共查询到20条相似文献，搜索用时 554 毫秒
1.
Let E be a Banach space. We prove the instability of the trivial solution of the differential equation
where f: [0, +∞) × E → ℝ is a continuous mapping for which
__________
Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 404–414, July–September, 2005. 相似文献
2.
Stability of a class of neural network models with delay 总被引：6，自引：0，他引：6
ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ,ｔｈｅｏｒｅｔｉｃａｌａｎｄａｐｌｉｅｄｓｔｕｄｉｅｓｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｈａｖｅｂｅｎｔｈｅｎｅｗｆｏｃｕｓｏｆｓｔｕｄｉｅｓｉｎｔｈｅｗｏｒｌｄ．Ｉｔｉｓｗｅｌ＿ｋｎｏｗｎｔｈａｔｑｕ... 相似文献
3.
李永昆 《应用数学和力学(英文版)》2000,21(7):849-854
ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎｌｉｎｅａｒａｕｔｏｎｏｍｏｕｓｄｅｌａｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｘ′(ｔ) ∑ｍｉ=1ｐｉｆｉ(ｘ(ｔ-τｉ) ) =0 (1 )ａｎｄｔｈｅｌｉｎｅａｒｅｑｕａｔｉｏｎｘ′(ｔ) ∑ｍｉ=1ｐｉｘ(ｔ-τｉ) =0 ,(2 )ｗｈｅｒｅ ,ｐｉ ∈ (0 ,∞ ) ,τｉ ∈ [0 ,∞ )ａｎｄｆｉ ∈Ｃ(Ｒ ,Ｒ)ｆｏｒｉ =1 ,… ,ｍ .ＩｎＲｅｆ.[1 ] ,ｔｈｅｌｉｎｅａｒｉｚｅｄｏｓｃｉｌｌａｔｉｏｎｓｏｆＥｑ .(1 )ｗａｓｓｔｕｄｉｅｄａｎｄｉｔｗａｓｐｒｏｖｅｄｔｈａｔｉｆｔ… 相似文献
4.
On the existence of periodic solutions to higher dimensional periodic system with delay 总被引：1，自引：0，他引：1
Ｃｏｎｓｉｄｅｒｉｎｇｔｈｅｈｉｇｈｅｒｄｉｍｅｎｓｉｏｎａｌｐｅｒｉｏｄｉｃｓｙｓｔｅｍｓｗｉｔｈｄｅｌａｙｏｆｔｈｅｆｏｒｍｘ′（ｔ）＝Ａ（ｔ,ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ,ｘ（ｔ－τ））,（１）ｘ′（ｔ）＝ｇｒａｄＧ（ｘ（ｔ））＋ｆ（ｔ,ｘ（ｔ－... 相似文献
5.
In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles.
We find a fractional Lagrangian L(x(t), where
a
c
D
t
α
x(t)) and 0<α<1, such that the following is the corresponding Euler–Lagrange
At last, exact solutions for some Euler–Lagrange equations are presented. In particular, we consider the following equations
where g(t) and f(t) are suitable functions.
D. Baleanu is on leave of absence from Institute of Space Sciences, P.O. BOX MG-23, 76900 Magurele-Bucharest, Romania. e-mail:
baleanu@venus.nipne.ro. 相似文献
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| (2) |
| (3) |
6.
Let X be a uniformly smooth real Banach space. Let T:X → X be continuos and strongly accretive operator. For a given f ε X,
define S: X → X by Sx =f−Tx+x, for all x ε X. Let {an}
n=0
∞
, {βn}
n=0
∞
be two real sequences in (0, 1) satisfying:
;
Assume that {un}
n=0
∞
and {υn}
n=0
∞
are two sequences in X satisfying ‖un‖ = 0(αn) and ‖υn‖ → 0 as n → ∞. For arbitrary x0 ε X, the iteration sequence {xn} is defined by
Moreover, suppose that {Sxn} and {Syn} are bounded, then {xn} converges strongly to the unique fixed point of S. 相似文献
| ((i)) |
| ((ii)) |
| (1) |
7.
Iterative solution of nonlinear equations with strongly accretive operators in Banach spaces 总被引：1，自引：0，他引：1
周海云 《应用数学和力学(英文版)》1999,20(3):282-289
1IntroductionandPreliminariesLetXbearealBanachspacewithnormIJ'11andadualX'.ThenormalizeddualitymappingJ:X~ZxisdefinedbyJx={x'eX*I(x,x')=11x112=11x if'},where',')denotesthegeneralizeddualitypairing.Itiswell-knownthatifX isstrictlyconvex,Jissingle-valuedandJ(tx)=tjxforallt201xeX.IfX*isuniformlyconvex,thenJisuniformlycontinuousonanyboundedsubsetSofX(of.Browde,fljandBarbuL2]).AnoperatorTwithdomainD(T)andrangeR(T)inXissaidtobeaccretiveifforeveryx,y6D(T),thereexistsajeJ(x--y)suchthat(T… 相似文献
8.
On nonlinear hyperbolic equation in unbounded domain 总被引：2，自引：0，他引：2
The following nonlinear hyperbolic equation is discussed in this paper: where The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x. 相似文献
9.
云天铨 《应用数学和力学(英文版)》1995,16(5):443-449
In this paper, the solution of a 2-D weak singular integral equation of the first kind
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相似文献
10.
朱勇 《应用数学和力学(英文版)》1998,19(11):1059-1063
I.IntroductionItiswell-knobal.nthatKorteweg-deVriesequationisacanonicalmodeltodescribethebalanceofthenonlineareffectandthedispersiveeffectofaphysicalsystem.Thisequationpossessestheso-called'soliton"solution,whichhasbeenfoundnumericallybyZabuskyandKruskall'].Ho-c'Jlever,sometimesthebalanceofnonlinearityanddispersionofasystemmayleadtoa,integroditTerentialequationinsteadofadifferentialequation.Forinstance,inthestudyofvortexbreakdownofanunboundedrotatingfluidLeibovich12]derivedfollowingnonline… 相似文献
11.
郭艾 《应用数学和力学(英文版)》1999,20(6):683-689
１ＰｒｏｂｌｅｍｓａｎｄＭａｉｎＲｅｓｕｌｔｓＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｔｕｄｙｔｈｅｎｏｎｌｉｎｅａｒｖｉｂｒａｔｉｏｎｓｏｆｉｎｆｉｎｉｔｅｒｏｄｓｗｉｔｈｖｉｓｃｏｅｌａｓｔｉｃｉｔｙ．Ｔｈｅｃｏｎｓｔｉｔｕｔｉｏｎｌａｗｏｆｔｈｅｒｏｄｓ... 相似文献
12.
黄先开 《应用数学和力学(英文版)》1999,20(10):1116-1120
ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｒｅｃｅｎｔｙｅａｒｓ,ｗｉｔｈａｌｏｔｏｆａｐｐｌｉｃａｔｉｏｎｓｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｓ,ｍａｎｙａｕｔｈｏｒｓ［１～３］ａｒｅｉｎｔｅｒｅｓｔｅｄｉｎｔｈｅｒｅｓｅａｒｃｈｏｆｔｈｅｓｔｒｕｃｔｕｒｅａｎｄｐｅｒｆｏｒｍａｎｃｅｆｏｒｔｈｅｓｅｎｅｔｗｏｒｋｓ．ＢｅｃａｕｓｅＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｗｅｌｌｓｉｍｕｌａｔｅｔｈｅｅｃｏｌｏｇｉｃａｌｓｙｓｔｅｍ,ｍａｎｙｓｔｕｄｉｅｓａｒｅｃｏｎｃｅｎｔｒａｔｅｄｏｎｔｈ… 相似文献
13.
By using comparison theorem and constructing suitable Lyapunov functional, we study the following periodic Lotka–Volterra model with M-predators and N-preys by pure-delay type
14.
We prove the following statement:
Theorem 1.
Let
E and
be an arbitrary infinite-dimensional Banach space and a continuous mapping, respectively. Then, for every
and > 0, there exists a continuous mapping
such that
15.
ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎｘｎ 1=ｘｎ(ａ ｂｘｎ)ｘｎ- 1, ｎ=0 ,1 ,2 ,… ,(1 )ｗｈｅｒｅａ ,ｂ∈ [0 ,∞ )ｗｉｔｈａ ｂ>0 (2 )ａｎｄｗｈｅｒｅｔｈｅｉｎｉｔｉａｌｖａｌｕｅｓｘ- 1ａｎｄｘ0 ａｒｅａｒｂｉｔｒａｒｙｐｏｓｉｔｉｖｅｎｕｍｂｅｒｓ.Ｅｑ .(1 )ｉｓｒｅｇａｒｄｅｄａｓａｇｅｎｅｒａｌｉｚｅｄＬｙｎｅｓｓｅｑｕａｔｉｏｎｂｙＧ .Ｌａｄａｓｉｎ [1 ] .Ｏｂｖｉｏｕｓｌｙ ,ｕｎｄｅｒｃｏｎｄｉｔｉｏｎ (2 ) ,… 相似文献
16.
李永昆 《应用数学和力学(英文版)》1999,20(5):579-584
ＩｎｔｒｏｄｕｃｔｉｏｎＡｔｐｒｅｓｅｎｔ,ｔｈｅｒｅａｒｅｏｎｌｙａｆｅｗｐａｐｅｒｓ［１～３］ｈａｖｉｎｇｂｅｎｐｕｂｌｉｓｈｅｄｏｎｔｈｅｇｌｏｂａｌｅｘｉｓｔｅｎｃｅｏｆｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｆｏｒｎｅｕｔｒａｌｄｅｌａｙｐｏｐｕ... 相似文献
17.
18.
We investigate the dynamics of the semiflow φ induced on H01(Ω) by the Cauchy problem of the semilinear parabolic equation
19.
Georgy M. Kobelkov 《Journal of Mathematical Fluid Mechanics》2007,9(4):588-610
For the system of equations describing the large-scale ocean dynamics, an existence and uniqueness theorem is proved “in the
large”. This system is obtained from the 3D Navier–Stokes equations by changing the equation for the vertical velocity component
u
3 under the assumption of smallness of a domain in z-direction, and a nonlinear equation for the density function ρ is added. More precisely, it is proved that for an arbitrary
time interval [0, T], any viscosity coefficients and any initial conditions
20.
We study the limit of the hyperbolic–parabolic approximation
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