共查询到20条相似文献，搜索用时 31 毫秒
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
2.
１ＰｒｏｂｌｅｍｓａｎｄＭａｉｎＲｅｓｕｌｔｓＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｔｕｄｙｔｈｅｎｏｎｌｉｎｅａｒｖｉｂｒａｔｉｏｎｓｏｆｉｎｆｉｎｉｔｅｒｏｄｓｗｉｔｈｖｉｓｃｏｅｌａｓｔｉｃｉｔｙ．Ｔｈｅｃｏｎｓｔｉｔｕｔｉｏｎｌａｗｏｆｔｈｅｒｏｄｓ... 相似文献
3.
Using an Orlicz–Sobolev Space setting, we consider an eigenvalue problem for a system of the form
We prove that the solution to a suitable minimizing problem, with a restriction, yields a solution to this problem for a certain λ. The differential operators involved lack homogeneity and in addition the Orlicz–Sobolev spaces needed may not be reflexive and the corresponding functional in the minimization problem is in general neither everywhere defined nor a fortiori C
1. 相似文献
4.
ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｒｅｃｅｎｔｙｅａｒｓ,ｗｉｔｈａｌｏｔｏｆａｐｐｌｉｃａｔｉｏｎｓｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｓ,ｍａｎｙａｕｔｈｏｒｓ［１～３］ａｒｅｉｎｔｅｒｅｓｔｅｄｉｎｔｈｅｒｅｓｅａｒｃｈｏｆｔｈｅｓｔｒｕｃｔｕｒｅａｎｄｐｅｒｆｏｒｍａｎｃｅｆｏｒｔｈｅｓｅｎｅｔｗｏｒｋｓ．ＢｅｃａｕｓｅＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｗｅｌｌｓｉｍｕｌａｔｅｔｈｅｅｃｏｌｏｇｉｃａｌｓｙｓｔｅｍ,ｍａｎｙｓｔｕｄｉｅｓａｒｅｃｏｎｃｅｎｔｒａｔｅｄｏｎｔｈ… 相似文献
5.
ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ,ｔｈｅｏｒｅｔｉｃａｌａｎｄａｐｌｉｅｄｓｔｕｄｉｅｓｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｈａｖｅｂｅｎｔｈｅｎｅｗｆｏｃｕｓｏｆｓｔｕｄｉｅｓｉｎｔｈｅｗｏｒｌｄ．Ｉｔｉｓｗｅｌ＿ｋｎｏｗｎｔｈａｔｑｕ... 相似文献
6.
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
7.
Let u, p be a weak solution of the stationary Navier-Stokes equations in a bounded domain N, 5N . If u, p satisfy the additional conditions |
相似文献
8.
The rank 1 convexity of stored energy functions corresponding to isotropic and physically linear elastic constitutive relations
formulated in terms of generalized stress and strain measures [Hill, R.: J. Mech. Phys. Solids 16, 229–242 ( 1968)] is analyzed. This class of elastic materials contains as special cases the stress-strain relationships based on Seth strain
measures [Seth, B.: Generalized strain measure with application to physical problems. In: Reiner, M., Abir, D. (eds.) Second-order
Effects in Elasticity, Plasticity, and Fluid Dynamics, pp. 162–172. Pergamon, Oxford, New York ( 1964)] such as the St.Venant–Kirchhoff law or the Hencky law. The stored energy function of such materials has the form
where is a function satisfying , and α
1, α
2, α
3 are the singular values of the deformation gradient . Two general situations are determined under which is not rank 1 convex: (a) if (simultaneously) the Hessian of W at α is positive definite, , and f is strictly monotonic, and/or (b) if f is a Seth strain measure corresponding to any . No hypotheses about the range of f are necessary.
相似文献
9.
Our aim is to establish some sufficient conditions for the oscillation of the second-order quasilinear neutral functional
dynamic equation
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( p(t)( [ y(t) + r(t)y( t(t) ) ]D )g )D + f( t,y( d(t) ) = 0, t ? [ t0,￥ )\mathbbT, {\left( {p(t){{\left( {{{\left[ {y(t) + r(t)y\left( {\tau (t)} \right)} \right]}^\Delta }} \right)}^\gamma }} \right)^\Delta } + f\left( {t,y\left( {\delta (t)} \right)} \right. = 0,\quad t \in {\left[ {{t_0},\infty } \right)_\mathbb{T}}, 相似文献
10.
The thermal decomposition of CS 2 highly diluted in Ar was studied behind reflected shock waves by monitoring time-dependent absorption profiles of S( 3P) and S( 1D) using atomic resonance absorption spectroscopy (ARAS). The rate coefficient of the reaction: |
相似文献
11.
We consider the initial boundary-value problem for a system of quasilinear partial functional differential equations of the
first order
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$ {*{20}{c}} {{\partial_t}{z_i}\left( {t,x} \right) + \sum\limits_{j = 1}^n {{\rho_{ij}}\left( {t,x,V\left( {z;t,x} \right)} \right){\partial_{{x_j}}}{z_i}\left( {t,x} \right) = {G_i}\left( {t,x,V\left( {z;t,x} \right)} \right),} } \hfill & {1 \leq i \leq m,} \hfill \\ $ \begin{array}{*{20}{c}} {{\partial_t}{z_i}\left( {t,x} \right) + \sum\limits_{j = 1}^n {{\rho_{ij}}\left( {t,x,V\left( {z;t,x} \right)} \right){\partial_{{x_j}}}{z_i}\left( {t,x} \right) = {G_i}\left( {t,x,V\left( {z;t,x} \right)} \right),} } \hfill & {1 \leq i \leq m,} \hfill \\ \end{array} 相似文献
12.
This paper considers the second-order differential difference equation with the constant delay > 0 and the piecewise constant function
with Differential equations of this type occur in control systems, e.g., in heating systems and the pupil light reflex, if the controlling function is determined by a constant delay > 0 and the switch recognizes only the positions on [ f(>) = a] and off [ f(>) = b], depending on a constant threshold value . By the nonsmooth nonlinearity the differential equation allows detailed analysis. It turns out that there is a rich solution structure. For a fixed set of parameters a, b, , , infinitely many different periodic orbits of different minimal periods exist. There may be coexistence of three asymptotically stable periodic orbits (multistability of limit cycles). Stability or instability of orbits can be proven. 相似文献
13.
In recent years,there is a wide interest in Sarkovskii’s theorem and related study.According to Sarkovskii’s theorem,if the continuous self-map f of the closed interval has a3-periodic orbit,then f must has an n-periodic orbit for any positive integer n.But f can nothave all n-periodic orbits for some n.Example.LetEvidently f has only one kind of3-periodic orbit in the two kinds of3-periodic orbits,whichexplains that it isn’t far enough to uncover the relation between periodic orbits by theinformation which Sarkovskii’s theorem has offered.In this paper,we raise the concept oftype of periodic orbits,and give a feasible algorithm which decldes the relation ofimplication between the two kinds of periodic orbits. 相似文献
14.
We establish a general weak* lower semicontinuity result in the space BD(Ω) of functions of bounded deformation for functionals
of the form
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$ {ll} \,\mathcal{F}(u) := &\int_\Omega f (x, \mathcal{E} u) \;{\rm d} x + \int_\Omega f^\infty \left( x, \frac{{\rm d} E^s u}{{\rm d} |{E^s u}|} \right) \;{\rm d} |{E^s u}| \\ &+ \int_{\partial \Omega} f^\infty \left( x, u|_{\partial \Omega} \odot n_\Omega \right) \;{\rm d} \mathcal{H}^{d-1}, \qquad u \in {\rm BD}(\Omega). $ \begin{array}{ll} \,\mathcal{F}(u) := &\int_\Omega f (x, \mathcal{E} u) \;{\rm d} x + \int_\Omega f^\infty \left( x, \frac{{\rm d} E^s u}{{\rm d} |{E^s u}|} \right) \;{\rm d} |{E^s u}| \\ &+ \int_{\partial \Omega} f^\infty \left( x, u|_{\partial \Omega} \odot n_\Omega \right) \;{\rm d} \mathcal{H}^{d-1}, \qquad u \in {\rm BD}(\Omega). \end{array} 相似文献
15.
This paper deals with connected branches of nonstationary periodic trajectories of Hamilton equations
emanating from the degenerate stationary point
for H being the generalized Hénon-Heiles (HH) Hamiltonian:
or the generalized Yang-Mills (YM) Hamiltonian:
The existence of such branches has been proved. Minimal periods of searched trajectories near x0 have been described. 相似文献
16.
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
A set of easily verifiable sufficient conditions are obtained for the existence and global attractivity of a unique positive almost periodic solution of the above model, which improve and generalize some known results. 相似文献
17.
The fundamental theorem of surface theory classically asserts that, if a field of positive-definite symmetric matrices ( a
αβ
) of order two and a field of symmetric matrices ( b
αβ
) of order two together satisfy the Gauss and Codazzi-Mainardi equations in a simply connected open subset ω of , then there exists an immersion such that these fields are the first and second fundamental forms of the surface , and this surface is unique up to proper isometries in . The main purpose of this paper is to identify new compatibility conditions, expressed again in terms of the functions a
αβ
and b
αβ
, that likewise lead to a similar existence and uniqueness theorem. These conditions take the form of the matrix equation where A
1 and A
2 are antisymmetric matrix fields of order three that are functions of the fields ( a
αβ
) and ( b
αβ
), the field ( a
αβ
) appearing in particular through the square root U of the matrix field The main novelty in the proof of existence then lies in an explicit use of the rotation field R that appears in the polar factorization of the restriction to the unknown surface of the gradient of the canonical three-dimensional extension of the unknown immersion . In this sense, the present approach is more “geometrical” than the classical one. As in the recent extension of the fundamental
theorem of surface theory set out by S. M ardare [20–22], the unknown immersion is found in the present approach to exist in function spaces “with little regularity”, such as , p > 2. This work also constitutes a first step towards the mathematical justification of models for nonlinearly elastic shells
where rotation fields are introduced as bona fide unknowns. 相似文献
18.
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 {a n}
n=0
∞
, {β n}
n=0
∞
be two real sequences in (0, 1) satisfying: ; Assume that {u n}
n=0
∞
and {υ n}
n=0
∞
are two sequences in X satisfying ‖u n‖ = 0(α n) and ‖υ n‖ → 0 as n → ∞. For arbitrary x 0 ε X, the iteration sequence {x n} is defined by Moreover, suppose that {Sx n} and {Sy n} are bounded, then {x n} converges strongly to the unique fixed point of S. 相似文献
19.
We study the dynamics and regularity of level sets in solutions of the semilinear parabolic equation where is a ring-shaped domain, a and μ are given positive constants, is the Heaviside maximal monotone graph: if s > 0, if s < 0. Such equations arise in climatology (the so-called Budyko energy balance model), as well as in other contexts such as
combustion. We show that under certain conditions on the initial data the level sets are n-dimensional hypersurfaces in the ( x, t)-space and show that the dynamics of Γ
μ
is governed by a differential equation which generalizes the classical Darcy law in filtration theory. This differential
equation expresses the velocity of advancement of the level surface Γ
μ
through spatial derivatives of the solution u. Our approach is based on the introduction of a local set of Lagrangian coordinates: the equation is formally considered
as the mass balance law in the motion of a fluid and the passage to Lagrangian coordinates allows us to watch the trajectory
of each of the fluid particles. 相似文献
20.
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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