Remarks on Quasilinear Hyperbolic Equations with Dynamic Boundary Conditions

In this paper the non-existence of global solutions of two fourth-order hyperbolic equations with dynamic boundary conditions is considered. Here we prove stronger results than that of M. Kirane, S. Kouachi and N. Tatar by a different method.     

Hyperbolic Equations Admitting Differential Substitutions

We show that the first n–1 Laplace invariants of a scalar hyperbolic equation obtained from an equation of the same form under a differential substitution of the nth order have a zeroth order with respect to one of the characteristics. It follows that all Laplace invariants of an equation admitting substitutions of an arbitrarily high order must have a zeroth order. Three special cases of such equations are considered: those admitting autosubstitutions, those obtained from a linear equation by a differential substitution, and those with solutions depending simultaneously on both an arbitrary function of x and an arbitrary function of y.     

二阶复微分方程的亚纯元素解及代数元素解

研究了一类二阶亚纯系数复微分方程的亚纯元素解及代数元素解的存在性问题,得到了几个有关解的存在性定理.     

一类二阶常微分方程m点边值问题的解法

该文研究一类二阶常微分方程,给出了所述线性方程在几种m点边界条件下解的存在惟一性及其解的解析表达式,作为应用的例子,作者对一类非线性边值问题给出了正解的迭代求法.     

Hilbert空间中的二阶微分方程问题

运用多值分析、单调算子理论和Schauder不动点定理讨论了一类具有多点边值条件的二阶微分包含问题．作为一个预备性的结果，给出了一类二阶发展方程的解的存在唯一性和对初值的连续依赖性．最后，给出了以上结论在最优化和偏微分方程方面的两个应用．     

Orthogonal Polynomials and Second-order Differential Equations

We show that a sequence of polynomials can be eigenfunctionsof a second-order differential operator only under severe restrictions.     

On Nonlinear Hyperbolic Functional Differential Equations

In this paper, existence of weak solutions of second order evolution equations is proved and some properties of the solutions are shown. The results are applied to higher order nonlinear hyperbolic functional differential equations.     

Some Approximations of the Characteristics of Second Order Hyperbolic Partial Differential Equations

The characteristic curves of the quasi-linear hyperbolic partialdifferential equation of the second order, having unequallyspaced, discreate initial conditions, are approximated by L₂parabolas, L₁ parabolas and cubic splines.     

Remarks on the Linearization of Differential Equations

The Hamiltonian formalism and the theory of canonical transformationsare used in this paper, first of all, to show that, given anordinary non-linear differential equation it is always possiblein principle to find a variable transformation reducing it toa linear equation, or a system of linear equations. The proofgiven is not to be construed as a general practical method forfinding this transformation; it merely shows that such a transformationmust always exist. It is suggested that this may also hold true for partial differentialequations. The conjecture is made plausible, in two cases, bythe use of canonical transformation procedures for linearizingsimple non-linear partial differential equations—one beinga slight generalization of Burger's equation and the other anequation in three independent variables reminiscent of the Eulerequations for fluid flow.     

Some Remarks on Signs in Functional Equations

We discuss the computation of the sign in certain functional equations.     

Some Remarks on Stability of Generalized Equations

The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by C ² inequalities. Instead of the linear independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian–Fromovitz and the constant rank qualification conditions. Based on the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constraints are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.     

二阶非线性脉冲微分方程的振动性

考虑二阶脉冲微分方程(r(t)(x′(t))σ)′+f(t,x(t),x′(t))=0,t t0,t≠tk,k=1,2,…x(tk+)=gk(x(tk)),x′(tk+)=hk(x′(tk)),k=1,2,…(E)其中0 t0相似文献   

Optimum Runge-Kutta-Fehlberg Methods for Second-order Differential Equations

^* Presently at Deparment of Mathematics, Indian Institute of Technology, Madras, India. The optimum Runge-Kutta method of a particular order is theone whose truncation error is minimum. In this paper, we havederived optimum Runge-Kutta mehtods of 0(h^m+4), 0(h^m+5) and0(h^m+6) for m = 0(1)8, which can be directly used for solvingthe second order differential equation yⁿ = f(x, y, y'). Thesemethods are based on a transformation similar to that of Fehlbergand require two, three and four evaluations of f(x, y, y') respectively,for each step. The numercial solutions of one example obtainedwith these methods are given. It has been assumed that f(x,y, y')is sufficiently differentiable in the entire region ofintegration.     

Infinite Systems of Hyperbolic Functional Differential Equations

We consider initial-value problems for infinite systems of first-order partial functional differential equations. The unknown function is the functional argument in equations and the partial derivations appear in the classical sense. A theorem on the existence of a solution and its continuous dependence upon initial data is proved. The Cauchy problem is transformed into a system of functional integral equations. The existence of a solution of this system is proved by using integral inequalities and the iterative method. Infinite differential systems with deviated argument and differential integral systems can be derived from the general model by specializing given operators.     

关于齐次四元Monge-Ampère方程的一些注记北大核心CSCD

本文考虑了四元数空间Hn中齐次四元Monge-Ampère方程的狄利克雷问题解的正则性.首先,当区域是边界为C1,1的强拟凸域时,作者给出了解的Lipschitz估计.其次,考虑了四元MongeAmpère算子的收敛性.最后,讨论了齐次四元Monge-Ampère方程的粘性次解与F-次调和函数之间的关系.     

Quasilinear Stochastic Hyperbolic Differential Equations with Nondecreasing Coefficient

In this note we prove a result of existence and uniqueness of solutions for a certain class of hyperbolic stochastic differential equations with additive white noise and nondecreasing coefficient. We then show the convergence of Euler's approximation scheme for this equation.     

中立型时滞双曲微分方程的振动性(英文)

考虑一类中立型时滞双曲微分方程 ,得到了该方程振动的一个充分条件 .     

一类中立型双曲微分方程的振动性定理

本文运用Philos方法,获得了一类具连续偏差变元的中立型双曲微分方程的振动性的充分性条件.