problem of heat conduction of laminated anisotropic inhomogeneous plates by the method of initial functions

The problem of stationary heat conduction of laminated plates of constant and variable thickness is formulated in the three-dimensional statement. We reduce the three-dimensional problem to a twodimensional one by the method of initial functions. For plates with layers of variable thickness, a system of resolving equations with variable coefficients is obtained. The obtained two-dimensional boundary-value problems are analyzed. For plates with homogeneous layers of constant thickness, we construct a solution in an analytic form. It is shown that this solution coincides with a solution obtained by the method of separation of variables.     

The effect of redundancy on probability bounds

Lower bounds on the probability of a union obtained by applying optimal bounds to subsets of events can provide excellent bounds. Comparisons are made with bounds obtained by linear programming and in the cases considered, the best bound is obtained with a subset that contains no redundant events contributing to the union. It is shown that redundant events may increase or decrease the value of a lower bound but surprisingly even removal of a non-redundant event can increase the bound.     

On the maximal multiplicative complexity of a family of bilinear forms

The number of nonscalar multiplications required to evaluate a general family of bilinear forms is investigated. An upper bound is obtained which is about half that obtained from naive arguments. In certain cases the best possible upper bound is obtained.     

Continuity of second-order contingent derivative of the efficient set map for parametrized multiobjective optimization

In this paper, some relationships between the second-order contingent derivative of a set-valued map and its profile map are obtained. By virtue of the second-order contingent derivatives of set-valued maps, upper semicontinuity and lower semicontinuity are obtained for efficient set maps of parametrized multiobjective optimization. Several examples are provided to show the results obtained.