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1.
 Let Y=(X,{R i }0≤i≤D) denote a symmetric association scheme with D≥3, and assume Y is not an ordinary cycle. Suppose Y is bipartite P-polynomial with respect to the given ordering A 0, A 1,…, A D of the associate matrices, and Q-polynomial with respect to the ordering E 0, E 1,…,E D of the primitive idempotents. Then the eigenvalues and dual eigenvalues satisfy exactly one of (i)–(iv). (i)
(ii) D is even, and
(iii) θ* 0>θ0, and
(iv) θ* 0>θ0, D is odd, and
Received: February 13, 1996 / Revised: October 16, 1996  相似文献   

2.
   Abstract. This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat equation (with Dirichlet boundary conditions in the bounded domain D ⊂ R d and multiplicative noise):
and for the corresponding backward dual equation:
We prove the null controllability of the backward equation and obtain partial results for the controllability of the forward equation. \par  相似文献   

3.
Let Ω ⊂ ℝ n be a smooth, bounded domain. We study the existence and regularity of diffeomorphisms of Ω satisfying the volume form equation
f*(g)=f,     \textin W, \phi^\ast(g)=f, \quad \text{in }\Omega,  相似文献   

4.
Letr, s ∈ [0, 1], and letX be a Banach space satisfying theM(r, s)-inequality, that is,
where π X is the canonical projection fromX *** ontoX *. We show some examples of Banach spaces not containingc 0, having the point of continuity property and satisfying the above inequality forr not necessarily equal to one. On the other hand, we prove that a Banach spaceX satisfying the above inequality fors=1 admits an equivalent locally uniformly rotund norm whose dual norm is also locally uniformly rotund. If, in addition,X satisfies
wheneveru *,v * ∈X * with ‖u *‖≤‖v *‖ and (x α * ) is a bounded weak* null net inX *, thenX can be renormed to satisfy the,M(r, 1) and theM(1, s)-inequality such thatX * has the weak* asymptotic-norming property I with respect toB X .  相似文献   

5.
Let Ω be a bounded open subset of ℝ n , n > 2. In Ω we deduce the global differentiability result
for the solutions u ∈ H 1 (Ω, ℝ n ) of the Dirichlet problem
with controlled growth and nonlinearity q = 2. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.  相似文献   

6.
In ℝ m ×ℝ n−m , endowed with coordinates x=(x′,x″), we consider bounded solutions of the PDE
We prove a geometric inequality, from which a symmetry result follows.   相似文献   

7.
Let
I m is the identity matrix of order m. Let W(λ) be an entire matrix valued function of order 2m, W(0) = I 2m , the values of W(λ) are j mm -unitary at the imaginary axis and strictly j mm -expansive in the open right half-plane. The blocks of order m of the matrix W(λ) with appropriate signs are treated as coefficients of algebraic Riccati equation. It is proved that for any λ with positive real part this equation has a unique contractive solution θ(λ). The matrix valued function θ(λ) can be represented in a form θ(λ) = θ A (iλ) where θ A (μ) is the characteristic function of some maximal dissipative operator A. This operator is in a natural way constructed starting from the Hamiltonian system of the form
with periodic coefficients.  相似文献   

8.
Let Ω be an open bounded domain in ℝN(N ≥ 3) and . We are concerned with two kinds of critical elliptic problems. The first one is
(*)
where 0 ∈ Ω, , 2 < m < 2* and λ > 0. By using the fountain theorem and concentration estimates, if N ≥ 7 and θ > 0, we establish the existence of infinitely many solutions for the following regularization of (*) with small number ϵ > 0
Then if θ > 0 is suitably small, we obtain many solutions for problem (*) by taking the process of approximation. The second problem is
where q ∈ (0, 1), t > 0. By using similar methods as in (*), we prove that if N ≥ 7, and t > 0, there exist infinitely many solutions with positive energy. In particular, we give a positive answer to one open problem proposed by Ambrosetti, Brezis and Cerami [1].  相似文献   

9.
We prove regularity results for solutions of some nonlinear Dirichlet problems for an equation in the form
where Ω is a bounded open subset of , N  ≥  2, α, θ and p are real constants such that: α  >  0, 0  ≤  θ  ≤  1 and 1  <  p  <  N. A limit case is also considered.   相似文献   

10.
In this paper, we consider the discrete nonlinear delay population model exhibiting the Allee effect
((*))
where a, b and c are constants and p, q and τ are positive integers. First, we study the local stability of the equilibrium points. Next, we establish some oscillation results of nonlinear delay difference equations with positive and negative coefficients and apply them to investigate the oscillatory character of all positive solutions of equation (*) about the positive steady state x * and prove that every nonoscillatory solution tends to x *.   相似文献   

11.
The Cauchy problem for a semilinear hyperbolic system of the type
is considered, with each matrix function A k being diagonal, bounded and locally Lipschitz in x. Discrete models for the Boltzmann equation furnish examples of such systems. For bounded initial data, and right-hand side that is locally Lipschitz and locally bounded in u, local existence and uniqueness results in L∞ are well known, together with some estimates on weak solutions. More precise estimates for weak solutions of the above Cauchy problem will be given, supplemented by estimates on the maximal time of existence for the solution, as well as the local existence and uniqueness in L p setting (1 < p < ∞). This work is supported in part by the Croatian MZOS through project 037-0372787-2795.  相似文献   

12.
We consider the equation
If Ω is of class C 2, we show that this problem has a non-trivial solution u λ for each λ ∊ (8 π, λ*). The value λ* depends on the domain and is bounded from below by 2 j 0 2 π, where j 0 is the first zero of the Bessel function of the first kind of order zero (λ*≥ 2 j 0 2 π > 8 π). Moreover, the family of solution u λ blows-up as λ → 8 π.  相似文献   

13.
We study the weak* lower semicontinuity properties of functionals of the form
where Ω is a bounded open set of R N and u∈W 1,∞(Ω). Without a continuity assumption on f(⋅,ξ) we show that the supremal functional F is weakly* lower semicontinuous if and only if it is a level convex functional (i.e. it has convex sub-levels). In particular if F is weakly* lower semicontinuous, then it can be represented through a level convex function. Finally a counterexample shows that in general it is not possible to represent F through the level convex envelope of f.  相似文献   

14.
In this paper we will discuss the correspondence between generalized Clifford algebras and the gl(N; C). We will also examine the limit
. Indeed, in this situation the generators of C∞r are identified with the infinite matrix
where Ei, j denotes the basis of the gl(∞; C) algebra.  相似文献   

15.
The following regularity of weak solutions of a class of elliptic equations of the form are investigated.  相似文献   

16.
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If E *(t)=E(t)-2πΔ*(t/2π) with , then we obtain
and
It is also shown how bounds for moments of | E *(t)| lead to bounds for moments of .  相似文献   

17.
Summary.   A turning-point theory is developed for the second-order difference equation
where the coefficients A n and B n have asymptotic expansions of the form
θ≠0 being a real number. In particular, it is shown how the Airy functions arise in the uniform asymptotic expansions of the solutions to this three-term recurrence relation. As an illustration of the main result, a uniform asymptotic expansion is derived for the orthogonal polynomials associated with the Freud weight exp(−x 4 ), xℝ. Received February 21, 2002 / Revised version received April 8, 2002 / Published online October 29, 2002 Mathematics Subject Classification (1991): 41A60, 39A10, 33C45 The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1132 | 00P)  相似文献   

18.
We study the existence of sign changing solutions to the slightly subcritical problem
where ω is a smooth bounded domain in ℝ N , N ≥ 3, p = (N + 2)/(N − 2) and ɛ > 0. We prove that, for ɛ small enough, there exist N pairs of solutions which change sign exactly once. Moreover, the nodal surface of these solutions intersects the boundary of ω, provided some suitable conditions are satisfied.The second and the third authors are supported by M.U.R.S.T. project “Metodi variazionali e topologici nello studio di fenomeni non lineari” Mathematics Subject Classification (2000) 35J20, 35J65  相似文献   

19.
It is proved in Benamara-Nikolski [1] that if the spectrum σ(T) of a contractionT with finite defects (rank(I−T * T)=rank (I−TT *)<∞) does not coincide with , then the contraction is similar to a normal operator if and only if
The examples of Kupin-Treil [9] show that the result is no longer true if we replace the condition rank (I−T * T)<∞ by its weakened versionG, whereG denotes the class of nuclear operators. We prove in this paper that, however, the following theorem holds  相似文献   

20.
In this paper we consider the Lane–Emden problem adapted for the p-Laplacian
where Ω is a bounded domain in , n ≥ 2, λ > 0 and p < q < p* (with if p < n, and p* = ∞ otherwise). After some recalls about the existence of ground state and least energy nodal solutions, we prove that, when q → p, accumulation points of ground state solutions or of least energy nodal solutions are, up to a “good” scaling, respectively first or second eigenfunctions of  −Δ p . Received: 29 April 2008  相似文献   

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