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In this paper,the bifurcation problem g(x, λ) = 0 with symmetry con-dition is studied. An extended system is introduced for computing the simple high order symmetry-breaking bifurcation point. Numerical example is given. Key words Bifurcation problem, Symmetry-breaking bifurcation point, High order Singularities 相似文献
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We discuss a kind of codimension-tvro nonlinear higher order system, by normai form theory the system can be reduced into system equivalent toBogdanov, Takens, Carr have been studied it's local bifurcations for n - 2, after that, Wang Mingshu, Luo Dingjun, Li Jibin, Wang Xian and others studied the global bifurcations for n = 3. In this paper, we study the bifurcations for n - 4, and give all the local bifurcation curves of the system. 相似文献
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本文考虑以下2阶边值问题:其中.在关于A,B;P,Q,f的一定条件下,证明了以上问题存在分歧点.所用的主要工具是Krasnoselskii的局部分歧定理与KreinRutman定理. 相似文献
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王贺元 《高等学校计算数学学报(英文版)》2001,10(2)
1 IntroductionConsider the parameter dependent equationu"+ (λ+ s(μ) ) f( u) -μsinx =0 in ( 0 ,π)u( 0 ) =u(π) =0 ( 1 .1 )whereλ,μ∈R are parameters and f:R→R and S:R→R are smooth odd functions anda) f′( 0 ) =1 , b) f ( 0 )≠ 0 , c) s( 0 ) =0 , d) s′( 0 ) =1 . ( 1 .2 )Let S:u( x)→ u(π-x) ,Γ ={ S,I} ,then ( 1 .1 ) isΓ -equivariant.The equality ( 1 .2 a) isjust a normalization of f at x=0 .Otherwise,one may reseek the parameter x to ensure( 1 .2 a) .To simplify an… 相似文献
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EXISTENCE AND ASYMPTOTIC ESTIMATE OF SOLUTION FOR THIRD ORDER BOUNDARY VALUE PROBLEM 总被引:1,自引:0,他引:1
This article shows the existence and asymptotic estimates of solutions of singularly perturbed boundary value problems for a class of third order nonlinear differential equations εx'" = f(t,x,x',ε), x(0) = A, x'(0) = x'(1), x"(0) = x"(1). 相似文献
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THE SINGULAR SECOND ORDER NONLINEAR EIGENVALUE PROBLEM WITH INFINITELY MANY POSITIVE SOLUTIONS 总被引:1,自引:0,他引:1
1 IntroductionIn this paper we consider positive solutions for second order non1ineareigenVaue problem of the fOrmwhere A > 0, a,P,7,b 2 0 and p = 7P a7 6cr > 0.Positive solutions of nonlinear eigenvalue problem such as (P) have beenstudied extensiveIy by many authors (see tll-[61 and the references therein).However, to my best knowledge, less attention has been given to infinitelymany positive solutions. It must be pointed out that in all existing literaturesconcerning multiple positiv… 相似文献
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Peng Shiguo 《Annals of Differential Equations》2005,21(2):192-197
In this paper, by utilizing a fixed point theorem on cone in Banach space, the author disscusses the periodic boundary value problem of second order differential systems. Some results on the existence of positive solutions are derived. 相似文献
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一类核密度含高阶奇性Cauchy型积分的边值定理 总被引:2,自引:0,他引:2
本文推广「1」,「6」中的结果,讨论了一类开口弧核密度含高阶奇且情形更一般的Cauchy型积分的边值定理,积分号下求导及H连续性。 相似文献
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In this paper,the F-equivariant (s,t)-equivalence relation and F-equivariant infinitesimally (r,s)-stability of F-equivariant bifurcation problem are defined. The criterion for F-equivariant infinitesimally (r, s)-stability is proven when F is a compact finite Lie group . Transversality condition is used to characterize the stability. 相似文献
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王同科 《高等学校计算数学学报(英文版)》2002,11(2):213-225
1 IntroductionFinitevolumeelementmethodorFVEMusesavolumeintegralformulationofthedif ferentialequationwithafinitepartitioningsetofvolumetodiscretizetheequation ,thenre strictstheadmissiblefunctionstoalinearfiniteelementspacetodiscretizethesolution ([1 -4 ] ) .… 相似文献
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二阶非线性边值问题解的存在唯一性定理 总被引:4,自引:0,他引:4
考虑方程y‘’+f(t,y,y‘)=0在边值条件y(a)=A,y(b)=B下解的存在唯一性,要求f满足L^2-Caratheodory条件,在L^2空间中利用映象原理得到解唯一存在的最优结果。 相似文献
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非线性三阶微分方程的四点边值问题 总被引:4,自引:0,他引:4
用上下解方法研究了三阶非线性微分方程四点边值问题u=f(t,u,u″),a≤t≤b,u(a)=u(a0),u′(a)-δu″(a)=A,u(b)=u(b0),{其中a<a0≤b0<b,δ≥0,A是给定常数.证明了f在适当条件下,上述边值问题有解的充要条件是存在一个下解α和上解β使得α(t)≤β(t),a≤t≤b. 相似文献
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Qingliu Yao 《Annals of Differential Equations》2014,(4):458-465
The existence of multiple positive solutions is studied for a nonlinear nonauto- nomous second-order boundary value problem with nonhomogeneous boundary con- ditions. In order to describe the growth behaviors of nonlinearity on some bounded sets, two height functions are introduced. By considering the integrals of the height functions and applying the Krasnosel'skii fixed point theorems on a cone, several new results are proved. 相似文献
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2p和2q阶联立微分方程组的正解性 总被引:1,自引:0,他引:1
利用锥上不动点指数理论研究2p,2q阶非线性高阶常微分方程组边值问题,通过相应的线性问题的第一特征值,建立了其正解的存在性与多解性定理.讨论了其参数$\lambda,\mu$对其正解存在性与多解性的影响,给出了利用特征值刻划的较为本质的结果.突破了以往文献要求方程组同阶和非线性项单调,在零点或无穷远点超线性或次线性增长的限制. 相似文献
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本文对可压缩流体力学高精度拉格朗日格式及其保正性质近年来的发展给出回顾与综述.文中分别介绍了一维、二维可压缩流体力学方程中心型拉格朗日格式的设计步骤,回顾了高精度拉格朗日格式以及高精度保正拉格朗日格式的研究进展. 相似文献