共查询到20条相似文献,搜索用时 109 毫秒
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赵丽琴 《数学物理学报(B辑英文版)》2007,(2)
In this article, the author studies the boundedness and convergence for the non-Lienard type differential equation (x|·)=a(y)-f(x) (y|·)=b(y)β(x)-g(x) e(t) where a(y),b(y),f(x),g(x),β(x) are real continuous functions in y∈R or x∈R,β(x)≥0 for all x and e(t) is a real continuous function on R = {t: t≥0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended. 相似文献
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Xiangxing Tao & Yunpin Wu 《分析论及其应用》2012,28(3):224-231
In this paper,the authors prove that the multilinear fractional integral operator T A 1,A 2 ,α and the relevant maximal operator M A 1,A 2 ,α with rough kernel are both bounded from L p (1 p ∞) to L q and from L p to L n/(n α),∞ with power weight,respectively,where T A 1,A 2 ,α (f)(x)=R n R m 1 (A 1 ;x,y)R m 2 (A 2 ;x,y) | x y | n α +m 1 +m 2 2 (x y) f (y)dy and M A 1,A 2 ,α (f)(x)=sup r0 1 r n α +m 1 +m 2 2 | x y | r 2 ∏ i=1 R m i (A i ;x,y)(x y) f (y) | dy,and 0 α n, ∈ L s (S n 1) (s ≥ 1) is a homogeneous function of degree zero in R n,A i is a function defined on R n and R m i (A i ;x,y) denotes the m i t h remainder of Taylor series of A i at x about y.More precisely,R m i (A i ;x,y)=A i (x) ∑ | γ | m i 1 γ ! D γ A i (y)(x y) r,where D γ (A i) ∈ BMO(R n) for | γ |=m i 1(m i 1),i=1,2. 相似文献
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We study positive solutions to the following higher order Schr¨odinger system with Dirichlet boundary conditions on a half space:(-△)α2 u(x)=uβ1(x)vγ1(x),in Rn+,(-)α2 v(x)=uβ2(x)vγ2(x),in Rn+,u=uxn==α2-1uxnα2-1=0,onRn+,v=vxn==α2-1vxnα2-1=0,onRn+,(0.1)whereαis any even number between 0 and n.This PDE system is closely related to the integral system u(x)=Rn+G(x,y)uβ1(y)vγ1(y)dy,v(x)=Rn+G(x,y)uβ2(y)vγ2(y)dy,(0.2)where G is the corresponding Green’s function on the half space.More precisely,we show that every solution to(0.2)satisfies(0.1),and we believe that the converse is also true.We establish a Liouville type theorem—the non-existence of positive solutions to(0.2)under a very weak condition that u and v are only locally integrable.Some new ideas are involved in the proof,which can be applied to a system of more equations. 相似文献
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Zong Xiju~ Zhao Yi~ Yin Zhaoyang~ Chi Tao~ Dept.of Math. Zhongshan Univ. Guangzhou China. First Middle School of Tengzhou Shandong China. School of Control Science Engineering Jinan Univ. Jinan China 《高校应用数学学报(英文版)》2007,(3)
In this paper,the boundary control problem of a distributed parameter system described by the Schrdinger equation posed on finite intervalα≤x≤β: iyt yxx |y|~2y=0, y(α,t)=h_`1(t),y(β,t)=h_2(t)for t>0(S) is considered.It is shown that by choosing appropriate control inputs(h_j),(j=1,2)one can always guide the system(S)from a given initial stateφ∈H~s(α,β),(s∈R)to a terminal stateΨ∈H~s(α,β),in the time period[0,T].The exact boundary controllability is obtained by considering a related initial value control problem of Schrdinger equation posed on the whole line R.The discovered smoothing properties of Schrdinger equation have played important roles in our approach;this may be the first step to prove the results on boundary controllability of(semi-linear)nonlinear Schrdinger equation. 相似文献
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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
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Let T:X → X be a transformation.For any x ∈[0,1) and r > 0,the recurrence time τr(x) of x under T in its r-neighborhood is defined as τr(x)=inf k 1:d (Tk(x),x) < r.For 0 αβ∞,let E(α,β) be the set of points with prescribed recurrence time as follows E (α,β)=x ∈ X:lim r→0 inf[log τr(x)/-log r]=α,lim r→0 sup[log τr(x)/-log r]=β.In this note,we consider the Gauss transformation T on [0,1),and determine the size of E (α,β) by showing that dim H E (α,β)=1 no matter what α and β are.This can be compared with Feng and Wu’s result [Nonlinearity,14 (2001),81-85] on the symbolic space. 相似文献
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刘德明 《数学物理学报(B辑英文版)》1991,(1)
In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x~2+α_2xy+α_5x~2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx~j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles. 相似文献
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The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2-norm of Mercer kernel matrices reproducing by the kernels K(α,β)(x,y):=∞∑k=0 C(α,β)k Qk(α,β)(x)Qk(α,β)(y),where Qα,βk(x) are the Jacobi polynomials of order k on (0, 1), Cα,βk > 0 are real numbers,and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by K(α,β)(x,y). 相似文献
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In this article, the author studies the boundedness and convergence for the {(x) = a(y) - f(x),(y) = b(y)β(x) - g(x) e(t),where a(y), b(y), f(x),g(x),β(x) are real continuous functions in y ∈ R or x ∈ R,β(x) ≥ 0 for all x and e(t) is a real continuous function on R = {t: t ≥ 0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended. 相似文献
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Let Q2 = [0, 1]2 be the unit square in two dimension Euclidean space R2. We study the Lp boundedness properties of the oscillatory integral operators Tα,β defined on the set S(R3) of Schwartz test functions f by Tα,βf(x,y,z) = Q2 f(x - t,y - s,z - tksj)e-it-β1s-β2t-1-α1s-1-α2dtds, where β1 > α1 0, β2 > α2 0 and (k, j) ∈ R2. As applications, we obtain some Lp boundedness results of rough singular integral operators on the product spaces. 相似文献
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We introduce two new linear differential operators which are invariant with respect to the unitary group SU(n). They constitute analogues of the twistor and the Rarita-Schwinger operator in the orthogonal case. The natural setting for doing this is Hermitian Clifford Analysis. Such operators are constructed by twisting the two versions of the Hermitian Dirac operator 6z_ and 6z_ and then projecting on irreducible modules for the unitary group. We then study some properties of their spaces of nullsolutions and we find a formulation of the Hermitian Rarita-Schwinger operators in terms of Hermitian monogenic polynomials. 相似文献
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Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions,i.e.,null solutions to a first order vector valued rotation invariant differential operator (θ) ca... 相似文献
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