函数的振动熵

本文定义了振动函数与函数的振动熵。对函数的振动性质进行了初步的讨论。振动熵是对函数振动程度的度量(振动愈剧烈振动熵的值愈大)。导数是振动熵的特例。     

二阶线性时滞微分方程的广义振动性

本文主要研究了二阶线性时滞微分方程的广义振动性和广义非振动性,给出了方程广义振动和广义非振动的一些判定定理,同时给出了一类方程广义非振动的充要条件.     

高阶线性时滞微分方程的广义振动性

该文考虑了一类高阶线性常系数时滞微分方程 y( n) (t) py′(t) qy(t-τ) =0的广义振动性和广义非振动性 ,给出了一些该类方程广义振动和广义非振动的判定定理 .文中的定理 4还给出了一类非振动但广义振动的方程的判别法则     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

具有振动系数时滞差分方程解的振动性

本文研究了一类具振动系数时滞差分方程解的振动性,给出了一个新的振动准则,改进了已有文献中许多相关的结果．     

一类二阶线性微分方程的振动性及非振动性

本文研究了二阶线性方程的振动性及非振动性问题，建立了若干新的振动与非振动性结果，它们改进并推广了若干已知的定理。     

高阶泛函微分方程的振动性质*

本文借助于Lebesgue测度等工具研究了一类高阶非线性泛函微分方程的振动性质.文中指出.在一定条件下,方程的非振动解仅有两类,而且给出了每一类非振动解存在的必要条件,同时也建立了方程振动的若干充分判据.     

二阶泛函微分方程的振动性质

在本文中，我们研究了一类较广泛的二阶非线性泛函微分方程的振动性质。文中指出，在一定条件下，方程的非振动解仅有两类，而且给出了每一类非振动解存在的必要条件，同时也建立了方程振动的若干充分判据。     

单自由度体系有阻尼自由振动振幅包络线的性质研究与数学证明

针对单自由度体系有阻尼自由振动,探究了振幅包络线与振动位移一时间曲线(以下简称振动曲线)的交点个数、振幅包络线与振动曲线交点位置以及振幅包络线值与结构阻尼比的关系三方面的问题.通过理论推导,给出了一条振幅包络线在单周期内与振动曲线只有一个切点且切点位于振动曲线峰值点稍靠右侧处的证明过程.通过改变相关参数的取值,发现了在某些初始条件下在振动初始阶段振幅包络线的绝对值不与结构的阻尼比呈负相关的有趣现象,并给出了直观的图像说明与理论证明.     

二阶中立型差分方程的振动性

研究了一类变系数的二阶中立型时滞差分方程的振动性,得到了该类方程振动及解的一阶差分振动的充分条件。     

Asymptotic null controllability of nonlinear perturbed systems

In this paper, sufficient conditions are obtained for the asymptotic null controllability of the system $$\dot x(t) = g(t,x(t)) + B(t,x(t))u(t) + f(t,x(t),u(t)).$$ The results are obtained by using the Leray-Schauder fixed-point theorem.     

Well-posedness of a class of operator-differential equations

We consider a linear first-order ordinary operator-differential equation A(t)u′(t) + B(t)u(t) = f(t) in a Banach space, where the operator A(t) is not invertible in general. Sufficient conditions for the existence, uniqueness, and well-posedness of the Cauchy problem for this equation are obtained.     

Glivenko Classes of Sequents for Temporal Logic with Time Gaps

Let LB be a sequent calculus of the first-order classical temporal logic TB with time gaps. Let, further, LBJ be the intuitionistic counterpart of LB. In this paper, we consider conditions under which a sequent is derivable in the calculus LBJ if and only if it is derivable in the calculus LB. Such conditions are defined for sequents with one formula in the succedent (purely Glivenko -classes) and for sequents with the empty succedent (Glivenko -classes).     

On the optimal control of systems described by implicit evolution equations

We obtain conditions for the existence and uniqueness of an optimal control for the linear nonstationary operator-differential equation

$\frac{d}{{dt}}[A(t)y(t)] + B(t)y(t) = K(t)u(t) + f(t)$

with a quadratic performance criterion. The operators A(t) and B(t) are closed and may have nontrivial kernels. The results are applied to differential-algebraic equations and to partial differential equations that do not belong to the Cauchy-Kowalewskaya type.

     

Oscillations and Convergence in an Almost Periodic Competition System

Sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a competition system modelled by the nonautonomous Lotka–Volterra delay differential equations $$\begin{gathered} \frac{{{\text{d}}N_1 (t)}}{{{\text{d}}t}} = N_1 (t)\left[ {r_1 (t) - a_{11} (t)N_1 (t - \tau (t)) - a_{12} (t)N_2 (t - \tau (t))} \right], \hfill \\ \frac{{{\text{d}}N_2 (t)}}{{{\text{d}}t}} = N_2 (t)\left[ {r_2 (t) - a_{21} (t)N_1 (t - \tau (t)) - a_{22} (t)N_2 (t - \tau (t))} \right], \hfill \\ \end{gathered} $$ in which $ \tau ,r_i ,a_{ij} (i,j = 1,2) $ are continuous positive almost periodic functions; conditions are also obtained for all positive solutions of the above system to 'oscillate' about the unique almost periodic solution. Some ecobiological consequences of the convergence to almost periodicity and delay induced oscillations are briefly discussed.     

Convergence of solutions of nonlinear differential equations

Summary Solutions of are said to converge if every pair of solutions x(t), y(t) satisfy x(t) − y(t) →0 as t → ∞. An invariance principle of LaSalle is used to determine conditions under which the solutions of converge. In certain cases the approach used does not require boundedness of solutions as has been required in most previous results on convergence of solutions. The results of this investigation are applied to a number of nonlinear second order differential equations. Sufficient conditions are also found for the convergence of solutions of certain functional differential equations. Entrata in Redazione il 10 febbraio 1976.     

Total controllability to affine manifolds of control systems

A system is totallyG-controllable if every pointx ₀ of the state spaceE ⁿ can be steered to the targetG in finite time and can be held inG forever afterward. Sufficient conditions are developed for the totalG-controllability of the linear system (a) $$\dot x(t) = A(t)x(t) + B(t)u(t)$$ and its perturbation (b) $$\dot x(t) = A(t)x(t) + B(t)u(t) + F(t,x(t),u(t)),$$ where the targetG is an affine manifold inE ⁿ. We state conditions on the perturbation functionF which guarantee that, if (a) is totallyG-controllable, then so is (b). These conditions onF are natural and are obtained by solving a system of nonlinear integral equations by the Leray-Schauder fixed-point theorem.     

Linear periodic control systems: Controllability with restrained controls

Consider the problem of null-controllability for a linear non-autonomous system of the form , whereX andU are Banach spaces,A(t) andB(t) are linear bounded operators for eacht 0, and is a subset containing 0 (but not necessarily as an interior point). Some necessary and sufficient conditions for local and global null-controllability are proved whenA(·) andB(·) are periodic continuous functions. The proofs of the main results are based on discretization and on consideration of the corresponding linear discrete-time systems.     

On local times for non-homogeneous Markov processes

Summary Random sets of the typeM _B()={t:(t,x _t())B} associated with measurable setsB from the phase space of a non-homogeneous Markov process are considered.The process is supposed to satisfy Dynkin's regularity conditions. When the setB coincides with the set of all points that are regular for it, special properties (well known in the homogeneous case) appear: namely,¯M _B is a.s. perfect and there exist predictable (under certain conditions also continuous) local times forB.     

Asymptotic Properties in a Delay Differential Inequality with Periodic Coefficients

New criteria are proposed for investigating the asymptotic behavior of the delay inequality $$u^{\prime} (t) \leq - a(t) u(t) + b(t) u(t - \tau)$$ and the corresponding differential equation $$x^{\prime} (t) = - a(t) x(t) + b(t) x(t - \tau)$$ , assuming continuous and periodic coefficients, ${b(t) \geq 0}$ . Our strategy requires conditions on coefficients in average form. The presence of impulsive effects is also considered.