一类二阶泛函微分方程周期解存在性问题

利用重合度理论研究一类二阶泛函微分方程x″(t)+f(t,x_t)x′~n+β(t)g(x(t-τ(t)))=p(t)的周期解问题,本文得到了周期解存在的新的结果。     

Existence of Positive Solutions for a Nonlinear Second Order Periodic Boundary Value Problem

By using the first eigenvalue corresponding to the relevant linear operator and the topological degree theorem, sufficient conditions for the existence of positive solutions for a nonlinear second order periodic boundary value problem are given. Our results improve and generalize some preliminary works.     

二阶积分微分方程周期边值问题的解的存在性

通过对比结果,用单调迭代方法证明了Banach空间中二阶积分微分方程的周期边值问题的最大最小解的存在性定理。     

On the Existence,Uniqueness, and Nonexistence of Solutions of One Boundary-Value Problem for a Semilinear Hyperbolic Equation

Ukrainian Mathematical Journal - We consider a boundary-value problem for a semilinear hyperbolic equation with iterated multidimensional wave operator in the principal part. The theorems on...     

On the Existence of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equation

By means of the continuation theorem of coincidence degree theory, some new results on the non-existence, existence and unique existence of periodic solutions for a kind of second order neutral functional differential equation are obtained.     

一类高阶差分方程周期解的存在性

本文应用临界点理论获得了一类高阶差分方程k∑i=0(xn-i xn i) f(xn 1,xn,xn-1) =0, n∈z,k∈N非平凡M-周期解存在的充分条件.     

一类二阶具偏差变元的微分方程周期解的存在性

利用重合度理论研究一类二阶具偏差变元的微分方程x″(t)=f(t,x(t),x(t-τ(t)))+e(t)的周期解问题,得到了周期解存在的充分条件.     

一类二阶微分方程同宿解的存在性

讨论下列二阶微分方程(y|¨)+ay+U_y(t,y)=0.的同宿解的存在性,其中t∈R,y∈Rⁿ,n∈N,a>0是一个常数,U(t,y)∈Cn,n∈N,a>0是一个常数,U(t,y)∈C¹(R×R1(R×Rⁿ,R),U_y(t,y)表示U(t,y)关于y的梯度.引入快同宿解的概念并给出方程存在快同宿解的判定准则.     

One Initial Boundary-Value Problem for Integro-Differential Equation of the Second Order With Power Nonlinearity

In the Sobolev space W _∞ ² (?⁺) we investigate one initial boundary-value problem for integro-differential equation of the second order with power nonlinearity on a semi-axis. Assuming that summary-difference even kernel serves for the considered kernel as minorant in the sense of M. A. Krasnosel’skii, we prove the existence of a nonnegative (nontrivial) solution in the Sobolev spaceW _∞ ² (?⁺). We also calculate the limits of constructed solution at infinity.     

具偏差变元的二阶p-Laplacian方程周期解存在性问题

本文研究一类具偏差变元的二阶p-Laplacian方程((?)p(y'(t)))'+f(y'(t))+g(y(t-τ(t)))=e(t)的周期解问题.利用Mawhin重合度拓展定理得到了周期解存在性的新的结果.     

二阶非线性中立型泛函微分方程周期解的存在性

利用κ-集压缩算子拓扑度抽象连续定理,研究了一类二阶泛函微分方程周期解的存在性,获得了方程周期解存在的充分条件,这些结果推广并改进了已有文献的相关结果.     

二阶非线性中立型泛函微分方程周期解的存在性

本文利用重合度理论,研究二阶非线性中立型泛函微分方程[x(t)+cx(t- τ)]11+g(t,x(t-σ)=p(t)的周期解的存在性,给出该方程存在周期解的充分性定理.     

Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order

On the basis of the exact solution of the linear Dirichlet problem , we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation u _tt – u _xx = f(x, t, u, u _t).     

On Periodic Solutions of Second Order Linear Difference Equations

In this paper, we apply a new procedure initially developed in Refs. [H. El-Owaidy and H.Y. Mohamed. "On the periodic solutions for nth order difference equations". Journal of Applied Mathematics and Computation , (to appear); "The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations". Journal of Applied Mathematics and Computation , (to appear)] to simplify the use of Carvalho's method to the case of discrete difference equations, in order to find the periodic solutions of second order linear difference equations. We can also find the complex periodic solutions.     

二阶Nuemann特征值问题的正解

利用锥上的不动点定理证明了二阶Nuemann特征值问题-u″＋Mu=λa（t）f（u（t））m0≤t≤1 u′（0）=u′（1）=0是的正解存在性结果．     

Existence and Life Span of Periodic Solutions for the First Order Quasilinear Hyperbolic Equations

g1.IntroductionWeconsiderthefollowingfirstorderquasilinearhyperbolicequationswithinternaIdissipa-tlveterm:U, A(U)U. F(U)=o(1.1)whereUeR2isunknownvectorfunction,A(U)is2X2knownsmoothmatrix,F(U)is2X2knownsmoothvectorfunction.Itiswell-knownthatCauchyproblemoftheequations(l.1)hasbeenwidelystudied(Ll-6J),however,theequations(l.1)withperiedicinitialdatahasbeenhardlystudiedandonesfindthatitiscomplicatedforproblemwithperiodicinitialdata.Becausetheperiodicdis-turbanceLlirectlyinfluencesthebounde…     

一类高阶非线性双曲型方程初边值问题解的爆破

本文研究一类高阶非线性双曲型方程的初边值问题，证明问题局部广义解的存在性与唯一性，同时给出解爆破的充分条件。     

关于二阶中立型方程周期解的存在性

本文主要研究二阶常系数线性中立型方程在｜ｃ｜＝１条件下周期解的存在性，并将文［２］中定理３的条件进一步减弱．