二阶非线性微分方程的斜周期边值问题

In this paper a uniqueness theorem for a skewperiodic boundary value problem is obtained. By using the optimal control method, we derive the best estimate for the integration mean ensuring that the results hold.     

二阶非线性脉冲微分方程的 Sturm-Liouville边值问题(英文)

本文采用一个改进的单调迭代技巧 ,获得了二阶非线性脉冲微分方程的 Sturm-L iouville边值问题的极解     

2n阶非线性微分方程的第二边值问题

Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.     

跨越共振的非线性常微分方程的第二边值问题

使用最优控制理论方法和Schauder不动点定理证明了非线性常微分方程第二边值问题解的存在性和唯一性,并且给出了其可解性的最优估计,特别地,我们考虑的问题可以是跨越共振的.     

Boundary Value Problems for Nonlinear Differential Equations of Second Order inBanach Spaces

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二阶奇异非线性微分方程边值问题的正解

分别在0≤f₀+<M₁,m₁<f_∞-≤∞和0≤f_∞+<M₁,m₁<f₀-≤∞的情形下研究了非线性奇异边值问题u″+g(t)f(u)=0,0<t<1,αu(0)-βu′(0)=0,γu(1)+δu′(1)=0正解的存在性,其中f₀+=₀f(u)/u,f_∞-=_∞f(u)/u,f₀-=₀f(u)/u,f_∞+=_∞f(u)/u,g在区间[0,1]的端点可以具有奇性。     

二阶非线性微分方程组的正规解及极限边值问题

本文对微分方程组其中a(t)>0,r(t)>0,t≥t₀;f(x)对x>0正值递减;g(y)>0,给出存在正规解,有界正规解或两类无穷区间[c,∞)(c≥t₀)上边值问题解的充要条件.同时给出若干例子说明结果的条件.     

一类二阶泛函微分方程的周期边值问题

讨论了一类二阶泛函微分方程的周期边值问题,给出了上、下解的一个新的概念,并且得到了一个新的比较结果.同时,修正了相关文献中的一个错误.     

n阶非线性微分方程的非线性三点边值问题

本文利用广义对接方法,建立了n阶非线性微分方程y(n)=f(x,y,y',…, y(n-1))满足非线性三点边界条件的非线性三点边值问题解的存在性与唯一性定理,所得结果将已有的很多相应结果作为特例.     

n阶非线性常微分方程的非线性两点边值问题

本文利用打靶法,给出了ｎ阶非线性常微分方程具有非线性两点边界条件的边值问题存在解与存在唯一解的一般性结果,并将所得结果应用于Ｌｉｐｓｃｈｉｔｚ方程的两点过值问题,给出了存在解与存在唯一解的具体的充分条件。     

Boundary Value Problems for Third-Order Nonlinear Ordinary Differential Equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.     

Nonlinear Boundary Value Problems for Second Order Differential Inclusions

In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form x ↦ a(x, x′)′. In this problem the maximal monotone term is required to be defined everywhere in the state space ℝ^N. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ↦ (a(x)x′)′. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side.     

非线性项有非线性增长的2阶泛函微分方程边值问题

本文考虑下述２阶泛函微分方程边值问题：x″(t)=f(t,x_t,x′(t))(00=φ,x(b)=B.对于ｆ有非线性增长的情况，得出了上述问题可解的某些充分条件。     

二阶非线性泛函差分方程的边值问题

应用临界点理论,获得了一类二阶泛函差分方程边值问题解的存在性和多重性的充分条件.     

具有p-Laplacian算子的二阶微分方程Picard边值问题(英文)

Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations {[φ（x（t））] ＋ kx（t） ＋ g（t,x（t）） = p（t）,t ∈（0,π） x（0） = x（π） = 0 are established,where [φ（x）] =（｜x ｜p-2x） with p 1.Our result is new even when [φ（x）] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.     

一类二阶微分系统边值问题解的存在性

通过推广上下解的概念,利用上下解方法讨论了二阶微分系统-x″(t)=f(t,x)分别在边值条件x(0)=0,x′(1)=0和x(0)=A,x(1)=B下解的存在性.     

非线性二阶常微分方程组边值问题的正解

本文利用拓扑方法研究了下列非线性二阶常微分方程组边值问题在某些条件下,我们证明了上述边值问题正解的存在性和个数.     

二阶非线性微分方程组多点边值问题的正解

该文使用不动点指数理论,研究二阶奇异非线性微分方程组多点边值问题的正解和多个正解的存在性.给出某些保证解的存在性的极限条件,这些条件适用于较一般的函数.