共查询到20条相似文献,搜索用时 93 毫秒
1.
广义Gelfand模型的正解 总被引:22,自引:2,他引:20
姚庆六 《高校应用数学学报(A辑)》2001,16(4):407-413
在不要求极限limτ→0f(τ)/τ,limτ→∞f(τ)τ存在的情况下,讨论了二阶边值问题u″(t) λh(t)f(u(t))=0,0≤t≤1,u(0)=u(1)=0的正解存在性和多重性。 相似文献
2.
非线性奇异三阶微分方程周期边值问题的正解 总被引:2,自引:0,他引:2
讨论非线性奇异三阶微分方程的周期边值问题{u″+ρ^3u=f(t,u),t∈I=(0,2π),ρ∈(0,1/√3)是常数 u^(i)(0)=u^(t)(2π),i=0,1,2
的正解存在性问题.通过与一个线性算子相关的第一特征值的讨论,运用不动点指数定理,得到了正解存在的结果. 相似文献
3.
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. 相似文献
4.
5.
几类半线性椭圆共振问题 总被引:1,自引:0,他引:1
设Ω∪→R^n是一个有界正则区域,{λk}是-△在H0(Ω)上的一列特征值。假定对某个给定的k,λk是单重的,φ为其相应的特征函数,∫φ^2=1,固定h∈H^-1使∫hφ=0。对于方程(P1){-△u-λu g(x,u)=tφ h,u=0。σΩ本文利用连通技巧和闭联集理论,推广了文[1]、[3]、[4]中的一些结果。我们获得定理1 假设g:R^*→R满足(g1)g是具有周期原函数的连续周期函数,λk(k≥)简单。如果对任意s ∈R,有(H′4{λk-1≤λ g′(s)≤λk 1k>1。const≤λ g′(s)≤λ2。则任意h∈H^1,E←τ1,τ2∈R。τ1≤0≤τ2使(i)(P1)有解当且仅当t∈[τ1,τ2]。(ii)如果t∈[τ1,τ2]-{0},则(P1)至少有两个不同的解。定理2 假设(H′4)成立,λk简单,g满足(H2)任意s,g按x在Ω上可测;g∈C^1对a.e.x∈Ω。(H5)g有界limsg(x,s)=μ>0。|s|→∞则任意h∈H′0, E←τ1,τ2∈R,τ1<0<τ2使(i)(P1)有解当且仅当t∈[τ1,τ2]。(ii)若t∈[τ1,τ2]-{0},则(Pt)至少有两个不同的解。定理3 [3,prop.2.4]中的条件q<v(-△-λkI)换成q≤v(-△-λkI)结论仍然成立。 相似文献
6.
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
7.
该文研究了p-Laplacian动力边值问题(g(u^△(t)))△+a(t)f(t,u(t))=0,t∈[0,T]T,u(0)=u(T)=w,u△(0)=-u^△(T)正解的存在性.其中W是非负实数,g(v)=|v|p-2v1 P>1.根据对称技巧和五泛函不动点定理,证明了边值问题至少有三个正的对称解,同时,给出了一个例子验证了我们的结果。 相似文献
8.
9.
利用不动点和度理论,证明了四阶周期边值问题u(4)(t)-βu″(t)+αu(t)=λf(t,u(t)),0≤t≤1,u(i)(0)=u(i)(1),i=0,1,2,3,至少存在两个正解,其中β>-2π2,0<α<(1/2β+2π2)2,α/π4+β/π2+1>0,f:[0,1]×[0,+∞)→[0,+∞)是连续函数,λ>0是常数. 相似文献
10.
利用锥拉伸锥压缩不动点定理,证明了在一定条件下,下列非线性奇数阶方程(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,u(0)=u′(τ)=u″(1)=0u(2j+1)(0)=u(2j+1)(1)=0,j=1,2,…,q-1.单个和多个正解的存在性,其中λ>0,12<τ<1,q∈N.得到了λ的区间Λ,对一切λ∈Λ,该问题至少有一个正解,同样也得到了该问题至少有两个正解λ相应的区间. 相似文献
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.
《数学学报(英文版)》2014,(10)
<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China. 相似文献
13.
14.
《运筹学学报》2014,(3)
正August 10-14,2015Beijin,China The 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
15.
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
16.
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
17.
《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
18.
19.
《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
20.
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