二阶奇异非线性边值条件的上下解方法

本文利用上下解方法,讨论奇性边值问题(py’)’+ p(t)q(t)f(t,y,py’)=0,0相似文献   

Topological Properties of Solution Sets of Lipschitzian Quantum Stochastic Differential Inclusions

We establish a continuous mapping of the space of the matrix elements of an arbitrary nonempty set of quasi solutions of Lipschitzian quantum stochastic differential inclusion (QSDI) into the space of the matrix elements of its solutions. As a corollary, we furnish a generalization of a previous selection result. In particular, when the coefficients of the inclusion are integrably bounded, we show that the space of the matrix elements of solutions is an absolute retract, contractible, locally and integrally connected in an arbitrary dimension. Permanent address: E.O. Ayoola, Department of Mathematics, University of Ibadan, Ibadan, Nigeria.     

边界条件含特征参数的奇异不连续Sturm-Liouville算子的渐近特征

研究有限区间内一类边界条件含特征参数的不连续奇异Sturm-Liouville问题.利用函数论和算子理论的方法,证明该问题的自伴性,得到其特征值的相关性质,基本解及其特征值的渐近公式.     

二阶模糊线性微分方程边值问题的模糊近似解

讨论了二阶模糊线性微分方程边值问题{y+p(t)y'+q(t)y=g(t),t∈[a,b],t∈[a,b]y(a)=(a),y(b)=(β),(α),(β)∈E1的模糊近似解,即利用配置法将微分方程转化为函数线性方程组,针对其系数函数的符号的不同,通过计算函数线性方程组获得了原模糊微分方程的模糊近似解.     

一类多偏差变元的二阶微分方程周期解

本文利用重合度理论研究了一类二阶多偏差变元的微分方程 x＂（t）＋f（t,x（t）,x（t-τ0（t））,x＇（t））＋∑nj=1g（x（t-τj（t）））=p（t） 的周期解问题，得到了存在周期解的新的结果．     

Multiple Solutions for a Differential Inclusion Problem with Nonhomogeneous Boundary Conditions

In this paper, we use a mountain pass theorem with Cerami type conditions for locally Lipschitz functions to investigate the existence of at least one nontrivial solution for a differential inclusion problem involving the p-Laplacian and with nonlinear and nonsmooth boundary conditions. Moreover, by a symmetric version of the mountain pass theorem, we prove the existence of infinitely many solutions.     

Stability Properties in Some Classes of Second Order Partial Differential Equations

The main purpose of this note is to investigate the stability problem in a certain class of partial differential equations.     

一类二阶脉冲微分方程三点边值问题解的存在性

运用Leray-Schaudar原理,获得一类二阶脉冲微分方程三点边值问题解的存在性定理,并给出实例.     

共振条件下一类三阶m-点边值问题解的存在性

考虑共振情形下三阶微分方程m-点边值问题x＇＇＇（t）=f（t,x（t）,x＇（t）,x＂（t））＋p（t）,t∈（0,1）, x（0）=0,x＂（0）=0,x＇（0）=0,x＇（1）=∑i=1^m-2 aix＇（ξi）,其中ai≥0，0〈ξ1〈ξ2〈…〈ξm-2〈1且∑i=1^m-2 ai=1．利用Mawhin重合度拓展定理，得到该问题解存在性的新的结果．     

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.     

二阶周期线性微分方程解的几个性质

In this paper,the zeros of solutions of periodic second order linear differential equation y ＋ Ay = 0,where A（z） = B（e z ）,B（ζ） = g（ζ） ＋ p j=1 b ？j ζ ？j ,g（ζ） is a transcendental entire function of lower order no more than 1/2,and p is an odd positive integer,are studied.It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity.     

半直线上含导数项的二阶微分方程组边值问题的正解

应用Sadovskii不动点定理不动点理论讨论半直线上含导数项的二阶微分方程组,得到了在边值条件为非负常数时的正解的存在性定理     

含两参数的二阶常微分方程Cauchy问题解的多重层性质

研究含两参数的二阶常微分方程Cauchy问题解的多重层性质,根据不同层次引用不同的伸长变量,分别构造了具有不同量级的边界层校正项,从而证得关于解的一致有效的渐近展开式和有关的余项估计.     

一类分数阶微分方程多点边值问题的多重正解

利用锥不动点等定理证明一类分数阶微分方程m点边值问题多重正解的存在性,应用Leray-Schauder非线性抉择定理和Guo-Krasnosel'skii不动点定理得到了边值问题(1)的多重正解的存在性.     

二阶周期边值问题的多重正解

考虑如下周期边值问题:其中x~([1])(t)=p(t)x'(t).总假设p(t)>0,q(t)>0,且f(t,x)是[0,1]×(0,+∞)→[0,+∞)的连续函数,f在z=0可以有奇性.利用锥不动点定理以及格林函数的正性,给出周期边值问题单个和多个正解存在性证明的一种新方法.在实际中,定理的条件很容易验证.     

On Some Second Order Differential Equations with Convergent Solutions

Via a special integral transformation, asymptotic integration results for ordinary differential equations are used to establish accurate asymptotic developments for radial solutions of the elliptic equation Δu + K(|x|)e ^u = 0, |x| > x ₀ > 0, in the bidimensional case.