共查询到20条相似文献,搜索用时 171 毫秒
1.
Xiangsheng Xu 《Rendiconti del Circolo Matematico di Palermo》1991,40(1):69-101
Existence of a weak solution is established for the first boundary value problem for the equation (c(u))
t
=(φ(u
x
)
x
in the case wherec′(x), φ′(x) may oscillate near zero,c′(x), φ′(x) may be unbounded above, andc′(x), φ′(x) may not be bounded away from zero asx→0. Some regularity properties of the wea, solution are also obtained. 相似文献
2.
V. E. Slyusarchuk 《Ukrainian Mathematical Journal》1997,49(7):1089-1101
We establish conditions of asymptotic stability for all solutions of the equation X
n+1=F(X
n
), n≥0, in the Banach space E in the case where r(F′(x))<1 ∀ x ∈ E, r′(x) is the spectral radius of F′(x). An example of an equation with an unstable solution is given.
Ukrainian Academy of the Water Industry, Rovno. Translated from Ukrainskii Matematicheskii zhurnal, Vol. 49, No. 7, pp. 970–980.
July, 1997. 相似文献
3.
Antonio Tineo 《Annali di Matematica Pura ed Applicata》2003,182(2):129-141
In this paper we study the scalar equation x′=f(t,x), where f(t,x) has cubic non-linearities in x and we prove that this equation has at most three bounded separate solutions. We say that λ∈ℝ is a critical value of the
equation x′=f(t,x)+λx if this equation has a degenerate bounded solution and we exhibit two classes of functions f such that the above equation has a unique critical value.
Received: February 4, 2000; in final form: March 19, 2002?Published online: April 14, 2003
RID="*"
ID="*"This paper was partially supported by CDCHT, Universidad de los Andes. 相似文献
4.
Anna Capietto Walter Dambrosio Bin Liu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,59(2):1007-1034
We study a second order scalar equation of the form x′′ + V′(x) = p(t), where p is a π-perodic function and V is a singular potential. We give sufficient conditions on V, p ensuring that all solutions are bounded; we prove the existence of Aubry–Mather sets as well. 相似文献
5.
Ján Ohriska 《Central European Journal of Mathematics》2008,6(3):439-452
The aim of this paper is to derive sufficient conditions for the linear delay differential equation (r(t)y′(t))′ + p(t)y(τ(t)) = 0 to be oscillatory by using a generalization of the Lagrange mean-value theorem, the Riccati differential inequality
and the Sturm comparison theorem.
相似文献
6.
Yu. B. Yanushanets 《Journal of Mathematical Sciences》2000,102(4):4339-4347
We consider the fundamental solution E (t,x,s;s
0) of the Cauchy problem for the one-speed linear Boltzman equation (∂/∂t+c(s,grad
x)+γ)E(t,x,s;s
0)=γν∫ f((s, s′))E(t,x,s′; s0)ds′+Ωδ(t)δ(x)δ (s−s
0) that is assumed to be valid for any (t,x)∈Rn+1; morevoer, for t<0 the condition E(t,x,s; s0)=0 holds. By using the Fourier-laplace transform in space-time arguments, the problem reduces to the study of an integral
equation in the variables. For 0<ν≤1, the uniqueness and existence of the solution of the original problem are proved for any fixeds in the space of tempered distributions with supports in the front space-time cone. If the scattering media are of isotropic
type (f(.)=1), the solution of the integral equation is given in explicit form. In the approximation of “small mean-free paths,”
various weak limits of the solution are obtained with the help of a Tauberian-type theorem, for distributions. Bibliography:
4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 319–332.
Translated by Yu. B. Yanushanets. 相似文献
7.
For given , c < 0, we are concerned with the solution f
b
of the differential equation f ′′′ + ff ′′ + g(f ′) = 0 satisfying the initial conditions f(0) = a, f ′ (0) = b, f ′′ (0) = c, where g is some nonnegative subquadratic locally Lipschitz function. It is proven that there exists b
* > 0 such that f
b
exists on [0, + ∞) and is such that as t → + ∞, if and only if b ≥ b
*. This allows to answer questions about existence, uniqueness and boundedness of solutions to a boundary value problem arising
in fluid mechanics, and especially in boundary layer theory.
相似文献
8.
Some new oscillation criteria are established for the second-order matrix differential system(r(t)Z′(t))′ p(t)Z′(t) Q(t)F(Z′(t))G(Z(t)) = 0, t ≥ to > 0,are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. The results weaken the condition of Q(t) and generalize some well-known results of Wong (1999) to nonlinear matrix differential equation. 相似文献
9.
Artūras Dubickas 《Mediterranean Journal of Mathematics》2012,9(1):95-103
We prove that every set of n ≥ 3 points in
\mathbbR2{\mathbb{R}^2} can be slightly perturbed to a set of n points in
\mathbbQ2{\mathbb{Q}^2} so that at least 3(n − 2) of mutual distances between those new points are rational numbers. Some special rational triangles that are arbitrarily
close to a given triangle are also considered. Given a triangle ABC, we show that for each ε > 0 there is a triangle A′B′C′ with rational sides and at least one rational median such that |AA′|, |BB′|, |CC′| < ε and a Heronian triangle A′′B′′C′′ with three rational internal angle bisectors such that
A¢¢, B¢¢, C¢¢ ? \mathbbQ2{A^{\prime\prime}, B^{\prime\prime}, C^{\prime\prime} \in \mathbb{Q}^2} and |AA′′|, |BB′′|, |CC′′| < ε. 相似文献
10.
E. I. Bunina 《Journal of Mathematical Sciences》2008,152(2):155-190
It is proved that (elementary) Chevalley groups G
π(Φ,K) and G
π′(Φ′,K′) (or E
π(Φ,K) and E
π′(Φ′,K′)) over infinite fields K and K′ of characteristic different from 2, with weight lattices Λ and Λ′, respectively, are elementarily equivalent if and only
if the root systems Φ and Φ′ are isomorphic, the fields K and K′ are elementarily equivalent, and the lattices Λ and Λ′ coincide.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 8, pp. 29–77, 2006. 相似文献
11.
We study the differential equationf″=N(f)f′
2
+M(f)f′+L(f), whereL, M, N are rational functions, and prove that if the differential equation has a transcendental meromorphic solutionf with order,p(f)>2, then the differential equation must be one of nine forms; and, moreover, we construct examples showing the existence of
these nine forms with a transcendental meromorphic solution. 相似文献
12.
A. Haraux 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(4):435-445
We examine the rate of decay to 0, as t → +∞., of the projection on the range of A of the solutions of an equation of the form u′ + Au + |u|
p−1
u = 0 or u′′ + u′ + Au + |u|
p−1
u = 0 in a bounded domain of
N
, where A = −Δ with Neumann boundary conditions or A = −Δ − λ1
I with Dirichlet boundary conditions. In general this decay is much faster than the decay of the projection on the kernel;
it is often exponential, but apparently not always. 相似文献
13.
An extension of Ezeilo's result 总被引:1,自引:0,他引:1
Rolf Reissig 《Annali di Matematica Pura ed Applicata》1972,92(1):199-209
Summary In a recent paper[1] Ezeilo considered the nonlinear third order differential equation x‴ + ω(x′)x″ + ω(x)x′ + ϑ(x, x′, x″)=p(t). He proved the
ultimate boundedness of the solutions on rather general conditions for the nonlinear terms ϕ, ϕ, ϑ. These conditions (in a
little weaker form) are also sufficient in order to prove the existence of forced oscillations in the case when the excitation
is ω-periodic. For this purpose the Lerag-Schauder principle in a form suggested by G. Güssefeldt[2] is applicable.
Dedicated to ProfessorKarl Klotter on his 70th birthday
Entrata in Redazione il 21 ottobre 1971. 相似文献
14.
Mohamed Ali Toumi 《Czechoslovak Mathematical Journal》2010,60(1):85-94
Let A and B be two Archimedean vector lattices and let (A′)′
n
and (B′)′
n
be their order continuous order biduals. If Ψ: A × A → B is a positive orthosymmetric bimorphism, then the triadjoint Ψ***: (A′)′
n
× (A′)′
n
→ (B′)′
n
of Ψ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost f-algebras. 相似文献
15.
Jürgen Pöschel 《Mathematische Annalen》2011,349(2):433-458
We describe a new, short proof of some facts relating the gap lengths of the spectrum of a potential q of Hill’s equation, −y′′ + qy = λy, to its regularity. For example, a real potential is in a weighted Gevrey-Sobolev space if and only if its gap lengths, γ
n
, belong to a similarly weighted sequence space. An extension of this result to complex potentials is proven as well. We also
recover Trubowitz results about analytic potentials. The proof essentially employs the implicit function theorem. 相似文献
16.
Jean-Paul Thouvenot 《Israel Journal of Mathematics》1975,21(2-3):215-232
Two Bernoulli shifts are given, (X, T) and (X′, T′), with independent generatorsR=P ∨Q andR′=P′ ∨Q′ respectively. (R andR′ are finite). One can chooseR such that if (X′, T′) can be made a factor of (X, T) in such a way that (P′)
T′
and (Q′)
T′
are full entropy factors of (P)
T
and (Q)
T
respectively thend (P ∨Q)=d(P′ ∨Q′). In addition it is proved that if (X, T) is a Bernoulli shift and ifS is a measure preserving transformation ofX that has the same factor algebras asT thenS=T orS=T
−1. A tool for this proof, which may be of independent interest is a relative version for very weak Bernoullicity.
Equipe de Recherche no 1 “Processus stochastique et applications” dépendant de la Section no 1 “Mathématiques, Informatique” associée au C.N.R.S. 相似文献
Equipe de Recherche no 1 “Processus stochastique et applications” dépendant de la Section no 1 “Mathématiques, Informatique” associée au C.N.R.S. 相似文献
17.
We study the persistence of the asymptotic stability of delay equations both under linear and nonlinear perturbations. Namely,
we consider nonautonomous linear delay equations v′ = L(t)v
t
with a nonuniform exponential contraction. Our main objective is to establish the persistence of the nonuniform exponential stability of the
zero solution both under nonautonomous linear perturbations, i.e., for the equation v′ = (L(t) + M(t))v
t
, thus discussing the so-called robustness problem, and under a large class of nonlinear perturbations, namely for the equation
v′ = L(t)v
t
+ f(t, v
t
). In addition, we consider general contractions e
−λρ(t) determined by an increasing function ρ that includes the usual exponential behavior with ρ(t) = t as a very special case. We also obtain corresponding results in the case of discrete time. 相似文献
18.
In this paper we study asymptotic properties of the third order trinomial delay differential equation (*) y‴(t) − p(t)y′(t) + g(t)y(τ(t)) = 0 by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results
in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria
from ordinary to delay equations.
Research was supported by S.G.A. No.1/003/09. 相似文献
19.
W. K. Min 《Acta Mathematica Hungarica》2009,125(4):387-393
The concept of θ(g, g′)-continuity was introduced by Császár [1]. In this paper, we investigate characterizations for θ(g, g′)-continuous functions and introduce the concept of weak θ(g, g′)-continuity, and study characterizations for weak θ(g, g′)-continuity and the relationships among θ(g, g′)-continuity, weak (g, g′)-continuity and weak θ(g, g′)-continuity. 相似文献
20.
陈晋南 《中国科学A辑(英文版)》2002,45(10):1335-1350
The boundary integral technique is used to study the effect of deformation on the steady, creeping, thermocapillary migration
of a fluid particle under conditions of axisymmetry, negligible thermal convection and an insulated tube wall. The spherical
radius of the fluid particle (i.e. the radius as if the particle were a sphere, a ′= (3V
p
′
/4π)1/3, V
p
′
is the particle volume) and that of the tube are denoted, respectively, by a′and b′. For small capillary numberCa = 0.05, only for a large fluid particle (a′/b′ = 0.8) is deformation significant. Fora′/b′= 0.8, hydrodynamic stresses squeeze the particle, reduce the interaction of the particle with the wall and thereby increase
the terminal velocity. For small particles a′/b′< 0.8 and Ca = 0.05 the fluid particles translate as spheres, due to the fact
that the fluid particle is too far away from the wall to be subject to distending hydrodynamic stresses. The deformable particle
moves faster than a spherical one in the thermocapillary migration. The increase in velocity with capillary number is larger
for thermocapillary motion than for buoyancy. 相似文献