共查询到20条相似文献,搜索用时 15 毫秒
1.
It is established that the linear problemu
u
–a
2
u
xx
=g(x,t),u(0,t) =u(x, t + T) =u(x,t) is always solvable in the function spaceA = {g:g(x,t) =g(x,t+T) =g( –x,t) = –g(–x,t)} provided thataTq = (2p – 1) and (2p – 1,q) = 1, wherepandq are integer numbers. To prove this statement, an exact solution is constructed in the form of an integral operator, which is used to prove the existence of a solution of a periodic boundary-value problem for a nonlinear second-order wave equation. The results obtained can be used when studying the solutions to nonlinear boundary-value problems by asymptotic methods.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1115–1121, August, 1993. 相似文献
2.
Alemdar Hasanov 《Applied mathematics and computation》2003,140(2-3):501-515
An inverse polynomial method of determining the unknown leading coefficient k=k(x) of the linear Sturm–Liouville operator Au=−(k(x)u′(x))′+q(x)u(x), x(0,1), is presented. As an additional condition only two measured data at the boundary (x=0,x=1) are used. In absence of a singular point (u′(x)≠0,u″(x)≠0,x[0,1]) the inverse problem is classified as a well-conditioned . If there exists at least one singular point, then the inverse problem is classified as moderately ill-conditioned (u′(x0)=0,x0(0,1);u′(x)≠0,x≠x0;u″(x)≠0,x[0,1]) and severely ill-conditioned (u′(x0)=u″(x0)=0,x0(0,1);u′(x)≠0,u″(x)≠0,x≠x0). For each of the cases direct problem solution is approximated by corresponding polynomials and the inverse problem is reformulated as a Cauchy problem for to the first order differential equation with respect the unknown function k=k(x). An approximate analytical solution of the each Cauchy problems are derived in explicit form. Numerical simulations all the above cases are given for noise free and noisy data. An accuracy of the presented approach is demonstrated on numerical test solutions. 相似文献
3.
In this paper, we establish existence results for positive solutions to the Lichnerowicz equations of the following type in
closed manifolds
-Du = A(x)u-p - B(x)uq, in M,-\Delta u = A(x)u^{-p} - B(x)u^{q},\quad {{\rm in}}\, M, 相似文献
4.
A distance-transitive graph is a graph in which for every two ordered pairs of vertices (u,v) and (u′,v′) such that the distance between u and v is equal to the distance between u′ and v′ there exists an automorphism of the graph mapping u to u′ and v to v′. A semiregular element of a permutation group is a non-identity element having all cycles of equal length in its cycle decomposition. It is shown that every distance-transitive graph admits a semiregular automorphism. 相似文献
5.
Hui-Sheng Ding Wei Long Gaston M. NGurkata 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4158-4164
In this paper, we establish some new theorems about the existence of almost automorphic solutions to nonautonomous evolution equations u′(t)=A(t)u(t)+f(t) and u′(t)=A(t)u(t)+f(t,u(t)) in Banach spaces. As we will see, our results allow for a more general A(t) to some extent. An example is also given to illustrate our results. In addition, by means of an example, we show that one cannot ensure the existence of almost automorphic solutions to u′(t)=A(t)u(t)+f(t) even if the evolution family U(t,s) generated by A(t) is exponentially stable and fAA(X). 相似文献
6.
A set S⊆V is called a q+-set (q--set, respectively) if S has at least two vertices and, for every u∈S, there exists v∈S,v≠u such that N+(u)∩N+(v)≠∅ (N-(u)∩N-(v)≠∅, respectively). A digraph D is called s-quadrangular if, for every q+-set S, we have |∪{N+(u)∩N+(v):u≠v,u,v∈S}|?|S| and, for every q--set S, we have |∪{N-(u)∩N-(v):u,v∈S)}?|S|. We conjecture that every strong s-quadrangular digraph has a Hamilton cycle and provide some support for this conjecture. 相似文献
7.
A digraph T is strong if for every pair of vertices u and v there exists a directed path from u to v and a directed path from v to u. Denote the in-degree and out-degree of a vertex v of T by d-(v) and d+(v), respectively. We define δ-(T)=minvV(T){d-(v)} and δ+(T)=minvV(T){d+(v)}. Let T0 be a 7-tournament which contains no transitive 4-subtournament. In this paper, we obtain some conditions on a strong tournament which cannot be partitioned into two cycles. We show that a strong tournament T with n6 vertices such that TT0 and max{δ+(T),δ-(T)}3 can be partitioned into two cycles. Finally, we give a sufficient condition for a tournament to be partitioned into k cycles. 相似文献
8.
José María Martell 《Journal of Mathematical Analysis and Applications》2004,294(1):223-236
We prove two-weight, weak type norm inequalities for potential operators and fractional integrals defined on spaces of homogeneous type. We show that the operators in question are bounded from Lp(v) to Lq,∞(u), 1<p?q<∞, provided the pair of weights (u,v) verifies a Muckenhoupt condition with a “power-bump” on the weight u. 相似文献
9.
Rieko Shimada 《Mathematical Methods in the Applied Sciences》2007,30(3):257-289
We obtain the Lp–Lq maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ?n (n?2). The Robin condition consists of two conditions: v ? u=0 and αu+β(T(u, p)v – 〈T(u, p)v, v〉v)=h on the boundary of the domain with α, β?0 and α+β=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and non‐slip one when α=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
10.
It is shown that when the random vector X in Rn has a mean and when the conditional expectation E(u′X|v′X) = 0 for all vectors u, v Rn which satisfy u′v = 0, then the distribution of X is orthogonally invariant. A version of this characterization is also established when X does not have a mean vector. 相似文献
11.
The problem of capture in a pursuit game which is described by a linear retarded functional differential equation is considered. The initial function belongs to the Sobolev space W2(1). The target is either a subset of W2(1) a point in W2(1), a subset of the Euclidean space En or a point of En. There is capture if the initial function can be forced to the target by the pursuer no matter what the quarry does. The concept of capture therefore formalizes the concepts of controllability under unpredictable disturbances. This is proved to be equivalent to the controllability of an associated linear retarded functional differential equation. There is nothing in (2) (6) or (7) below which restricts the control sets to be of the same dimension as the phase space. Our results can be applied in (2) for example, if the constraint sets Q′, P′ are subsets of Em and Ei respectively with q(t) = C(t) q′(t), − p(t) = B(t) p′(t), q′(t) ε Emp′(t) ε Er and B(t) is an n × r′-matrices and C(t) an n × m-matrix. 相似文献
12.
For a bounded linear injectionCon a Banach spaceXand a closed linear operatorA : D(A) X → Xwhich commutes withCwe prove that (1) the abstract Cauchy problem,u″(t) = Au(t),t R,u(0) = Cx,u′(0) = Cy, has a unique strong solution for everyx,y D(A) if and only if (2)A1 = AD(A2) generates aC1-cosine function onX1(D(A) with the graph norm), if (and only if, in caseAhas nonempty resolvent set) (3)Agenerates aC-cosine function onX. HereC1 = CX1. Under the assumption thatAis densely defined andC−1AC = A, statement (3) is also equivalent to each of the following statements: (4) the problemv″(t) = Av(t) + C(x + ty) + ∫t0 Cg(r) dr,t R,v(0) = v′(0) = 0, has a unique strong solution for everyg L1locandx, y X; (5) the problemw″(t) = Aw(t) + Cg(t),t R,w(0) = Cx,w′(0) = Cy, has a unique weak solution for everyg L1locandx, y X. Finally, as an application, it is shown that for any bounded operatorBwhich commutes withCand has range contained in the range ofC,A + Bis also a generator. 相似文献
13.
The authors determine the number of (n+m)×t matrices A1 of rank r+v, over a finite field GF(q), whose last m rows are those of a given matrix A of rank r+v over GF(q) and whose first n rows have a given rank u. 相似文献
14.
The generalized maximal operator M in martingale spaces is considered. For 1 < p ≤ q < ∞, the authors give a necessary and sufficient condition on the pair ([^(m)]\hat \mu , v) for M to be a bounded operator from martingale space L
p
(v) into L
q
([^(m)]\hat \mu ) or weak-L
q
([^(m)]\hat \mu ), where [^(m)]\hat \mu is a measure on Ω × ℕ and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed. 相似文献
15.
Let (M, g) be a smooth compact Riemannian manifold of dimension n ≥ 3. Denote Dg=-divg?{\Delta_g=-{\rm div}_g\nabla} the Laplace–Beltrami operator. We establish some local gradient estimates for the positive solutions of the Lichnerowicz
equation
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