共查询到20条相似文献,搜索用时 62 毫秒
1.
杜睿娟 《应用泛函分析学报》2008,10(1):71-75
讨论Nagumo条件下非线性常微分方程三阶两点边值问题{y″′=t,y,′,y″),t∈[0,1],y(0)=y′(0)=y′(1)=0解的存在性,其中f:[0,1]×R^3→R为连续函数. 相似文献
2.
奇异二阶边值问题的正解 总被引:65,自引:4,他引:65
本文分别在f超线性和次线性的情形研究非线性边值问题。u″+a(t)f(u)=0;αu(0)-βu′(0)=0,γu(1)+δu′(1)=0的正解的存在性.其中a在端点可以具有奇性. 相似文献
3.
非齐次边值条件下一类静态梁方程非负解的存在性 总被引:1,自引:1,他引:0
宋灵宇 《纯粹数学与应用数学》2003,19(1):72-77
运用Schauder不动点定理,在非齐次边值条件,讨论带导数项的一端简单支撑另一端滑动的静态梁方程y^(4)(x)=f(x,y(x),y′(x),y″,y^(3)(x)),x∈[0,1] y(0)=a,y′(1)=b,y″(0)=c,y^(3)(1)=d非负解的存在性,其中a≥0,b≥0,c≤0,d≤0。假定f在零点次线性增长,在无穷远点超线性增长,则上述非齐次边值问题当max{a,b,-c,-d}充分小时有非负解存在,当max{a,b,-c,-d}充分大时无非负解存在。 相似文献
4.
利用拓扑度理论和上下解方法讨论了一类三阶微分方程组{x′′′(t)+f1(t,y(t),x′(t),x″(t))=0,0≤t≤1,y′′′(t)+f2(t,x(t),y′(t),y″(t))=0,0≤t≤1在适当的条件下解的存在性. 相似文献
5.
本文以关于非线性全连续算子的锥不动点定理为工具,研究以下二阶系统边值问题x"(t)+λa(t)f(x(t),y(t)=0,y"(t)+λb(t)g(x(t),y(t))=0,x(0)=x(1)=y(0)=y(1)=0.在不假定f单调的情况下,本文得出了上述问题存在正解的若干充分条件. 相似文献
6.
In this paper, existence of solutions of third-order differential equation
y′″(t)=f(t,y(t),y′(t),y″(t))
with nonlinear three-point boundary condition
{g(y(a),y′(a),y″(a))=0,
h(y(b),y′(b))=0,
I(y(c),y′(c),y″(c))=0
is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a, b, c∈ R,a〈 b〈 c; f : [a,c]×R^3→R,g:R^3→R,h:R^2→R and I:R^3→R are continuous functions. The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem. As an application, an example with an explicit solution is given to demonstrate the validity of the results in this paper. 相似文献
y′″(t)=f(t,y(t),y′(t),y″(t))
with nonlinear three-point boundary condition
{g(y(a),y′(a),y″(a))=0,
h(y(b),y′(b))=0,
I(y(c),y′(c),y″(c))=0
is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a, b, c∈ R,a〈 b〈 c; f : [a,c]×R^3→R,g:R^3→R,h:R^2→R and I:R^3→R are continuous functions. The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem. As an application, an example with an explicit solution is given to demonstrate the validity of the results in this paper. 相似文献
7.
一维奇异p-Laplace方程的正解 总被引:14,自引:2,他引:12
本文获得了一维奇异p-Laplace方程的Dirichlet边值问题(|y′|p-2y′)′+g(t,y)=0,y(0)=y(1)=0,P>1的两个正解存在定理.这一结论是通过使用Leray-Schauder非线性抉择及上下解方法建立的. 相似文献
8.
有别于一般文献所使用的构造辅助函数方法,针对在[0,1]上连续,在(0,1)上可导,且满足f (0)=0,f (1)=1的函数 f (x),先用反证法可证,存在 a ,b ∈(0,1),使得 f′(a)<1< f′(b),进而利用导函数的介值性可证,存在ξ,η∈(0,1),使得 f′(ξ) f′(η)=1(ξ≠η)。 相似文献
9.
Nodal solutions for a nonlinear fourth-order eigenvalue problem 总被引:2,自引:0,他引:2
Ru Yun MA Bevan THOMPSON 《数学学报(英文版)》2008,24(1):27-34
We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y″″=λa(x)f(y),0〈x〈1,y(0)=y(1)=y″(0)=y″(1)=0where λ is a positive parameter, a ∈ C([0, 1], (0, ∞), f ∈C(R,R) satisfies f(u)u 〉 0 for all u ≠ 0. We give conditions on the ratio f(s)/s, at infinity and zero, that guarantee the existence of nodal solutions.The proof of our main results is based upon bifurcation techniques. 相似文献
10.
11.
Kunyang Wang Feng Dai 《分析论及其应用》2007,23(1):50-63
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths. 相似文献
12.
H. H. Cuenya M.D. Lorenzo C. N. Rodriguez 《分析论及其应用》2007,23(2):162-170
In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms. 相似文献
13.
Yuxian Zheng 《分析论及其应用》2006,22(2):136-140
In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p(R^n) into the Lebesgue space L^p with p 〈 1. 相似文献
14.
15.
《计算数学》2014,(2)
<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists 相似文献
16.
《中国科学 数学(英文版)》2014,(8)
<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by 相似文献
17.
W.M.Shah A.Liman 《分析论及其应用》2004,20(1):16-27
Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem. 相似文献
18.
In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 <α≤ 1). 相似文献
19.
A.Al-Shuaibi F.Al-Rawjih 《分析论及其应用》2004,20(1):28-34
Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated. 相似文献
20.
Francois Chaplais 《分析论及其应用》2006,22(4):301-318
In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f(u) of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation. 相似文献