共查询到20条相似文献,搜索用时 937 毫秒
1.
Abstract
By applying the topological degree theory, we establish some sufficient conditions for the existence on T-periodic solutions for the Liénard-type equation
Our results extend and improve some known results in the literature.
Supported by the National Natural Science Foundation of China (No. 10371034), the Doctor Program Foundation of the Ministry
of Education of China (20010532002) and Key Object of Chinese Ministry of Education ([2002]78). 相似文献
2.
MingXiong 《应用数学学报(英文版)》2004,20(4):665-674
Some results concerning existence of positive solutions for the singular boundary value problems u^(4)(t)=f(t,u(t)) t∈(0,1) u(0)=u(1)=0 u‘(0)=u‘(1)=0 have been given, where f(t, x) may be singular at t = 0, 1. 相似文献
3.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引:7,自引:0,他引:7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
where f(x, y) ≥ −M, and M is a positive constant. We show the
existence and multiplicity of positive solutions by applying the
fixed point theorem in cones.
*Supported by the NSFC (10271095).
GG-110-10736-1003, NWNU-KJCXGC-212 and the Foundation of Major
Project of Science and Technology of Chinese Education
Ministry 相似文献
4.
Abstract
The singular second-order m-point boundary value problem
, is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′(x))′ + q(x)ϕ(x) and ξ
i
∈ (0, 1) with 0 < ξ1 < ξ2 < · · · < ξ
m−2 < 1, a
i
∈ [0, ∞). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some
other m-point boundary value conditions.
Supported by the National Natural Science Foundation of China (No.10371066, No.10371013) 相似文献
5.
Aleksandar Ivić 《Central European Journal of Mathematics》2005,3(2):203-214
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
6.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
7.
M.Federson R.Bianconi L.Barbanti 《应用数学学报(英文版)》2004,20(4):623-640
We consider the multidimensional abstract linear integral equation of Volterra type x(t) (*)∫Rtα(s)x(s)ds=f(t),t∈R,(1)as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions. The functions x, α and f are Bauach space-valued defined on a compact interval R of R^n Rt is a subinterval of R depending on t ∈ R and (*) f denotes either the Bochner-Lebesgue integral or the Henstock integral. The results presented here generalize those in [1] and are in the spirit of [3]. As a consequence of our approach, it is possible to study the properties of (1) by transferring the properties of the discrete systems, The Henstock integral setting enables us to consider highly oscillating functions. 相似文献
8.
We investigate the maximum number of edges that a graph G can have if it does not contain a given graph H as a minor (subcontraction). Let
We define a parameter γ(H) of the graph H and show that, if H has t vertices, then
where α = 0.319. . . is an explicit constant and o(1) denotes a term tending to zero as t→∞. The extremal graphs are unions of pseudo-random graphs.
If H has t1+τ edges then
, equality holding for almost all H and for all regular H. We show how γ(H) might be evaluated for other graphs H also, such as complete multi-partite graphs.
* Research supported by EPSRC studentship 99801140. 相似文献
9.
Blow-up Solutions for Mixed Nonlinear Schrodinger Equations 总被引:1,自引:0,他引:1
ShaoBinTAN 《数学学报(英文版)》2004,20(1):115-124
This paper is concerned with the initial boundary-value problem for the following nonlinear evolution equation: Фt=iαФxx βФ^2Ф^-x γ|Ф|^2Фx ig(|Ф|^2)Ф Under certain conditions on the initial data and the function g(s),we study the existence and nonexistence of global solution for this equation.The blow-up solution and the blow-up time are also investigated. 相似文献
10.
Choonkil BAAK 《数学学报(英文版)》2006,22(6):1789-1796
Let X, Y be vector spaces. It is shown that if a mapping f : X → Y satisfies f((x+y)/2+z)+f((x-y)/2+z=f(x)+2f(z),(0.1) f((x+y)/2+z)-f((x-y)/2+z)f(y),(0.2) or 2f((x+y)/2+x)=f(x)+f(y)+2f(z)(0.3)for all x, y, z ∈ X, then the mapping f : X →Y is Cauchy additive.
Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras. 相似文献
11.
The Commutators of Fractional Integrals on Besov Spaces 总被引:1,自引:0,他引:1
Abstract
In this paper we consider the commutators of fractional integrals
on the Besov spaces
, where b is a locally integrable function and 0 < α < n. We first establish the equivalence between the boundedness of the commutators
and the paraproduct of J. M. Bony. Then we obtain two conditions on the boundedness of the commutators. One of these conditions
is necessary and the other is sufficient.
The first author is supported by NNSF of China (Nos. 19901021, 10371080), Beijing Natural Science Foundation (No. 1013006)
and Scientific Research Foundation for Returned Overseas Chinese Scholars. The second author is supported by the National
973 project (G19990751) 相似文献
12.
Bing-wen Liu Li-hong Huang 《应用数学学报(英文版)》2006,22(2):287-296
In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form (x(t)+Bx(t-δ))"+Cx'(t)+g(x(t-τ))=p(t). 相似文献
13.
S. BERHANU F. CUCCU G. PORRU 《数学学报(英文版)》2007,23(3):479-486
For γ≥1 we consider the solution u=u(x) of the Dirichlet boundary value problem Δu + u^-γ=0 in Ω, u=0 on δΩ. For γ= 1 we find the estimate
u(x)=p(δ(x))[1+A(x)(log 1/δ(x)^-6],
where p(r) ≈ r r√2 log(1/r) near r = 0,δ(x) denotes the distance from x to δΩ, 0 〈ε 〈 1/2, and A(x) is a bounded function. For 1 〈 γ 〈 3 we find
u(x)=(γ+1/√2(γ-1)δ(x))^2/γ+[1+A(x)(δ(x))2γ-1/γ+1]
For γ3= we prove that
u(x)=(2δ(x))^1/2[1+A(x)δ(x)log 1/δ(x)] 相似文献
14.
Aleksandar Ivić 《Central European Journal of Mathematics》2004,2(4):494-508
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
with
, then we obtain
. We also show how our method of proof yields the bound
, where T
1/5+ε≤G≪T, T<t
1<...<t
R
≤2T, t
r
+1−t
r
≥5G (r=1, ..., R−1). 相似文献
15.
LiJunjie BianBaojun 《高校应用数学学报(英文版)》2000,15(3):273-280
The following regularity of weak solutions of a class of elliptic equations of the form are investigated. 相似文献
16.
In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential
equations of the form
. Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0. 相似文献
17.
Qi Kang RAN 《数学学报(英文版)》2005,21(4):705-714
In this paper, we prove that the weak solutions u∈Wloc^1, p (Ω) (1 〈p〈∞) of the following equation with vanishing mean oscillation coefficients A(x): -div[(A(x)△↓u·△↓u)p-2/2 A(x)△↓u+│F(x)│^p-2 F(x)]=B(x, u, △↓u), belong to Wloc^1, q (Ω)(A↓q∈(p, ∞), provided F ∈ Lloc^q(Ω) and B(x, u, h) satisfies proper growth conditions where Ω ∪→R^N(N≥2) is a bounded open set, A(x)=(A^ij(x)) N×N is a symmetric matrix function. 相似文献
18.
L. V. Kritskov 《Mathematical Notes》1999,65(4):454-461
Suppose thatА is a nonnegative self-adjoint extension to {
} of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {
} or the condition {
} in which the nonnegative function itχ(r) is such that {
}. For each α∈(0, 2], we establish an estimate of the generalized Fourier transforms of an arbitrary function {
} of the form {
} If, in addition, {
}, then, along with this estimate, a similar lower bound is established.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 542–551, April, 1999. 相似文献
19.
In the present paper, we derive the Laplace transforms of the integral functionals
and
where p and q are real numbers, {B
t
(μ)
: t ≥ 0} is a Brownian motion with drift μ > 0 (denoted BM(μ)), and {R
t
(3)
: t ≥ 0} is a 3-dimensional Bessel process (denoted BES(3)). The transforms are given in terms of Gauss' hypergeometric functions, and the results are closely related to some results
for functionals of Jacobi diffusions. This work generalizes and completes some results of Donati-Martin and Yor and Salminen
and Yor. Bibliography: 18 titles.
__________
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 51–78. 相似文献
20.
In this paper the invariance criterion is applied for the nonlinear equation
where g(u) is a smooth function on u. Some particular set of Lie generators are given. In the case of inviscid Burger’s equation [1]
the Lie projectable symmetry algebra is determined, and the inviscid Burger’s equation will be connected to some order differential
equations. The obtained differential equations are solved and some exact solutions of (2) are found.
E.H. El Kinani, Junior Associate at The Abdus Salam ICTP, Trieste, Italy. 相似文献
(0.1) |
(0.2) |