共查询到20条相似文献,搜索用时 29 毫秒
1.
I. Dobson 《Journal of Nonlinear Science》1993,3(1):307-327
Summary Engineering and physical systems are often modeled as nonlinear differential equations with a vector λ of parameters and operated
at a stable equilibrium. However, as the parameters λ vary from some nominal value λ0, the stability of the equilibrium can be lost in a saddle-node or Hopf bifurcation. The spatial relation in parameter space
of λ0 to the critical set of parameters at which the stable equilibrium bifurcates determines the robustness of the system stability
to parameter variations and is important in applications. We propose computing a parameter vector λ* at which the stable equilibrium bifurcates which is locally closest in parameter space to the nominal parameters λ0. Iterative and direct methods for computing these locally closest bifurcations are described. The methods are extensions
of standard, one-parameter methods of computing bifurcations and are based on formulas for the normal vector to hypersurfaces
of the bifurcation set. Conditions on the hypersurface curvature are given to ensure the local convergence of the iterative
method and the regularity of solutions of the direct method. Formulas are derived for the curvature of the saddle node bifurcation
set. The methods are extended to transcritical and pitchfork bifurcations and parametrized maps, and the sensitivity to λ0 of the distance to a closest bifurcation is derived. The application of the methods is illustrated by computing the proximity
to the closest voltage collapse instability of a simple electric power system. 相似文献
2.
Tetsutaro Shibata 《Annales Henri Poincare》2008,9(6):1217-1227
We consider the nonlinear eigenvalue problem
,
where f(u) = u
p
+ h(u) (p > 1) and λ > 0 is a parameter. Typical example of h(u) is with 1 < q < (p+ 1)/2. We establish the precise asymptotic formula for L
m
-bifurcation branch λ = λ
m
(α) of positive solutions as α → ∞, where α > 0 is the L
m
-norm of the positive solution associated with .
Submitted: September 27, 2007. Accepted: May 28, 2008. 相似文献
3.
Global stability of a virus dynamics model with intracellular delay and CTL immune response 下载免费PDF全文
In this paper, the global stability of a virus dynamics model with intracellular delay, Crowley–Martin functional response of the infection rate, and CTL immune response is studied. By constructing suitable Lyapunov functions and using LaSalles invariance principle, the global dynamics is established; it is proved that if the basic reproductive number, R0, is less than or equal to one, the infection‐free equilibrium is globally asymptotically stable; if R0 is more than one, and if immune response reproductive number, R0, is less than one, the immune‐free equilibrium is globally asymptotically stable, and if R0 is more than one, the endemic equilibrium is globally asymptotically stable. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
4.
Philip Korman 《NoDEA : Nonlinear Differential Equations and Applications》2008,15(3):335-346
The problem (where B is a unit ball in R
n
)
, with , is known to have a curve of positive solutions bifurcating from infinity at λ = λ1, the principal eigenvalue. It turns out that a similar situation may occur, when g(u) is oscillatory for large u, instead of being small. In case n = 1, we can also prove existence of infinitely many solutions at λ = λ1 on this curve. Similarly, we consider oscillatory bifurcation from zero.
相似文献
5.
We consider the problem −Δu=|u|
p−1u+λu in Ω with
on δΩ, where Ω is a bounded domain inR
N
,p=(N+2)/(N−2) is the critical Sobolev exponent,n the outward pointing normal and λ a constant. Our main result is that if Ω is a ball inR
N
, then for every λ∈R the problem admits infinitely many solutions. Next we prove that for every bounded domain Ω inR
3, symmetric with respect to a plane, there exists a constant μ>0 such that for every λ<μ this problem has at least one non-trivial
solution.
This work was supported by the Paris VI-Leiden exchange program
Supported by the Netherlands organisation for scientific research NWO, under number 611-306-016. 相似文献
6.
The Riemann–Silberstein–Majorana–Oppenheimer complex approach to the Maxwell electrodynamics is investigated within the matrix
formalism. Within the squaring procedure we construct four types of formal solutions of the Maxwell equations on the base
of scalar D’Alembert solutions. General problem of separating physical electromagnetic solutions in the linear space λ0Ψ0 + λ1Ψ1 + λ2Ψ2 + λ3Ψ3 is investigated, the Maxwell equations reduce to a new form including parameters λ
a
. Several particular cases, plane waves and cylindrical waves, are considered in detail. Possible extension of the technique
to a curved space–time models is discussed. 相似文献
7.
Xianling Fan Shao-Gao Deng 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):255-271
We study the existence and multiplicity of positive solutions for the inhomogeneous Neumann boundary value problems involving
the p(x)-Laplacian of the form
where Ω is a bounded smooth domain in , and p(x) > 1 for with and φ ≢ 0 on ∂Ω. Using the sub-supersolution method and the variational method, under appropriate assumptions on f, we prove that, there exists λ* > 0 such that the problem has at least two positive solutions if λ = λ*, has at least one positive solution if λ = λ*, and has no positive solution if λ = λ*. To prove the result we establish a special strong comparison principle for the Neumann problems.
The research was supported by the National Natural Science Foundation of China 10371052,10671084). 相似文献
8.
T. I. Seidman S. A. Avdonin S. A. Ivanov 《Journal of Fourier Analysis and Applications》2000,6(3):233-254
Under a suitable sparsity condition on the exponents Λ=(λk=τk+iσk), it is shown that the individual terms
can be obtained from observation of the L2 function
through the ‘window’ t∈[0, δ]—with an l2 estimate (uniform for such Λ) asymptotically as t, δ→0. Some applications are given to control theory for partial differential
equations. 相似文献
9.
Marcello Lucia 《Calculus of Variations and Partial Differential Equations》2006,26(3):313-330
We consider the equation
If Ω is of class C
2, we show that this problem has a non-trivial solution u
λ for each λ ∊ (8 π, λ*). The value λ* depends on the domain and is bounded from below by 2 j
0
2 π, where j
0 is the first zero of the Bessel function of the first kind of order zero (λ*≥ 2 j
0
2 π > 8 π). Moreover, the family of solution u
λ blows-up as λ → 8 π. 相似文献
10.
Meng Wang 《数学学报(英文版)》2012,28(1):145-170
We study the self-dual Chern-Simons Higgs equation on a compact Riemann surface with the Neumann boundary condition.In the previous paper,we show that the Chern-Simons Higgs equation with parameter λ0 has at least two solutions(uλ1,uλ2) for λ sufficiently large,which satisfy that uλ1→u0 almost everywhere as λ→∞,and that uλ2→∞ almost everywhere as λ→∞,where u 0 is a(negative) Green function on M.In this paper,we study the asymptotic behavior of the solutions as λ→∞,and prove that uλ2-uλ2 converges to a solution of the Kazdan-Warner equation if the geodesic curvature of the boundary M is negative,or the geodesic curvature is nonpositive and the Gauss curvature is negative where the geodesic curvature is zero. 相似文献
11.
In this paper, a delayed HIV/AIDS epidemic model with saturation incidence is proposed and analyzed. The equilibria and their stability are investigated. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. It is found that if the threshold R 0<1, then the disease-free equilibrium is globally asymptotically stable, and if the threshold R 0>1, the system is permanent and the endemic equilibrium is asymptotically stable under certain conditions. 相似文献
12.
Yukihiko Nakata 《Journal of Mathematical Analysis and Applications》2011,375(1):14-27
In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection R0 and for CTL response R1 such that R1<R0. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if R0?1, an infected equilibrium without immune response is globally asymptotically stable if R1?1<R0 and an infected equilibrium with immune response is globally asymptotically stable if R1>1. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if R1>1. 相似文献
13.
Sandra Lucente 《Annali dell'Universita di Ferrara》2006,52(2):317-335
Abstract In this paper, we deal with some global existence results for the large data smooth solutions of the Cauchy Problem associated
with the semilinear weakly hyperbolic equations
Here u=u(x,t),
and for λ≥ 0, aλ≥ 0 is a continuous function that behaves as |t–t0|λ close to some t0>0. We conjecture the existence of a critical exponent pc(λ1,λ2,n) such that for p≤ pc(λ1,λ2,n) a global existence theorem holds. For suitable λ1,λ2,n, we recall some known results and add new ones.
Keywords: Critical exponents for semilinear equations, Weak hyperbolicity 相似文献
14.
V. P. Il'in 《Journal of Mathematical Sciences》1996,78(2):142-180
An anisotropic Sobolev and Nikol'skii-Besov space on a domain G is determined by its integro-differential (shortly, ID) parameters.
On the other hand, the geometry of G is characterized by the set Λ(G) of all vectors λ=(λ1,..., λn) such that G satisfies the λ-horn condition. We study the dependence of the totality of possible embeddings upon the set
Λ(G) and theID-parameters of the space. We consider only embeddings with q≥pi, where pi are the integral parameters of the space and q is the integral embedding parameter. For a given space, we introduce its initial
matrix A0 determined by theID-parameters. A0 turns out to be a Z-matrix. On the basis of a natural classification of Z-matrices, a classification of anisotropic spaces
is introduced. This classification allows one to restate the existence of an embedding with q≥pi in terms of certain specific properties of A0. Let A0 be a nondegenerate M-matrix. Any vector λ∈Λ(G) gives rise to a certain set of admissible values of the embedding parameters.
We call λ optimal if this set is the largest possible. It turns out that the optimal vector λ
G
*
is determined by Λ(G) and A0, and may be found by a linear optimization procedure. The following cases are possible: a)
, b)
, c) λ
G
*
does not exist. In case a) the set of admissible values of the embedding parameters is the biggest, while in case c) no embeddings
with q≥pi exist. In case b) the so-called saturation phenomenon occurs, i.e., certain variations of some differential parameters of
the space do not change the set of admissible values of the embedding parameters. The latter fact has some applications to
the problem of extension of all functions belonging to the given space from G to En. Bibliography: 20 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 201, 1992, pp. 22–94.
Translated by A. A. Mekler. 相似文献
15.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |
16.
Dr. Wolfgang Watzlawek 《Monatshefte für Mathematik》1976,81(3):225-233
Cauchy's problem for the equationu
xx
+x
–1
u
x
=u
t
( real) was discussed byD. Colton if –1,–2,–3, ... Now existence and uniqueness theorems and representations of the solutions are given for the cases =–1,–2, –3,... The methods ofD. Colton and of this paper are different but the results are similar. 相似文献
17.
We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0?1, then the disease-free equilibrium is globally asymptotically stable; if R0>1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals. 相似文献
18.
M. A. Freedman 《Semigroup Forum》1987,36(1):117-126
In [2], Crandall and Evans show existence of mild solution to an abstract Cauchy Problem: u′(t)+Au(t)∋f(t), 0≤t≤T, u(0)=x0, where A is an accretive operator in a general Banach space X and f ε L1(0,T;X). Their method involves proving convergence in the L∞-norm of a sequence of step function approximations αn(σ, τ) to the solution of a first order partial differential equation. We consider a more general Cauchy Problem and show
a.e. existence of mild solution by proving convergence of the step functions αn(σ, τ) in the L1-norm. Fundamental to the proof is a nonhomogeneous random walk in the plane. 相似文献
19.
Tiziana Giorgi Robert Smits 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,124(1):600-618
We consider the principal eigenvalue λ
1Ω(α) corresponding to Δu = λ (α) u in
W, \frac?u?v = au \Omega, \frac{\partial u}{\partial v} = \alpha u on ∂Ω, with α a fixed real, and W ì Rn\Omega \subset {\mathcal{R}}^n a C
0,1 bounded domain. If α > 0 and small, we derive bounds for λ
1Ω(α) in terms of a Stekloff-type eigenvalue; while for α > 0 large we study the behavior of its growth in terms of maximum curvature.
We analyze how domain monotonicity of the principal eigenvalue depends on the geometry of the domain, and prove that domains
which exhibit domain monotonicity for every α are calibrable. We conjecture that a domain has the domain monotonicity property for some α if and only if it is calibrable. 相似文献
20.
Sergio Campanato 《Annali di Matematica Pura ed Applicata》1967,75(1):261-276
Sommario Si dimostrano alcune maggiorazioni che si possono riguardare come una generalizzazione della classica maggiorazione di Poincaré.
Se ne deducono, a scopo illustrativo, delle maggiorazioni interpolatorie per funzioni u ∈H
λ
m, p
e u ∈ H2, p ∩L
P0, λ.
Questo lavoro è stato parzialmente finanziato da ? the United States Air Force ? in continuazione del contratto AF EOAR, grant
65-42. 相似文献