共查询到20条相似文献,搜索用时 62 毫秒
1.
We study the boundary-value problemu
tt
-u
xx
=g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of, and-periodic functions (q and s are natural numbers). We obtain the results only for sets of periods, and which characterize the classes of π-, 2π -, and 4π-periodic functions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 281–284, February, 1999. 相似文献
2.
Thomas Bartsch Shuangjie Peng 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(5):778-804
We study the radially symmetric Schr?dinger equation
with N ≥ 1, ɛ > 0 and p > 1. As ɛ→ 0, we prove the existence of positive radially symmetric solutions concentrating simultaneously on k spheres. The radii are localized near non-degenerate critical points of the function
Supported by the Alexander von Humboldt foundation in Germany and NSFC (No:10571069) in China. 相似文献
3.
Local and Global Existence of Solutions to Initial Value Problems of Nonlinear Kaup-Kupershmidt Equations 总被引:6,自引:0,他引:6
Shuang Ping TAO Shang Bin CUI 《数学学报(英文版)》2005,21(4):881-892
This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt + α1 uδ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x,t)∈ E R^2, and δu/δt + α2 δu/δx δ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x, t) ∈R^2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup- Kupershmidt equations. The results show that a local solution exists if the initial function u0(x) ∈ H^s(R), and s ≥ 5/4 for the first equation and s≥301/108 for the second equation. 相似文献
4.
Thierry Horsin Molinaro 《manuscripta mathematica》1993,78(1):317-333
This paper is concerned with the evolution of harmonic maps from an open set Ω of ℝm into an n-dimensionnal ellipsoid
where a ∈ (0, 1]
We prove the existence of a smooth solution of the equation of evolution of harmonic maps if the initial data lies in a compact
subset of the upper hemisphere of an ellispoid. 相似文献
5.
Local and Global Existence of Solutions to
Initial Value Problems of Modified Nonlinear
Kawahara Equations 总被引:3,自引:0,他引:3
Shuang Ping TAO Shang Bin CUI 《数学学报(英文版)》2005,21(5):1035-1044
This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation the first partial dervative of u to t ,the second the third +α the second partial dervative of u to x ,the second the third +β the third partial dervative of u to x ,the second the thire +γ the fifth partial dervative of u to x = 0,(x,t)∈R^2.We first establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then we apply such estimates to prove local and global existence of solutions for the initial value problem of the modified nonlinear Karahara equation. The results show that a local solution exists if the initial function uo(x) ∈ H^s(R) with s ≥ 1/4, and a global solution exists if s ≥ 2. 相似文献
6.
Yu Qing Chen 《Designs, Codes and Cryptography》1998,13(3):247-250
In this paper, we will give a construction of a family of
-difference sets in thegroup
, where q is any power of 2, K is any group with
and G is an abelian 2-group of order
which contains anelementary abelian subgroup of index 2. 相似文献
7.
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
8.
Classification of positive solutions to an integral system with the poly-harmonic extension operator
In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R~+_n:{u(x)=c_n,a∫_?R_+~n(x_n~(1-a_v)(y)/|x-y|~(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n~(1-a_uθ)(x)/|x-y|~(n-a))dx,y∈ ?R_+~n,where n 2, 2-n a 1, κ, θ 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system. 相似文献
9.
G. P. Lopushanskaya 《Ukrainian Mathematical Journal》1999,51(1):51-65
We prove certain properties of solutions of the equation
in a domain ω ⊂R
3, which are similar to the properties of harmonic functions. By using the potential method, we investigate basic boundary-value
problems for this equation.
Lvov University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 48–59, January, 1999. 相似文献
10.
Mohammad Sal Moslehian 《Bulletin of the Brazilian Mathematical Society》2007,38(4):611-622
In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C*-ternary ring homomorphisms associated to the Trif functional equation
相似文献
11.
P. Ding 《Journal of Mathematical Sciences》2006,137(2):4645-4653
Let p be a prime number, n be a positive integer, and ƒ(x) = axk + bx. We put
where e(t) = exp(2πit). This special exponential sum has been widely studied in connection with Waring’s problem. We write n in the form n
= Qk + r, where 0 ≤ r ≤ k − 1 and Q ≥ 0. Let α = ord
p(k), β = ord
p(k − 1), and θ = ord
p(b). We define
and J = [ζ]. Moreover, we denote V = min(Q, J). Improving the preceding result, we establish the theorem. Theorem. Let k ≥ 2 and n ≥ 2. If p > 2, then
. An example showing that this result is best possible is given. Bibliography: 15 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 63–75. 相似文献
12.
Di Zhao 《中国科学A辑(英文版)》1999,42(9):897-904
LetM be a compact Riemann manifold with the Ricci curvature ≽ - R(R = const. > 0) . Denote by d the diameter ofM. Then the first eigenvalue λ1 ofM satisfies
. Moreover if
, then
相似文献
13.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
where φ
r
is the perfect Euler spline, on the segment [a, b] of monotonicity of x for q ≥ 1 and for arbitrary q > 0 in the case where r = 2 or r = 3.
As a corollary, we prove the well-known Ligun inequality for periodic functions x ∈ L
∞
r
, namely,
for q ∈ [0, 1) in the case where r = 2 or r = 3.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1338–1349, October, 2008. 相似文献
14.
Let
be a nondecreasing sequence of positive numbers and let l
1,α be the space of real sequences
for which
. We associate every sequence ξ from l
1,α with a sequence
, where ϕ(·) is a permutation of the natural series such that
, j ∈ ℕ. If p is a bounded seminorm on l
1,α and
, then
Using this equality, we obtain several known statements.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 1002–1006, July, 2005. 相似文献
15.
I. G. Danilenko 《Ukrainian Mathematical Journal》1998,50(5):831-833
For a function ƒ continuous on [0, 1] and satisfying the equalities we prove that where ω4(t,ƒ) is the fourth modulus of smoothness of the function ƒ.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 732–734, May, 1998. 相似文献
16.
V. M. Dil’nyi 《Ukrainian Mathematical Journal》2008,60(9):1477-1482
We present an equivalent definition of functions analytic in the half-plane ℂ+ = {z: Re z > 0} for which
.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1270–1274, September, 2008. 相似文献
17.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(u^mi)xixi in R^n × (O,∞), where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n(2 + ∑i^n=1 mi). 相似文献
18.
On a Binary Diophantine Inequality Involving Prime Numbers 总被引:1,自引:0,他引:1
M. B. S. Laporta 《Acta Mathematica Hungarica》1999,83(3):179-187
Let 1 < c < 15/14 and N a sufficiently large real number. In this paper we prove that, for all (N, 2N\ A with
, the inequality
has solutions in primes
. 相似文献
19.
M. M. Kabardov 《Vestnik St. Petersburg University: Mathematics》2009,42(3):169-174
The Euler-Knopp transformation is considered in terms of the problems of regularity and acceleration of the rate of convergence.
The object of study is the hypergeometric series
$
_n F_{n - 1} (a;b;z) = \sum\limits_{k = 0}^\infty {\frac{{(a_1 )_1 \cdots (a_n )_k }}
{{(b_1 )_k \cdots (b_{n - 1} )_k }}} \frac{{z^k }}
{{k!}} = \sum\limits_{k = 0}^\infty {\lambda _k z^k } .
$
_n F_{n - 1} (a;b;z) = \sum\limits_{k = 0}^\infty {\frac{{(a_1 )_1 \cdots (a_n )_k }}
{{(b_1 )_k \cdots (b_{n - 1} )_k }}} \frac{{z^k }}
{{k!}} = \sum\limits_{k = 0}^\infty {\lambda _k z^k } .
相似文献
20.
We obtain new sharp Kolmogorov-type inequalities, in particular the following sharp inequality for 2π-periodic functions x ∈ L
∞
r
(T):
|