共查询到20条相似文献,搜索用时 31 毫秒
1.
Giuseppe Maria Coclite Angelo Favini Gisèle Ruiz Goldstein Jerome A. Goldstein Silvia Romanelli 《Semigroup Forum》2008,77(1):101-108
The solution u of the well-posed problem
depends continuously on (a
ij
,β,γ,q).
Dedicated to Karl H. Hofmann on his 75th birthday. 相似文献
2.
We consider the following system of integral equations $${u_{i}(t)=\int\nolimits_{I} g_{i}(t, s)f(s, u_{1}(s), u_{2}(s), \cdots, u_{n}(s))ds, \quad t \in I, \ 1 \leq i\leq n}$$ where I is an interval of $\mathbb{R}$ . Our aim is to establish criteria such that the above system has a constant-sign periodic and almost periodic solution (u 1, u 2,…,u n ) when I is an infinite interval of $\mathbb{R}$ , and a constant-sign periodic solution when I is a finite interval of $\mathbb{R}$ . The above problem is also extended to that on $\mathbb{R}$ $$u_{i} {\left( t \right)} = {\int_\mathbb{R} {g_{i} {\left( {t,s} \right)}f_{i} {\left( {s,u_{1} {\left( s \right)},u_{2} {\left( s \right)}, \cdots ,u_{n} {\left( s \right)}} \right)}ds\quad t \in \mathbb{R},\quad 1 \leqslant i \leqslant n.} }$$ 相似文献
3.
In this paper we consider a class of gradient systems of type $$\begin{array}{ll} -c_{i} \Delta u_{i} + V_{i}(x)u_{i} = P_{u_i}(u),\qquad u_{1}, \ldots, u_{k} >\; 0\; \text{in}\; \Omega,\\ \quad u_{1} = \cdots = u_{k} = 0 \text{ on } \partial \Omega, \end{array}$$ in a bounded domain ${\Omega \subseteq \mathbb{R}^N}$ . Under suitable assumptions on V i and P, we prove the existence of ground-state solutions for this problem. Moreover, for k = 2, assuming that the domain Ω and the potentials V i are radially symmetric, we prove that the ground state solutions are foliated Schwarz symmetric with respect to antipodal points. We provide several examples for our abstract framework. 相似文献
4.
Marina GHISI Massimo GOBBINO 《数学学报(英文版)》2006,22(4):1161-1170
We consider the Cauchy problem εu^″ε + δu′ε + Auε = 0, uε(0) = uo, u′ε(0) = ul, where ε 〉 0, δ 〉 0, H is a Hilbert space, and A is a self-adjoint linear non-negative operator on H with dense domain D(A). We study the convergence of (uε) to the solution of the limit problem ,δu' + Au = 0, u(0) = u0.
For initial data (u0, u1) ∈ D(A1/2)× H, we prove global-in-time convergence with respect to strong topologies.
Moreover, we estimate the convergence rate in the case where (u0, u1)∈ D(A3/2) ∈ D(A1/2), and we show that this regularity requirement is sharp for our estimates. We give also an upper bound for |u′ε(t)| which does not depend on ε. 相似文献
5.
Ioannis Parissis 《Journal of Geometric Analysis》2010,20(3):771-785
Let ℳ denote the maximal function along the polynomial curve (γ
1
t,…,γ
d
t
d
):
$\mathcal{M}(f)(x)=\sup_{r>0}\frac{1}{2r}\int_{|t|\leq r}|f(x_1-\gamma_1t,\ldots,x_d-\gamma_dt^d)|\,dt.$\mathcal{M}(f)(x)=\sup_{r>0}\frac{1}{2r}\int_{|t|\leq r}|f(x_1-\gamma_1t,\ldots,x_d-\gamma_dt^d)|\,dt. 相似文献
6.
Let H be an infinite-dimensional real Hilbert space equipped with the scalar product (⋅,⋅)
H
. Let us consider three linear bounded operators,
7.
Let R be a commutative Noetherian ring, be an ideal of R and M be a finitely generated R-module. Melkersson and Schenzel asked whether the set becomes stable for a fixed integer i and sufficiently large j. This paper is concerned with this question. In fact, we prove that if s ≥ 0 and n ≥ 0 such that for all i with i < n, then is finite for all i with i < n, and is finite for all i with i ≤ n, where for a subset T of Spec(R), we set . Also, among other things, we show that if n ≥ 0, R is semi-local and is finite for all i with i < n, then is finite for all i with i ≤ n.
K. Khashyarmanesh was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM)
Iran (No. 86130027). 相似文献
8.
Arkadi Nemirovski 《Mathematical Programming》2007,109(2-3):283-317
Let B
i
be deterministic real symmetric m × m matrices, and ξ
i
be independent random scalars with zero mean and “of order of one” (e.g.,
). We are interested to know under what conditions “typical norm” of the random matrix
is of order of 1. An evident necessary condition is
, which, essentially, translates to
; a natural conjecture is that the latter condition is sufficient as well. In the paper, we prove a relaxed version of this
conjecture, specifically, that under the above condition the typical norm of S
N
is
:
for all Ω > 0 We outline some applications of this result, primarily in investigating the quality of semidefinite relaxations
of a general quadratic optimization problem with orthogonality constraints
, where F is quadratic in X = (X
1,... ,X
k
). We show that when F is convex in every one of X
j
, a natural semidefinite relaxation of the problem is tight within a factor slowly growing with the size m of the matrices
.
Research was partly supported by the Binational Science Foundation grant #2002038. 相似文献
9.
Sufficient conditions are established for the oscillation of proper solutions of the system
10.
We consider the following system of integral equations $$u_i(t)=\int^1_0g_i(t,s)f(s,u_1(s),u_2(s),\cdots,u_n(s))ds,\quad t\in \lbrack 0,1\rbrack,1\leq i\leq n.$$ Our aim is to establish criteria such that the above system has a constant-sign solution (u1, u2, …, u n) ∈ (Lp[0, 1])n, where the integer 1 ≤ p < ∞ is fixed. We shall tackle the case when f is ‘nonnegative’ as well as the case when f is ‘semipositone’. The above problem is also extended to that on the half-line [0, ∞) $$u_i(t)=\int^1_0g_i(t,s)f(s,u_1(s),u_2(s),\cdots,u_n(s))ds,\quad t\in \lbrack 0,\infty ),1\leq i\leq n.$$ 相似文献
11.
Linghai ZHANG 《数学年刊B辑(英文版)》2008,29(2):179-198
Let u=u(x,t,uo)represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt+δux+γHuxx+βuxxx+f(u)x=αuxx,u(x,0)=uo(x), whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f(0)=0,|f(u)|→∞as |u|→∞,and f∈C^1(R),and there exist the following limits Lo=lim sup/u→o f(u)/u^3 and L∞=lim sup/u→∞ f(u)/u^5 Suppose that the initial function u0∈L^I(R)∩H^2(R).By using energy estimates,Fourier transform,Plancherel's identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv(xxt)+δvx+γHv(xx)+βv(xxx)=αv(xx),v(x,0)=vo(x), the author justifies the following limits(with sharp rates of decay) lim t→∞[(1+t)^(m+1/2)∫|uxm(x,t)|^2dx]=1/2π(π/2α)^(1/2)m!!/(4α)^m[∫R uo(x)dx]^2, if∫R uo(x)dx≠0, where 0!!=1,1!!=1 and m!!=1·3…(2m-3)…(2m-1).Moreover lim t→∞[(1+t)^(m+3/2)∫R|uxm(x,t)|^2dx]=1/2π(x/2α)^(1/2)(m+1)!!/(4α)^(m+1)[∫Rρo(x)dx]^2, if the initial function uo(x)=ρo′(x),for some functionρo∈C^1(R)∩L^1(R)and∫Rρo(x)dx≠0. 相似文献
12.
Existence of positive solutions for the nonlinear fractional differential equation
D
αu = f(x,u), 0 < α < 1 has been given (S. Zhang. J. Math. Anal. Appl. 252 (2000), 804–812) where D
α denotes Riemann–Liouville fractional derivative. In the present work we extend this analysis for n-term non autonomous fractional
differential equations. We investigate existence of positive solutions for the following initial value problem
13.
14.
On a periodic boundary value problem for cyclic feedback type linear functional differential systems
Sulkhan Mukhigulashvili 《Archiv der Mathematik》2006,87(3):255-260
Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problem
15.
16.
M. N. Yakovlev 《Journal of Mathematical Sciences》1996,79(3):1146-1149
Let $\gamma ,\delta \in \mathbb{R}^n $ with $\gamma _j ,\delta _j \in \{ 0,1\} $ . A comparison pair for a system of equations fi(u1,…,un)=0 (i=1,…,n) is a pair of vectors $v,w \in \mathbb{R}^n ,v \leqslant w$ , such that $$\begin{array}{*{20}c} {\gamma _i f_i (u_1 , \ldots ,u_{i - 1} ,v_i ,u_i + 1, \ldots ,u_n ) \leqslant 0,} \\ {\delta _i f_i (u_1 , \ldots ,u_{i - 1} ,w_i ,u_i + 1, \ldots ,u_n ) \geqslant 0} \\ \end{array} $$ for $\gamma _j u_j \geqslant v_j ,\delta _j u_j \leqslant w_j (j = 1, \ldots ,n)$ . The presence of comparison pairs enables one to essentially weaken the assumptions of the existence theorem. Bibliography: 1 title. 相似文献
17.
We study the asymptotic behavior for solutions to nonlocal diffusion models of the form u
t
= J * u – u in the whole with an initial condition u(x, 0) = u
0(x). Under suitable hypotheses on J (involving its Fourier transform) and u
0, it is proved an expansion of the form
18.
R. Cavazzoni 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(2):193-204
In this paper we present a parabolic approach to studying the diffusive long time behaviour of solutions to the Cauchy problem:
19.
Thomas Bartsch Zhi-Qiang Wang Juncheng Wei 《Journal of Fixed Point Theory and Applications》2007,2(2):353-367
We consider the existence of bound states for the coupled elliptic system
20.
A large set of Kirkman triple systems of order v, denoted by LKTS(v), is a collection , where every is a KTS(v) and all form a partition of all triples on X. In this article, we give a new construction for LKTS(6v + 3) via OLKTS(2v + 1) with a special property and obtain new results for LKTS, that is there exists an LKTS(3v) for , where p, q ≥ 0, r
i
, s
j
≥ 1, q
i
is a prime power and mod 12.
相似文献
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