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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(00)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.
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.
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.
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.
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.
STABILITY OF THE RAREFACTION WAVE FOR THE GENERALIZED KDV-BURGERS EQUATION   总被引:3,自引:2,他引:1  
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.
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.
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.
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   

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