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1.
We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II1. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues
and eigenfunctions of the problems asm→−0.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999. 相似文献
2.
L. Berrahmoune 《Rendiconti del Circolo Matematico di Palermo》1999,48(1):111-122
Let Ω be a bounded open domain in ℝ
N
,A an unbounded, selfadjoint, positive and coercive linear operator onL
2 (Ω). We consider feedback stabilization for the distributed bilinear control systemy″(t)+Ay(t)+Dy′(t)+u(t)By(t)=0, whereD andB are linear bounded operators fromL
2(Ω) toL
2(Ω). Under suitable assumptions onB andD, a nonlinear feedback ensuring uniform exponential decay of solutions is given. Various applications to vibrating processes
are presented. 相似文献
3.
Ludvik Janos 《Annali di Matematica Pura ed Applicata》1977,112(1):273-283
Summary We consider the boundary value problem αz″(x)+m(x)y(x)=0, αy″(x)+p(x)z(x)=0, xε[0, 1], y(0)=y(1)=z(0)=0, where the functions m(x) and p(x) are assumed integrable and positive everywhere in [0, 1]. As the main result we obtain the inequalities
for n=1, 2, ... where δn(m, p) stands for the product
of the first n eigenvalues αi(m, p) of the above system and where δn(m) abbreviates δn(m, m).
Entrata in Redazione il 6 febbraio 1976. 相似文献
4.
E. G. Goluzina 《Journal of Mathematical Sciences》1996,79(5):1304-1307
We study the structural properties of the class Mk,λ,b(k≥2, 0≤λ≤1, b∈ℂ\{0}) of functions f(z)=z+ ... which are regular in |z|<1 and satisfy the conditions f(z)f′(z)z−1≠0 and
, where J(z)=λ(1+b−1zf″(z)/f′(z)+(1−λ)(b−1zf′(z)/f(z)+1−b−1). The value regions of some functionals on this class are found. The case λ=1 was considered in our previous paper. Bibliography:
4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 55–60.
Translated by O. A. Ivanov. 相似文献
5.
A property of a continuous functionf(x), x ∈ E
2, similar to the classical intermediate value property is established. Namely, let a Jordan compactJ ⊂ E
2 be the domain of definition off. Then, for each parametrizationx(t), 0≦t≦T,x(0)=x(T), of the boundary Fr(J) ofJ there exists a unique real λ and a unique connected component Φ of the level set {x ∈ J: f(x)=λ} with the following property: any connected subset Ω ofJ containing “opposite” points of Fr(J) (i.e. pointsx(t′) andx(t″) such thatt″−t′=T/2) has a common element with Φ. 相似文献
6.
Criterion of periodicity of solutions of a certain differential equation with a periodic coefficient
F. Neuman 《Annali di Matematica Pura ed Applicata》1967,75(1):385-396
Summary In this paper the differential equation (1) y″=q(t)y is considered where q(t) is a real continuous function with period π.
There is proved a necessary and sufficient condition for the stability of the trivial solution of Equation (1) when the zeros
of the characteristic equation λ2 - Aλ+1=0, coincide. Moreover, there is shown the construction of all Equations (1) admitting only periodic or half-periodic
solutions with period π. 相似文献
7.
On the Isolated Points of the Spectrum of Paranormal Operators 总被引:1,自引:0,他引:1
Atsushi Uchiyama 《Integral Equations and Operator Theory》2006,55(1):145-151
For paranormal operator T on a separable complex Hilbert space
we show that (1) Weyl’s theorem holds for T, i.e., σ(T) \ w(T) = π00(T) and (2) every Riesz idempotent E with respect to a non-zero isolated point λ of σ(T) is self-adjoint (i.e., it is an orthogonal projection) and satisfies that ranE = ker(T − λ) = ker(T − λ)*. 相似文献
8.
Giovanni Sansone 《Annali di Matematica Pura ed Applicata》1960,50(1):439-465
Sunto Premesso un risultato inedito delDini sulle soluzioni olomorfe dell’equazione xy″+y′=sin y in un intorno di x=0, si studiano gli integrali della medesima equazione nel campo reale, ed in particolare il loro comportamento per x→∞.
Ad Antonio Signorini nel suo 70mo compleanno. 相似文献
9.
Let A denote the class of functions which are analytic in |z|<1 and normalized so that f(0)=0 and f′(0)=1, and let R(α, β)⊂A
be the class of functions f such thatRe[f′(z)+αzf″(z)]>β,Re α>0, β<1. We determine conditions under which (i) f ∈ R(α1, β1), g ∈ R(α2, β2) implies that the convolution f×g of f and g is convex; (ii) f ∈ R(0, β1), g ∈ R(0, β2) implies that f×g is starlike; (iii) f≠A such that f′(z)[f(z)/z]μ-1 ≺ 1 + λz, μ>0, 0<λ<1, is starlike, and (iv) f≠A such that f′(z)+αzf″(z) ≺ 1 + λz, α>0, δ>0, is convex or starlike. Bibliography:
16 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 138–154. 相似文献
10.
Let M be a manifold with boundary δM≠Ф. Let A be a second-order elliptic partial differential operator given on M. Denote
by Rλ(x, y), x, y∈M, λε
\σ(A) the Schwartz kernel of (A−λI)−1. Consider the Gel'fand inverse boundary problem of the reconstruction of (M, A) via a given Rλ(x, y), x, y∈δM,λε
. We prove that if the principal symbol of A satisfies some geometric condition (the Bardos-Lebeau-Rauch condition), then
these data determine M uniquely, and they determine A to within the group of generalized gauge transformation on M. The above-mentioned
geometric condition means, roughly speaking, that any geodesic (in the metric generated by A) leaves M. Bibliography: 29 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 161–190.
Translated by Ya. Kurylev. 相似文献
11.
Aissa Guesmia 《Israel Journal of Mathematics》2001,125(1):83-92
We consider in this paper the evolution systemy″−Ay=0, whereA =∂
i(aij∂j) anda
ij ∈C
1 (ℝ+;W
1,∞ (Ω)) ∩W
1,∞ (Ω × ℝ+), with initial data given by (y
0,y
1) ∈L
2(Ω) ×H
−1 (Ω) and the nonhomogeneous conditiony=v on Γ ×]0,T[. Exact controllability means that there exist a timeT>0 and a controlv such thaty(T, v)=y′(T, v)=0. The main result of this paper is to prove that the above system is exactly controllable whenT is “sufficiently large”. Moreover, we obtain sharper estimates onT. 相似文献
12.
Adrian Constantin 《Annali dell'Universita di Ferrara》1995,41(1):1-4
LetH be a complex Hilbert space and letB be the space of all bounded linear operators fromH intoH with the strong operator topology. We will give a boundedness result for the solutions of the differential equationx′=A(t)x+f(t,x) whereA: I=[t
0, ∞)→B is continuous,f: I×H→H is also continuous and for every bounded setS⊂I×H there exists a constantM(S)>0 such that |f(t,x)−f(t,y)|≤M(S)|x−y|,(t,x), (t,y)∈S.
Sunto SiaH uno spazio di Hilbert complesso e siaB lo spazio degli operatori lineari limitati daH inH, con la topologia forte. In questo lavoro si prova un risultato di limitatezza per le soluzioni dell'equazione differenzialex′=A(t)x+f(t,x), doveA: I=[t 0, ∞)→B è continua,f: I×H→H è continua e per ogni insieme limitatoS⊂I×H esiste una costanteM(S)>0 tale che |f(t,x)−f(t,y)|≤M(S)|x−y| per ogni(t,x), (t,y)∈S.相似文献
13.
Sunto. L'Autore studia il problema ai limiti per l'equazioney
(n)
=λf(x, y, y′, ... y
(n−1)
) e da teoremi che assicurano l'esistenza e l'unicità di un valore
del parametroλ e di una soluzione dell'equazione in corrispondenza al
, soddisfacente a condizioni atte ad individuare un polinomio di gradon.
Lavoro pervenuto in redaziane il 30 settembre 1947.
Il presente lavoro costituisce la parte essenziale della mia tesi di licenza alla Scuola Normale Superiore di Pisa, discussa
nel giugno 1947. 相似文献
14.
L. Erbe 《Annali di Matematica Pura ed Applicata》1972,94(1):257-268
Summary Various sufficient conditions are obtained which guarantee that all continuable solutions of (1.1) y″+q(t)y′+p(t)f(y)=0 are
oscillatory. No explicit sign assumptions are made on p(t) although certain integral conditions are assumed to hold with regard
to f(y), p(t) and q(t). Examples are given of the form p(t) = λ/tμ + (βsint)/tα, λ, β, μ, α>0.
This research was supported by NRC Grant A-7673 and CMC Summer Research Grant.
Entrata in Redazione il 4 settembre 1971. 相似文献
15.
Angelo Tonolo 《Annali di Matematica Pura ed Applicata》1960,50(1):127-133
Sunto Per la funzione reale del punto P(x, y): F[ξ(P), η(P)], ove u=ξ(P), v=η(P) sono implicitamente definite nel campo reale dal
sistema delle due equazioni u−x+ϕ(u, v)=0, v−y+φ(u, v)=0 si dà uno sviluppo che estende quello ottenuto dalLevi-Civita per la funzione F[y(x)], ove y(x) è definita dalla equazione y−x+ϕ(y)=0.
Ad Antonio Signorini nel suo 70mo compleanno. 相似文献
16.
S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
17.
We prove the existence of a classical weak solution for the 2-D incompressible Euler equations with initial vorticity ω0=ω
0
′
+ ω
0
″
, where ω
0
′
is inL
1(R
2)⌢H
−1(R
2), compactly supported, and ω
0
″
is a compactly supported positive Radon measure inH
−1(R
2). 相似文献
18.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
19.
We study a system(D)x′=F(t,x
t) of functional differential equations, together with a scalar equation(S)x′=−a(t)f(x)+b(t)g(x(t−h)) as well as perturbed forms. A Liapunov functional is constructed which has a derivative of a nature that has been widely
discussed in the literature. On the basis of this example we prove results for (D) on asymptotic stability and equi-boundedness.
Supported in part by NSF of China, Key Project # 19331060 相似文献
20.
We explore connections between Krein's spectral shift function ζ(λ,H
0, H) associated with the pair of self-adjoint operators (H
0, H),H=H
0+V, in a Hilbert spaceH and the recently introduced concept of a spectral shift operator Ξ(J+K
*(H
0−λ−i0)−1
K) associated with the operator-valued Herglotz functionJ+K
*(H
0−z)−1
K, Im(z)>0 inH, whereV=KJK
* andJ=sgn(V). Our principal results include a new representation for ζ(λ,H
0,H) in terms of an averaged index for the Fredholm pair of self-adjoint spectral projections (E
J+A(λ)+tB(λ)(−∞, 0)),E
J((−∞, 0))), ℝ, whereA(λ)=Re(K
*(H
0−λ−i0−1
K),B(λ)=Im(K
*(H
0−λ-i0)−1
K) a.e. Moreover, introducing the new concept of a trindex for a pair of operators (A, P) inH, whereA is bounded andP is an orthogonal projection, we prove that ζ(λ,H
0, H) coincides with the trindex associated with the pair (Ξ(J+K
*(H
0−λ−i0)K), Ξ(J)). In addition, we discuss a variant of the Birman-Krein formula relating the trindex of a pair of Ξ operators and the Fredholm
determinant of the abstract scattering matrix.
We also provide a generalization of the classical Birman—Schwinger principle, replacing the traditional eigenvalue counting
functions by appropriate spectral shift functions. 相似文献