A link of stochastic differential equations to nonlinear parabolic equations

Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.     

A method for solving nonlinear spectral problems for a class of systems of differential algebraic equations

A method for calculating eigenvalues of a nonlinear spectral problem for one class of linear differential algebraic equations is proposed under the assumption of an analytical dependence on spectral parameter of the matrices appearing in the system of equations and the matrices determining boundary conditions.     

二阶非线性微分方程解的Sturm比较定理

通过几个微分不等式建立了一类非线性微分方程解的Sturm比较定理，推广了一些经典的结论。     

The existence of periodic solutions for a class of nonlinear functional differential equations

This paper is concerned with periodic solutions of first-order nonlinear functional differential equations with deviating arguments. Some new sufficient conditions for the existence of periodic solutions are obtained. The paper extends and improves some well-known results.     

A class of nonlocal singularly perturbed problems for nonlinear hyperbolic differential equation

The author discussed a class of singularly perturbed problems for differential equation fiee {1--7]). Now we consider the non1ocal singu1arly perturbed problem as follows:where E is a positive small parameter anHere x = (xl, x2,' ) x.) E n, fl denotes a bounded region in R", 0fl signilies a boundary offl for class Cl cr (cr 6 (0, 1) is H5lder exponent), T0 is a positive constant, L1 is a uniformlyelliptic operator, L2 is a first order differential operator, T is an integral operator, K(x…     

二阶非线性椭圆型微分方程解的振动比较定理

建立几个微分不等式,讨论了一类二阶非线性椭圆型微分方程解的振动性,得到几个新的振动比较定理．     

EXISTENCE OF SOLUTIONS OF NONLINEAR TWO AND THREE-POINT BOUNDARY VALUE PROBLEMS FOR FOURTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, the two and three-point boundsry problems (with nonlinear boundary conditions)for the genaral noniinear equations of fourth order are discussed.We have set some grups of the assurnpion coditions and proved the existence of solutins for corresponding boundary value problems under these conditons.     

On the structure of positive solutions of a class of fourth order nonlinear differential equations

A detailed analysis is made of the structure of positive solutions of fourth-order differential equations of the form

n阶非线性常微分方程非线性k点边值问题解的存在性

利用格林函数和上下解方法讨论了n阶非线性常微分方程之几类具有非线性k点边界条件的边值问题的存在性。     

一类具非线性边值条件的非线性方程的奇摄动问题

研究了一类具非线性边值条件的非线性方程的奇摄动问题,运用合成展开法构造了问题的形式渐近解,并用微分不等式理论证明了所得渐近解的一致有效性.     

Dynamics of a system of nonlinear differential equations

This is a qualitative analysis of a system of two nonlinear ordinary differential equations which arises in modeling the self-oscillations of the rate of heterogeneous catalytic reaction. The kinetic model under study accounts for the influence of the reaction environment on the catalyst; namely, we consider the reaction rate constant to be an exponential function of the surface concentration of oxygen with an exponent μ. We study the necessary and sufficient conditions for the existence of periodic solutions of differential equations as depending on μ. We formulate some sufficient conditions for all trajectories to converge to a steady state and study global behavior of the stable manifolds of singular saddle points.     

某些非线性三阶常微分方程的几个存在性结论

考察了某些非线性三阶常微分方程的存在性．主要结论的条件涉及非线性项在无穷远处的增长速度．改进和推广了某些现有的结论．     

Oscillation of even order nonlinear functional differential equations with damping

This paper is concerned with a class of even order nonlinear damped differential equations

一类具非线性边界条件的高阶方程的奇摄动问题

通过引入伸展变量和非常规的渐近序列{∈}）,运用合成展开法,对一类具非线性边界条件的非线性高阶微分方程的奇摄动问题构造了形式渐近解,再运用微分不等式理论证明了原问题解的存在性及所得渐近近似式的一致有效性．     

On a certain class of a nonlinear evolution partial differential equations

An existence result and a priori bound for the solution of a second-order nonlinear parabolic equation are established. Also a generalized tanh-function method is used for constructing exact travelling wave solutions for the nonlinear diffusion equation of Fisher type originated from the considered partial differential equation. And new multiple soliton solutions are obtained.     

二阶非线性泛函微分方程解的振动性质

研究了一类二阶非线性泛函微分方程解的振动性以及非振动解的有界性.在一定条件下,建立了几个新的振动性和有界性定理,其结果推广和改进了已有的一些结果.     

Some oscillation criteria for second order nonlinear functional ordinary differential equations

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) ＞ 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.