共查询到20条相似文献,搜索用时 46 毫秒
1.
Tetsutaro Shibata 《Journal d'Analyse Mathématique》1995,66(1):277-294
The nonlinear two-parameter Sturm-Liouville problemu
"+μg(u)=λf(u) is studied for μ, λ>0. By using Ljusternik-Schnirelman theory on the general level set developed by Zeidler, we shall show
the existence of ann-th variational eigenvalue λ=λn(μ). Furthermore, for specialf andg, the asymptotic formula of λ1(μ)) as μ→∞ is established. 相似文献
2.
Kwang C. Shin 《Potential Analysis》2011,35(2):145-174
For integers m ≥ 3 and 1 ≤ ℓ ≤ m − 1, we study the eigenvalue problems − u
″(z) + [( − 1)ℓ(iz)
m
− P(iz)]u(z) = λu(z) with the boundary conditions that u(z) decays to zero as z tends to infinity along the rays
argz=-\fracp2±\frac(l+1)pm+2\arg z=-\frac{\pi}{2}\pm \frac{(\ell+1)\pi}{m+2} in the complex plane, where P is a polynomial of degree at most m − 1. We provide asymptotic expansions of the eigenvalues λ
n
. Then we show that if the eigenvalue problem is PT\mathcal{PT}-symmetric, then the eigenvalues are all real and positive with at most finitely many exceptions. Moreover, we show that when
gcd(m,l)=1\gcd(m,\ell)=1, the eigenvalue problem has infinitely many real eigenvalues if and only if one of its translations or itself is PT\mathcal{PT}-symmetric. Also, we will prove some other interesting direct and inverse spectral results. 相似文献
3.
Tetsutaro Shibata 《Journal d'Analyse Mathématique》2001,83(1):109-120
We consider the perturbed elliptic Sine-Gordon equation on an interval-u″t+γsinu(t)=μf(u(t)),t ∈I := (-T, T),u(t) > 0,t ∈I,u(±T)=0 where λ, μ>0 are parameters andT>0 is a constant. By applying variational methods subject to the constraint depending on λ, we obtain eigenpairs (μ,u)=(μ(λ),u
λ) which solve this eigenvalue problem for a given λ>0. Then we study the asymptotic behavior ofu
λ and μ(λ) as λ→∞. Especially, we study the location of interior transition layers ofu
λ as λ→∞.
This research has been supported by the Japan Society for the Promotion of Science. 相似文献
4.
Caisheng Chen 《Journal of Evolution Equations》2006,6(1):29-43
In this paper, we study the global existence, L∞ estimates and decay estimates of solutions for the quasilinear parabolic system ut = div (|∇ u|m ∇ u) + f(u, v), vt = div (|∇ v|m ∇ v) + g(u,v) with zero Dirichlet boundary condition in a bounded domain Ω ⊂ RN. In particular, we find a critical value for the existence and nonexistence of global solutions to the equation ut = div (|∇ u|m ∇ u) + λ |u|α - 1 u. 相似文献
5.
Let (v,u×c,λ)-splitting BIBD denote a (v,u×c,λ)-splitting balanced incomplete block design of order v with block size u×c and index λ. Necessary conditions for the existence of a (v,u×c,λ)-splitting BIBD are v≥uc, λ(v−1)≡0 (mod c(u−1)) and λ
v(v−1)≡0 (mod (c
2
u(u−1))). We show in this paper that the necessary conditions for the existence of a (v,3×3,λ)-splitting BIBD are also sufficient with possible exceptions when (1) (v,λ)∈{(55,1),(39,9k):k=1,2,…}, (2) λ≡0 (mod 54) and v≡0 (mod 2). We also show that there exists a (v,3×4,1)-splitting BIBD when v≡1 (mod 96). As its application, we obtain a new infinite class of optimal 4-splitting authentication codes. 相似文献
6.
Eugenia O’Reilly-Regueiro 《Designs, Codes and Cryptography》2010,56(1):61-63
It has been shown that if a (v, k, λ)-symmetric design with λ ≤ 3 admits a flag-transitive automorphism group G which acts primitively on points, then G must be of affine or almost simple type. Here we extend the result to λ = 4. 相似文献
7.
Gerd Grubb 《Israel Journal of Mathematics》1971,10(1):32-95
The paper treats coerciveness inequalities (of the form Re(Au, u)≧c ‖u‖
s
2
−λ ‖u‖
0
2
,c>0,λ ∈ R) and semiboundedness inequalities (of the form Re (Au, u)≧−λ ‖u‖2) for the general boundary problems associated with an elliptic 2m-order differential operatorA in a compactn-dimensional manifold with boundary. In particular, we study the normal pseudo-differential boundary conditions, for which
we determine necessary and sufficient conditions for coerciveness withs=m, and for semiboundedness with ‖u‖ = ‖u‖m, in explicit form. 相似文献
8.
Joaquim Bruna 《Journal of Fourier Analysis and Applications》2006,12(1):71-82
We show that the discrete translation parameter sets Λ ⊂ ℝ for which some φ ∈ L1(ℝ) exists such that the translates φ(x − λ), λ ∈ Λ, span L1(ℝ) are exactly the uniqueness sets for certain quasianalytic classes, and give explicit constructions of such generators
φ. We also consider a similar situation for affine systems of the type φ(μx − λ), μ ∈ Γ, λ ∈ Λ. 相似文献
9.
Gerhard Gerlich 《Journal of Geometry》2005,82(1-2):63-70
In order to identify multipliers of abelian (υ, k, λ)-difference sets the First and the Second Multiplier Theorem of Hall, Ryser and Chowla, resp. of Hall and Menon, need
a divisor m of n = k − λ that is coprime to υ. Moreover, both theorems require that m > λ. The famous Multiplier Conjecture asserts that the restriction m > λ is not necessary.
We present a generalization of the Second Multiplier Theorem where m is not necessarily coprime to υ. Here the requirement that m > λ generalizes to the condition m/(υ, m) > λ. This gives rise to a generalized Multiplier Conjecture which asserts that this condition is not necessary. We disprove
this conjecture by showing that there exist counterexamples. 相似文献
10.
Evangelos A. Latos Dimitrios E. Tzanetis 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(2):137-151
We investigate the behaviour of solution u = u(x, t; λ) at λ = λ* for the non-local porous medium equation ${u_t = (u^n)_{xx} + {\lambda}f(u)/({\int_{-1}^1} f(u){\rm d}x)^2}We investigate the behaviour of solution u = u(x, t; λ) at λ = λ* for the non-local porous medium equation ut = (un)xx + lf(u)/(ò-11 f(u)dx)2{u_t = (u^n)_{xx} + {\lambda}f(u)/({\int_{-1}^1} f(u){\rm d}x)^2} with Dirichlet boundary conditions and positive initial data. The function f satisfies: f(s),−f ′ (s) > 0 for s ≥ 0 and s
n-1
f(s) is integrable at infinity. Due to the conditions on f, there exists a critical value of parameter λ, say λ*, such that for λ > λ* the solution u = u(x, t; λ) blows up globally in finite time, while for λ ≥ λ* the corresponding steady-state problem does not have any solution.
For 0 < λ < λ* there exists a unique steady-state solution w = w(x; λ) while u = u(x, t; λ) is global in time and converges to w as t → ∞. Here we show the global grow-up of critical solution u* = u(x, t; λ*) (u* (x, t) → ∞, as t → ∞ for all x ? (-1,1){x\in(-1,1)}. 相似文献
11.
LetA be a (nonlinear) operator in an ordered linear spaceX with resolvantJ
λ=(I+λA)-1 well-defined onX and non-decreasing for any smallλ>0, andν ∈X. We define sub-potential ofν with respect toA, as anyu ∈X satisfyingu≧J
λ(u+λv) for smallλ>0, and show that this coincides with the notion of sub-solution of the equationAu∋ν in some abstract cases where such notion is defined in a natural way. At last, we give some general properties of sub-potentials,
in particular an extension of the Kato inequality whenX is a lattice, and, for good set of constraintsU, existence of a largest solution for the control problem:u ∈U andu is a sub-potential ofν with respect toA.
相似文献
12.
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
13.
Let Φ(u × v, k, λ
a
, λ
c
) denote the largest possible size among all 2-D (u × v, k, λ
a
, λ
c
)-OOCs. In this paper, the exact value of Φ(u × v, k, λ
a
, k − 1) for λ
a
= k − 1 and k is determined. The case λ
a
= k − 1 is a generalization of a result in Yang (Inform Process Lett 40:85–87, 1991) which deals with one dimensional OOCs namely, u = 1. 相似文献
14.
Yutaka Hiramine 《Designs, Codes and Cryptography》2010,56(1):21-33
It is well known that there exists a transversal design TDλ[k; u] admitting a class regular automorphism group U if and only if there exists a generalized Hadamard matrix GH(u, λ) over U. Note that in this case the resulting transversal design is symmetric by Jungnickel’s result. In this article we define a
modified generalized Hadamard matrix and show that transversal designs which are not necessarily symmetric can be constructed from these under a modified condition
similar to class regularity even if it admits no class regular automorphism group. 相似文献
15.
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
16.
Tetsutaro Shibata 《Annali di Matematica Pura ed Applicata》2003,182(2):211-229
We consider the two-parameter nonlinear eigenvalue problem?−Δu = μu − λ(u + u
p
+ f(u)), u > 0 in Ω, u = 0 on ∂Ω,?where p>1 is a constant and μ,λ>0 are parameters. We establish the asymptotic formulas for the variational eigencurves λ=λ(μ,α) as
μ→∞, where α>0 is a normalizing parameter. We emphasize that the critical case from a viewpoint of the two-term asymptotics
of the eigencurve is p=3. Moreover, it is shown that p=5/3 is also a critical exponent from a view point of the three-term asymptotics when Ω is a ball or an annulus. This sort
of criticality for two-parameter problems seems to be new.
Received: February 9, 2002; in final form: April 3, 2002?Published online: April 14, 2003 相似文献
17.
Flávio Dickstein Miguel Loayza 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,24(10):1-23
We consider the Cauchy problem for the weakly coupled parabolic system ∂
t
w
λ−Δ w
λ = F(w
λ) in R
N
, where λ > 0, w
λ = (u
λ, v
λ), F(w
λ) = (v
λ
p
, u
λ
q
) for some p, q ≥ 1, pq > 1, and
wl(0) = (lj1, l\fracq+1p+1j2)w_{\lambda}(0) = ({\lambda}{\varphi}_1, {\lambda}^{\frac{q+1}{p+1}}{\varphi}_2), for some nonnegative functions φ1, φ2
?\in
C
0(R
N
). If (p, q) is sub-critical or either φ1 or φ2 has slow decay at ∞, w
λ blows up for all λ > 0. Under these conditions, we study the blowup of w
λ for λ small. 相似文献
18.
K. J. Horadam 《组合设计杂志》2000,8(5):330-346
A semiregular relative difference set (RDS) in a finite group E which avoids a central subgroup C is equivalent to a cocycle which satisfies an additional condition, called orthogonality. However the basic equivalence relation, cohomology, on cocycles, does not preserve orthogonality, leading to the perception that orthogonality is essentially a combinatorial property. We show this perception is false by discovering a natural atomic structure within cohomology classes, which discriminates between orthogonal and non‐orthogonal cocycles. This atomic structure is determined by an action we term the shift action of the group G = E/C on cocycles, which defines a stronger equivalence relation on cocycles than cohomology. We prove that for each triple (C, E, G), the set of equivalence classes of semiregular RDS in E relative to C is in one to one correspondence with the set of shift‐orbits of the (Aut(C) × Aut(G))‐orbits of orthogonal cocycles. This determines a new algorithm for detecting and classifying central semiregular RDS. We demonstrate it, and propose a 7‐parameter classification scheme for equivalence classes of central semiregular relative difference sets. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 330–346, 2000 相似文献
19.
We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II1. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues
and eigenfunctions of the problems asm→−0.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999. 相似文献
20.
We consider the nonlinear eigenvalue problem −Δu=λ f(u) in Ω u=0 on ∂Ω, where Ω is a ball or an annulus in RN (N ≥ 2) and λ > 0 is a parameter. It is known that if λ >> 1, then the corresponding positive solution uλ develops boundary layers under some conditions on f. We establish the asymptotic formulas for the slope of the boundary layers of uλ with the exact second term and the ‘optimal’ estimate of the third term. 相似文献