Singular Nonlinear Eigenvalue Problem for One Class of Second-Order Differential Equations

The eigenvalue problem for a singular nonlinear differential equation of the second order is considered on a semiaxis. For this problem, we establish sufficient conditions for the existence of a solution with given number of zeros monotonically decreasing to zero at infinity.     

一类二阶非线性脉冲微分方程解的振动性

讨论了一类二阶非线性脉冲微分方程解的振动性质,并得到了这类方程解的振动的一组充分条件.     

Periodic Positive Solution to a Class of Singular Second-Order Ordinary Differential Equations

This paper studies the existence of a positive solution to the second-order periodic boundary value problem

Boundary Value Problems for Singular Second-Order Functional Differential Equations

Abstract Positive solutions to the boundary value problem, y'=-f(x,y(w(x)) 0相似文献   

Periodic Solutions for a Class of Second-Order Ordinary Differential Equations

This paper is devoted to the study of periodic solutions for a class of second-order ordinary differential equations by utilizing a technique for obtaining solutions to free problems in the calculus of variations originating in the work of Carathéodory (Ref. 1, 1935). The key of this technique is to find some suitable transformation which transfers the periodic solution problem to an equivalent variational problem in which the minimizer is more easily determined. Some applications are presented to illustrate the utility of this technique.Supported by NSFC Grant 10401013, 985 Project of Jilin University and Graduate Innovation Lab of Jilin University. The authors thank Professor D. A. Carlson and the anonymous referees for valuable suggestions and helpful comments.     

非线性二阶奇异半正微分方程组非局部边值问题的多个正解

研究利用Leggett-Williams不动点定理和平移变换,讨论了非线性二阶奇异半正微分方程组非局部边值问题三个正解的存在性.文中的主要结果推广了以前相应的工作.     

Interval Oscillation Criteria for Second-Order Nonlinear Differential Equations

We present new interval oscillation criteria for certain classes of second-order nonlinear differential equations, which are different from the most known ones in the sense that they are based only on information on a sequence of subintervals of [t ₀, ) rather than on the whole half-line. We also present several examples that demonstrate wide possibilities of the results obtained.     

一类高阶非线性边值问题的奇异摄动

本文应用高阶微分不等式技巧和边界层校正法研究一类高阶非线性方程混合边值问题: e2yn=f(t,e,y,…,yn-2 Pj(ε)yj(0,ε)-qj(ε)yj+1(0,ε)=Aj(ε)(0≤j≤n-3)a₁(ε)y(n-2)(0,ε)-a₂(ε)yn-1(0,ε)=B(ε)b₁(ε)y(n-2)(1,ε)十b₂(ε)y(n-1)(1,ε)=C(ε)的奇异摄动。在较一般的条件下,证明了摄动解的存在性,并得到了摄动解直到n阶导函数的一致有效渐近展开式,从而推广和改进了前人的结果。     

A Nonoscillation Theorem for Second-Order Nonlinear Differential Equations with Decaying Coefficients

The purpose of this paper is to give sufficient conditions forall nontrivial solutions of the nonlinear differential equationx ' a(t)g(x) = 0 to be nonoscillatory. Here, g(x) satisfiesthe sign condition xg(x) > 0 if x 0, but is not assumedto be monotone increasing. This differential equation includesthe generalized Emden–Fowler equation as a special case.Our main result extends some nonoscillation theorems for thegeneralized Emden–Fowler equation. Proof is given by meansof some Liapunov functions and phase-plane analysis.     

Minimal Positive Solutions to Some Singular Second-Order Differential Equations

The existence of a minimal C¹[0, 1] positive solution is established for some second-order singular boundary value and initial value problems by new schemes, which are related to x′. Our nonlinearity may be singular at t = 0, 1, x = 0, or x′ = 0.     

具有强迫项的二阶非线性时滞微分方程的振动性

利用广义Riccati技巧和积分平均技巧,研究具有强迫项的二阶非线性时滞微分方程的振动性态,得到了这类方程振动的若干新的区间判别准则.     

一类二阶非线性方程奇异边值问题

本文证明了方程div（|Du|p-2Du） f(r.u（r），u'(r))=0（R1＜r＜R0）正对称解的存在性．这里f允许在u=0或。u’=0处奇异．     

Boundary Value Problems for Second－Order Singular Differential Equations on Infinite Intervals

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Interior Layers for Second-Order Singular Equations

Our aim in this article is to study singularly perturbed problems which display boundary layers in the interior of the domain. These interior boundary layers which supplement the usual boundary layers at the boundary, are generated by discontinuities in the data. Second-order linear elliptic one-dimensional and multi-dimensional problems are considered in this article.     

Asymptotic Expansions of the Cubic Spline Collocation Solution for Second-Order Ordinary Differential Equations

In this paper, we consider the following problem $$\begin{cases}u''(x)=f(x,u(x),u'(x)), a\leq x\leq b,\\u(a)=u(b)=0,\end{cases}$$ and obtain the theorem.     

带强迫项与阻尼项的二阶非线性微分方程振动性准则

通过构造不同的辅助函数w(t)和H(t,s)∈c(D,R),我们得到了方程(1.1)的新的振动性准则.     

带强迫项与阻尼项的二阶非线性微分方程的区间振动性

研究了一类二阶非线性微分方程的振动性.利用广义黎卡提变换和积分平均技巧建立了方程(1)的新的振动准则,推广了文献中已有的一些结果.     

A Superconsistent Chebyshev Collocation Method for Second-Order Differential Operators

A standard way to approximate the model problem –u =f, with u(±1)=0, is to collocate the differential equation at the zeros of T _n : x _i , i=1,...,n–1, having denoted by T _n the nth Chebyshev polynomial. We introduce an alternative set of collocation nodes z _i , i=1,...,n–1, which will provide better numerical performances. The approximated solution is still computed at the nodes {x _i }, but the equation is required to be satisfied at the new nodes {z _i }, which are determined by asking an extra degree of consistency in the discretization of the differential operator.     

On Entire Solutions of a Class of Second-Order Algebraic Differential Equations

Mathematical Notes - For second-order algebraic differential equations which have an explicit linear part, we describe all their possible solutions that are entire functions of finite order.