一类具有无穷多个周期解的二阶偏微分方程

本文首先给出了一类具有无穷多个周期解的无阻尼二阶线性偏微分方程所描述的系统。同时讨论了一类无阻尼非线性二阶偏微分方程存在多个周期解的情况，最后给出了一个判断有阻尼二阶偏微分系统存在周期解的方法。     

一类二阶常微分方程初值问题的无穷多解性

应用分离变量法,得到了一类二阶微分方程初值问题存在无穷多个非负解的充分必要条件,并给出了所有的无穷多个非负解．。     

一类偏积分微分方程二阶差分全离散格式

本文给出了数值求解一类偏积分微分方程的二阶差分全离散格式．时间方向采用了二阶向后差分格式,积分项的离散利用了Lubich的二阶卷积求积公式,给出了稳定性的证明、误差估计及收敛性的结果,并给出了数值例子．     

一类二阶变系数线性系统的解

给出一类二阶变系数线性系统的解的求法，并得到解的表达式．     

一类变系数微分方程的通解

本文给出了一类变系数二阶线性微分方程的通解公式，进而得到了一批变系数微分方程的通解．     

关于高维非线性椭圆型方程的正整解

建立一类高维二阶非线性椭圆型方程正整解的存在性定理，并给出解的有关性质．     

分析（E1）类的广义R—H—C边值可解性

本通过研究一类满足边界条件的二阶椭圆复线性方程组的广义混合型边值问题，提出了其可解条件，并就其解给出了明确的解析式．     

一类偏积分微分方程二阶差分全离散格式

本给出了数值求解一类偏积分微分方程的二阶全离散差分格式．采用了Crank-Nicolson格式；积分项的离散利用了Lubieh的二阶卷积积分公式；给出了稳定性的证明，误差估计及收敛性的结果．     

不稳定型二阶中立型方程正解的存在性与有界振动

本文研究一类不稳定型二阶中立型微分方程正解的存在性与有界振动．证明了在一定条件下不稳定型二阶中立型方程总存在无界正解，并给出了保证其方程的一切有界解都振动的充分条件，改进了文［１，２］中的有关条件．     

具有连续变量的多时滞二阶中立型差分方程的振动准则

本文用分析的方法研究了一类具有连续变量的多时滞二阶中立型差分方程解的振动性，给出了该类方程解振动和差分算子振动的几个充分条件．     

Nonlinear second-order multivalued boundary value problems

In this paper we study nonlinear second-order differential inclusions involving the ordinary vectorp-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the ‘convex’ and ‘nonconvex’ problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.     

二阶微分包含的边值问题及其应用

在Banach中讨论了一类二阶微分包含的边值问题和一类反馈控制问题.结合不动点定理,对解的存在性给出了两个充分性条件,最后应用前面的结果建立了反馈控制问题解的存在性定理.     

Comparison results for initial value problems of second-order impulsive integro-differential inclusions

In this paper, we present new maximum and minimum principles for the initial value problem for a class of second-order nonlinear impulsive integro-differential inclusions with discontinuous multivalued functions on the right hand side in a real Banach space. This allows us to lead on to the development of the comparison principle and monotone iterative technique for a nonlinear second-order impulsive integro-differential inclusion.     

随机二阶多值周期问题解的存在性

本文研究了随机二阶多值周期问题解的存在性,在非常一般的假定下建立了凸和非凸问题解的存在性定理,并给出了在随机周期反馈控制系统中的应用．     

Asymptotic behaviour of reaction–diffusion equations with non-damped impulsive effects

In this paper we consider non-autonomous reaction–diffusion systems with impulsive effects at fixed moments of time from the point of view of the theory of global attractors. For a translation-compact nonlinear term which does not provide the uniqueness of the Cauchy problem, and for different classes of non-damped multivalued impulse perturbations, we construct a multivalued non-autonomous dynamical system and prove for it the existence of a compact global attractor.     

Controllability for a class of second-order evolution differential inclusions without compactness

In this paper, we discuss the existence and controllability for a class of second-order evolution differential inclusions without compactness in Banach spaces. By applying the technique of weak topology and Glicksberg–Ky Fan fixed point theorem, we prove our main results without the hypotheses of compactness on the operator generated by the linear part and any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. Further, we extend our study to existence and controllability of second-order evolution differential inclusions with nonlocal conditions and impulses. Finally, an example is given for the illustration of the obtained theoretical results.     

On a new system of nonlinear A-monotone multivalued variational inclusions

In this paper, we introduce and study a new system of nonlinear A-monotone multivalued variational inclusions in Hilbert spaces. By using the concept and properties of A-monotone mappings, and the resolvent operator technique associated with A-monotone mappings due to Verma, we construct a new iterative algorithm for solving this system of nonlinear multivalued variational inclusions associated with A-monotone mappings in Hilbert spaces. We also prove the existence of solutions for the nonlinear multivalued variational inclusions and the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known corresponding results.     

Nonlinear elliptic differential equations with multivalued nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

Skorohod problem and multivalued stochastic evolution equations in Banach spaces

By solving a deterministic Skorohod problem in the framework of evolutional triple, we prove the existence and uniqueness of solutions to multivalued stochastic evolution equations involving maximal monotone operators. The existence and uniqueness of invariant measures associated with the solutions as Markov processes are also considered in the present paper. Moreover, we apply the results to stochastic differential equations with normal reflecting boundary conditions and with singular drift terms, as well as a class of multivalued nonlinear stochastic partial differential equations with possibly discontinuous coefficients.     

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A SECOND-ORDER DIFFERENTIAL INCLUSION

In this paper,the existence of positive periodic solutions to a second-order differential inclusion is considered.Some existence results are established by the fixed-point theorem for multivalued operators and Sobolev constant.