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1.
ON L_p—CONVERGENCE OF GRUNWALD INTERPOLATION 总被引:3,自引:0,他引:3
In this paper,the L_p-convergence of Grünwald interpolation G_n(f,x)based on the zerosof Jacobi polynomials J~((α,β))_n(x)(-1<α,β<1)is considered.L_p-convergence(0
0)of G_n(f,x)is obtained for-1<α,β≤0.Therefore,the results of[1]and [3-5]are improved. 相似文献
2.
赵晓强 《应用数学学报(英文版)》1990,6(1):40-43
In this paper, we consider nonlinear and nonautonomous systems with the trivial solution:dx/dt=f(t, x), x∈R~nwhere f(t+ω,x)+f(t, x), f(t, 0)=0. By using the theory of Brouwer topological degree, we obtainthe existence theorem of nontrivial ω-periodic solution. Finally the applied example of the theoremis cited. 相似文献
3.
Liang Ruixi Peng Jun Shen Jianhua 《Annals of Differential Equations》2006,22(4):502-510
The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures. 相似文献
4.
ON THE EXISTENCE OF NONTRIVIAL PERIODIC SOLUTIONS OF DIFFERENTIAL DIFFERENCE EQUATIONS 总被引:1,自引:0,他引:1
Wang Ke 《数学年刊B辑(英文版)》1990,11(4):438-444
This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),y(t-1)).)Some new existence criteria are obtained. 相似文献
5.
韦忠礼 《应用数学学报(英文版)》1999,15(1):94-97
1.IntroductionTheexistenceanduniquenessofsolutionsofdelaydifferentialequationsinaBanachspacehavebeenstudiedbymanyauthors(see[1--4]).Inthispaper,weshallapplythefixedpoillttheoremstoinvestigatetheexistenceofpositivesolutionsofnonlinearneutraldifferentialdifferenceequationsinaBanachspace.LetRbethefieldofrealnumbers,andletR ={tERIt20},to>0,J=[to, co)'ConsiderthenonlinearneutraldifferentialdifferenceequationinaBanachspaceE.mI(x(t)~Zci(t)x(t~ri))' ZPj(t)fj(x(t~D))=0,(1)i=1j=1wherefiEC[P,PI,f… 相似文献
6.
This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equationRoughly speaking, under the assumption that u_ < u+, the solution u(x,t) to Cauchy problem (1) satisfying sup \u(x,t) -uR(x/t)| -0 as t - , where uR(x/t) is the rarefac-tion wave of the non- viscous Burgers equation ut + f(u)x=0 with Riemann initial data 相似文献
7.
1IntroductionConsidertheretardedLi6nard--typeequationwherehisanonnegativeconstant,fitfi,WandgarecontinuousfunctionsonR.Recently,theboundedness,stability,oscillationandperiodicityofsolutionsofwhichisEq.(1)withoutdelayandW(x)=0,hasbeenwidelyinvestigated(of[1-5]).Clearly,iffi(x)=f(x),f200=0,W(x)=0,Eq.(1)isreducedtothewell-knownretardedLi6nardequationIn1963,Krasovskii[6]gaveasufficientconditionoftheuniformasymptoticstabilityofthezerosolutionforEq.(3).Hisworkcausedmuchinterest,itisseenbythewor… 相似文献
8.
《计算数学(英文版)》1994,(1)
1.IntroductionConsiderthenonlinearVolterraintegraJequationofthesecondkindHere,u(x)isanunknownfunction,f(x)andK(x,t,u)aregivencontinuousfunctionsdefined,respectively,on[a,b1andD={(x,t,u):aSx5b,aSt5x)-oc相似文献
9.
陈永劭 《应用数学学报(英文版)》1989,5(3):234-241
In this paper, we consider the oscillation of the second order neutral delay differential equations[x(t) cx(t-τ)]" p(t)x(t-σ)=0 (1)and obtain some sufficient conditions of the oscillation of (1) for the case c≥0, -1≤c<0 and c<-1. 相似文献
10.
Chen Xiru 《数学年刊B辑(英文版)》1984,5(3):374-374
The assertion of Th.1 in[1]should be replaced bylimsup n→∞ a_nn~(k/(2k m)=∞.(A)Since the proof of Th.1 in[1]is somewhat in error,we give here a sketch ofproof of(A).Choose f∈C_ka with f(x)≥a>0 for ‖x‖≤ε>0,and define h_δ(x)=f(x) e_(kδ)(x),where e_(kδ)(x),as well as d and C_(kα)~(n)(d) to appear in the following,are thesame as in[1].Choose ■>0 so that h_δ∈C_(kα) for δ∈(0,■).For each δ in(0,■),thereexists an integer n such that h_δ∈C_(kα)~(n)(d).Hence an integer N can be found such that 相似文献