共查询到20条相似文献,搜索用时 31 毫秒
1.
T. I. Seidman 《Israel Journal of Mathematics》1969,7(3):249-253
Forλεσ(A) (A a bounded linear operator on a Hilbert space) withλ a boundary point of the numerical range, the ‘spectral theory’ forλ is ‘just as ifA were normal’. IfA isnormal-like (the smallest disk containingσ(A) has radiusr=inf
z
‖A − z‖), then also sup {‖Ax‖2 − |〈x.Ax〉|2:‖x‖=1}=r
2.
This research was partially supported by Air Force Contract AF-AFOSR-62-414. 相似文献
2.
Tamar Burak 《Israel Journal of Mathematics》1972,12(1):79-93
Let A be the closed unbounded operator inL
p(G) that is associated with an elliptic boundary value problem for a bounded domainG. We prove the existence of a spectral projectionE determined by the set Γ = {λ;θ
1≦argλ≦θ
2} and show thatAE is the infinitesimal generator of an analytic semigroup provided that the following conditions hold: 1<p<∞; the boundary
ϖΓ of Γ is contained in the resolvent setp(A) ofA;π/2≦θ<θ
2≦3π/2 ; and there exists a constantc such that (I)││(λ-A)-1││≦c/│λ│ for λ∈ϖΓ. The following consequence is obtained: Suppose that there exist constantsM andc such that λ∈p(A) and estimate (I) holds provided that |λ|≧M and Re λ=0. Then there exist bounded projectionE
− andE
+ such thatA is completely reduced by the direct sum decompositionL
p(G)=E−Lp (G) ⊕E+Lp (G) and each of the operatorsAE
− and—AE
+ is the infinitestimal generator of an analytic semigroup. 相似文献
3.
B. de Malafosse 《Acta Mathematica Hungarica》2009,122(3):217-230
We deal with the sum of sequence spaces. Then we apply these results to characterize matrix transformations mapping between
s
h,l
(λ, μ) = s
α
0((Δ − λI)
h
) + s
β
(c)((Δ − μI)
l
) and s
γ
. Among other things the aim of this paper is to reduce the set (s
h,l
(λ, μ), s
γ
to a set of the form S
τ,γ
.
相似文献
4.
Franz Kinzl 《Semigroup Forum》1989,38(1):105-118
Let S be a locally compact semigroup. We study the sequence (λn) of the convolution powers of a probability measure λ on S and their shifts by a probability measure η on S. We shall give
sufficient conditions for lim ‖λn−η*λn‖ = 0 (where ‖.‖ denotes the norm). In particular we consider the case the η is a point measure and we study the subsemigroup
LO(λ) = {x ∈ S : lim ‖λn−δX*λn‖ = 0}. We shall give necessary and sufficient conditions for Lo(λ)=S. In this case we want to treat the problem of the convergence of the sequence (λn). 相似文献
5.
If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ(λ^2 + λB + A)^-1‖ and ‖B(λ^2 + λB + A)^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0. 相似文献
6.
Abstract. It is proved that the semilinear elliptic problem with zero boundary value 相似文献
7.
Meng Wang 《数学学报(英文版)》2012,28(1):145-170
We study the self-dual Chern-Simons Higgs equation on a compact Riemann surface with the Neumann boundary condition.In the previous paper,we show that the Chern-Simons Higgs equation with parameter λ0 has at least two solutions(uλ1,uλ2) for λ sufficiently large,which satisfy that uλ1→u0 almost everywhere as λ→∞,and that uλ2→∞ almost everywhere as λ→∞,where u 0 is a(negative) Green function on M.In this paper,we study the asymptotic behavior of the solutions as λ→∞,and prove that uλ2-uλ2 converges to a solution of the Kazdan-Warner equation if the geodesic curvature of the boundary M is negative,or the geodesic curvature is nonpositive and the Gauss curvature is negative where the geodesic curvature is zero. 相似文献
8.
Evangelos A. Latos Dimitrios E. Tzanetis 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(2):137-151
We investigate the behaviour of solution u = u(x, t; λ) at λ = λ* for the non-local porous medium equation ${u_t = (u^n)_{xx} + {\lambda}f(u)/({\int_{-1}^1} f(u){\rm d}x)^2}We investigate the behaviour of solution u = u(x, t; λ) at λ = λ* for the non-local porous medium equation ut = (un)xx + lf(u)/(ò-11 f(u)dx)2{u_t = (u^n)_{xx} + {\lambda}f(u)/({\int_{-1}^1} f(u){\rm d}x)^2} with Dirichlet boundary conditions and positive initial data. The function f satisfies: f(s),−f ′ (s) > 0 for s ≥ 0 and s
n-1
f(s) is integrable at infinity. Due to the conditions on f, there exists a critical value of parameter λ, say λ*, such that for λ > λ* the solution u = u(x, t; λ) blows up globally in finite time, while for λ ≥ λ* the corresponding steady-state problem does not have any solution.
For 0 < λ < λ* there exists a unique steady-state solution w = w(x; λ) while u = u(x, t; λ) is global in time and converges to w as t → ∞. Here we show the global grow-up of critical solution u* = u(x, t; λ*) (u* (x, t) → ∞, as t → ∞ for all x ? (-1,1){x\in(-1,1)}. 相似文献
9.
Let (v,u×c,λ)-splitting BIBD denote a (v,u×c,λ)-splitting balanced incomplete block design of order v with block size u×c and index λ. Necessary conditions for the existence of a (v,u×c,λ)-splitting BIBD are v≥uc, λ(v−1)≡0 (mod c(u−1)) and λ
v(v−1)≡0 (mod (c
2
u(u−1))). We show in this paper that the necessary conditions for the existence of a (v,3×3,λ)-splitting BIBD are also sufficient with possible exceptions when (1) (v,λ)∈{(55,1),(39,9k):k=1,2,…}, (2) λ≡0 (mod 54) and v≡0 (mod 2). We also show that there exists a (v,3×4,1)-splitting BIBD when v≡1 (mod 96). As its application, we obtain a new infinite class of optimal 4-splitting authentication codes. 相似文献
10.
We consider the nonlinear eigenvalue problem −Δu=λ f(u) in Ω u=0 on ∂Ω, where Ω is a ball or an annulus in RN (N ≥ 2) and λ > 0 is a parameter. It is known that if λ >> 1, then the corresponding positive solution uλ develops boundary layers under some conditions on f. We establish the asymptotic formulas for the slope of the boundary layers of uλ with the exact second term and the ‘optimal’ estimate of the third term. 相似文献
11.
Cristinel Mortici 《Czechoslovak Mathematical Journal》2006,56(2):689-695
Let T be a λ-contraction on a Banach space Y and let S be an almost λ-contraction, i.e. sum of an (ε, λ)-contraction with a continuous, bounded function which is less than ε in norm. According to the contraction principle, there is a unique element u in Y for which u = Tu: If moreover there exists v in Y with v = Sv, then we will give estimates for ‖u−v‖. Finally, we establish some inequalities related to the Cauchy problem. 相似文献
12.
Yu. M. Arlinskii 《Mathematical Notes》1997,61(5):537-546
Suppose thats[u, v] is a closed sesquilinear sectorial form with vertex at zero, half-angle α ∈ [0, π/2), and dense domainD(s) in a Hilbert spaceH, S is them-sectorial operator associated withs, S
R is the real part ofS, andT(t)=exp(−tS) is the contraction semigroup with generator −S, holomorphic in the sector |argt|<π/2−α. We characterizes in terms ofT(t). In particular, we prove that the following conditions a`2) the function ‖T(t)u‖ is differentiable at zero; 3) the function (T(t)u, u) is differentiable at zero.
Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 643–654, May, 1997.
Translated by V. E. Nazaikinskii 相似文献
13.
Kwang C. Shin 《Potential Analysis》2011,35(2):145-174
For integers m ≥ 3 and 1 ≤ ℓ ≤ m − 1, we study the eigenvalue problems − u
″(z) + [( − 1)ℓ(iz)
m
− P(iz)]u(z) = λu(z) with the boundary conditions that u(z) decays to zero as z tends to infinity along the rays
argz=-\fracp2±\frac(l+1)pm+2\arg z=-\frac{\pi}{2}\pm \frac{(\ell+1)\pi}{m+2} in the complex plane, where P is a polynomial of degree at most m − 1. We provide asymptotic expansions of the eigenvalues λ
n
. Then we show that if the eigenvalue problem is PT\mathcal{PT}-symmetric, then the eigenvalues are all real and positive with at most finitely many exceptions. Moreover, we show that when
gcd(m,l)=1\gcd(m,\ell)=1, the eigenvalue problem has infinitely many real eigenvalues if and only if one of its translations or itself is PT\mathcal{PT}-symmetric. Also, we will prove some other interesting direct and inverse spectral results. 相似文献
14.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |
15.
Let Φ(u × v, k, λ
a
, λ
c
) denote the largest possible size among all 2-D (u × v, k, λ
a
, λ
c
)-OOCs. In this paper, the exact value of Φ(u × v, k, λ
a
, k − 1) for λ
a
= k − 1 and k is determined. The case λ
a
= k − 1 is a generalization of a result in Yang (Inform Process Lett 40:85–87, 1991) which deals with one dimensional OOCs namely, u = 1. 相似文献
16.
For the equation K(t)u
xx
+ u
tt
− b
2
K(t)u = 0 in the rectangular domain D = “(x, t)‖ 0 < x < 1, −α < t < β”, where K(t) = (sgnt)|t|
m
, m > 0, and b > 0, α > 0, and β > 0 are given real numbers, we use the spectral method to obtain necessary and sufficient conditions for the unique solvability
of the boundary value problem u(0, t) = u(1, t), u
x
(0, t) = u
x
(1, t), −α ≤ t ≤ β, u(x, β) = φ(x), u(x,−α) = ψ(x), 0 ≤ x ≤ 1. 相似文献
17.
In this paper, we consider the global existence, uniqueness and L
∞ estimates of weak solutions to quasilinear parabolic equation of m-Laplacian type u
t
− div(|∇u|
m−2∇u) = u|u|
β−1 ∫Ω |u|
α
dx in Ω × (0,∞) with zero Dirichlet boundary condition in tdΩ. Further, we obtain the L
∞ estimate of the solution u(t) and ∇u(t) for t > 0 with the initial data u
0 ∈ L
q
(Ω) (q > 1), and the case α + β < m − 1. 相似文献
18.
E is a Banach lattice that is weakly sequentially complete and has a weak unitu. TLf
n=ϕ means that the infimum of |f
n−ϕ| andu converges strongly to zero.T is a positive contraction operator onE andA
n=(1/n)(I+T+...+T
n−1). Without an additional assumption onE, the “truncated limit” TLA
nf need not exist forf inE. This limit exists for eachf ifE satisfies the following additional assumption (C): For everyf inE
+ and for every numberα>0, there is a numberβ=β(f, α) such that ifg is inE
+, ‖g‖≦1, 0≦f′≦f and ‖f′‖>α then ‖f′+g‖≧‖g‖+β.
Research of this author is partially supported by NSERC Grant A3974.
Research of this author is partially supported by NSF Grant 8301619. 相似文献
19.
Jean-René Licois 《Journal d'Analyse Mathématique》1995,66(1):1-36
LetM be a compact riemannian manifold,h an odd function such thath(r)/r is non-decreasing with limit 0 at 0. Letf(r)=h(r)-γr and assume there exist non-negative constantsA andB and a realp>1 such thatf(r)>Ar
P-B. We prove that any non-negative solutionu ofu
tt+Δgu=f(u) onM x ℝ+ satisfying Dirichlet or Neumann boundary conditions on ϖM converges to a (stationary) solution of Δ
g
Φ=f(Φ) onM with exponential decay of ‖u-Φ‖C
2(M). For solutions with non-constant sign, we prove an homogenisation result for sufficiently small λ; further, we show that
for every λ the map (u(0,·),u
t(0,·))→(u(t,·), u
t(t,·)) defines a dynamical system onW
1/2(M)⊂C(M)×L
2(M) which possesses a compact maximal attractor.
相似文献
20.
Alain Haraux 《Journal d'Analyse Mathématique》2005,95(1):297-321
IfA=A
*≥0 on the real Hilbert spaceH=L
2
(Ω, dμ) withKerA=A
−1
({0})∈0, (I+A)−1 compact andf(u)=c|u|
p−1
u withc>0,p>1, the solutions ofu”+u’+Au+f(u)=0 tend to 0 in norm at least liket
−1/(p−1)
ast→∞. Here it is shown that the set of initial data of those solutions tending to 0 exponentially fast has near 0 the structure
of a manifold with codimension dim(Ker A). If, in addition,A=−Δ with Neumann homogeneous boundary conditions, we show that the following alternative holds true: eitheru(t) tends to 0 exponentially fast, or ‖u(t)‖≥γt
−1/(p−1) with γ>0 fort≥1. 相似文献