首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 15 毫秒
1.
§1Introduction ConsidertheHamilton-Jacobi-Bellmanequation max1≤v≤m[A(v)u(x)-f(v)(x)]=0,x∈Ω(1.1)withtheboundarycondition u(x)=0,x∈Ω(1.2)whereΩisabounded,smoothdomaininEuclideanspaceRd,d∈N;f(v)(x)aregiven functionsfromC2(Ω);A(v)aresecond-orderuniformlyellipticoperatorsoftheform A(v)=-d i,j=1a(v)ij2xixj+di=1b(v)ixi+c(v).(1.3)Intheaboveexpression(1.3)therearecoefficientsa(v)ij,b(v)i,c(v)∈C2(Ω)satisfying,forall1≤v≤m,a(v)ij(x)=a(v)ji(x),1≤i,j≤d,c(v)≥c0≥0,x∈Ω,a…  相似文献   

2.
In this note we prove the large deviation principle for the following process in R:dxt = b(xt, t)dt edwt, t E [0, 1], (1)where the initial point xo is fixed, wt is a Wiener process5 E > 0 is a small parameter whichtends to 0, b(x, t) is a bounded piecewise Lipschitz function of the form(b (x, t), x > 0t,b(xlt)={b--(::t)i x<0jf (2)where e is a smooth curve, bf are two bounded Lipschitz functions on (--oo, co) x [0, oo)satisfyingb--(0t, t) 2 b (0t, t). (3)If (3) is replaced with an opposite …  相似文献   

3.
1°在文献[1]中D.Bourgin与R.Duffin研究了絃振动方程在矩形区域上可适定的狄里赫利问题,他们指出对于问题:若设(i)a=T/s为K阶代数无理数,(ii)φ(x),φ_1(x)∈C~(K+4)[0≤x≤s],ψ(t),ψ_1(t)∈C~(K+4)[0≤t≤T],φ(0)=φ(s)=φ_1(0)=φ_1(s)=ψ(T)=ψ_1(0)=ψ_1(T)=0,则定解问题(A)存在唯一解y(x,t)∈C~2[0≤x≤s,0≤t≤T]。他们的结果系利用代数数论中Liouville定理。由于Liouville定理已被Roth在1955年改进成最佳形式,  相似文献   

4.
1 IntroductionLetΩ be a bounded domain in Rn and Ω be its boundary.ThenΣ =Ω× ( 0 ,1 ) is abounded domain in Rn+1 .We consider the following backwad problem of a prabolic equa-tion: u t= ni,j=1 xiaij( x) u xj -c( x) u,   ( x,t)∈Σ,( 1 )u| Ω× [0 ,1 ] =0 , ( 2 )u| t=1 =g( x) . ( 3 )   Where { aij( x) } are smooth functions given onΩ satisfyingaij( x) =aji( x) ,   1≤ i,j≤ n, ( 4)α0 ni=1ζ2i ≤ ni,j=1aij( x)ζiζj≤α1 ni=1ζ2i,   ζ∈ Rn,x∈Ω. ( 5)  Where0 <α…  相似文献   

5.
1.AContinuousProblemWeconsiderthefOllowingsingularlyperturbedboundaryvalueprob1em:whereEisasmallpositiveparameter.WeassumethatAccordingto[2],wecanproveLemma1.Suppo8ethatcondition(2)ls8atisfied.Therecxistsaunique8olutionuEC'(I)topro5lem(1),andthefOllowingrepresentationholds:u(x)=uo(x) Vo(x) Vl(x),whereVo(x)=atexp(-ry-),Vl(x)=Mexp(-ryap),andIu8t)(x)ISM,i=O,1,'',6,xEI(ThroughoutthepaperMdenotesanyconstantindePendentOfE).Theproofofthefollowinglemmaisbasedonthemonotonicityof(l),andcanb…  相似文献   

6.
1.IntroductionInthispaper,weareconcernedwiththebehaviorofsolutionsofthefollowingproblemwheretheinitialdata"o(x)satisfiesnoEW"oo(a,b)and"o(x)20a.e.in(a,6).(1.4)Definition1.AnonnegativefunctionuELoo([0,co);W'loo(n))withfi=(a,b)iscalledaweaksolutionoftheproblem(1.1)--(1.3)ifthefollowingconditionsarefulfilled:(i)acEL'(flx[0,F])foranyT>0,(n)usatisfiestheX..d.yvaluecondition(l.2)intheusualsense.(iii)FOranytestfunctiongbEC2)1(fix[0, co))withgb(a,t)~op(b,t)~0,thereholdstheintegralequalityRecellt…  相似文献   

7.
In this paper the author discusses the following first order functional differentialequations: x'(t) +integral from n=a to b p(t, ξ)x[g(t, ξ)]dσ(ξ)=0, (1) x'(t) +integral from n=a to b f(t, ξ, x[g(t, ξ)])dσ(ξ)=0. (2)Some suffcient conditions of oscillation and nonoseillafion are obtained, and two asymptolioproperties and their criteria are given. These criferia are better than those in [1, 2], and canbe used to the following equations: x'(t) + sum from i=1 to n p_i(t)x[g_i(t)] =0, (3) x'(t) + sum from i=1 to n f_i(t, x[g_i(t)] =0. (4)  相似文献   

8.
By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equation a(t)x"+F(x,x′)x′+g(x)=e(t),x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C1[0,2π],a(t)>0(0≤t≤2π),a(0)=a(2π),F(x,y)=f(x)+α| y|β,α>0,β>0 are all constants,f∈C(R,R),e∈C[0,2π]. An example is given as an application.  相似文献   

9.
该文考虑多滞量和正负系数中立型方程[x(t)-sum from n=1 to l(1/n)C_A(t)x(t-r_n)] sum from i=1 to (1/i)P_i(t)x()t-τ_i)-sum from j=1 to n(1/j)Q_j(t)x(t-σ_j)=0,其中C_A(k=1,…,l),P_i(i=1,…,m),Q_j(j=1…,n)∈C([to,∞co),R~ ),0≤τ_l<…<τ_m,0≤σ_1<…<σ_n,0相似文献   

10.
设对每一正数t, E(t)和A(t)是不相交事件,分别以J_1(t),J_2(t),J_2(t)记E(t)A(t),E(t)UA(t),以J(t,L)记(?)J_l(t),其中L(?){1,2,3}。如果对任意的00}是(?)再生现象,(p(t),a(t))是对应的P-a对,其中p(t):=P(E(t)),a(t):=P(A(t))设(?)p(t)=1 则(p(t),a(t))是p-a对当且仅当存在Markov转移函数P_t(·,·),标准状态x,可测集B,x(?)B,使P(t)=P_t,(x,{x}),a(t)=P_t(x,B);当且仅当a(t)连续,p(t)是p函数(设有典型测度μ),存在可测函数g(s)满足0≤g(s)≤μ(s,∞]和a(t)=integral from n=0 to t(p(t-s)g(s)ds).p-a对的积和极限仍为p-a对.给出p-a对为有限可分解和为不可分解的充分条件.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号