共查询到20条相似文献,搜索用时 15 毫秒
1.
Zuodong Yang 《Journal of Mathematical Analysis and Applications》2003,288(2):768-783
We show the existence of entire explosive positive radial solutions for quasilinear elliptic systems div(|∇u|m−2∇u)=p(|x|)g(v), div(|∇v|n−2∇v)=q(|x|)f(u) on , where f and g are positive and non-decreasing functions on (0,∞) satisfying the Keller-Osserman condition. 相似文献
2.
Alan V. Lair 《Journal of Mathematical Analysis and Applications》2010,365(1):103-449
We prove that the elliptic system Δu=p(|x|)vα, Δv=q(|x|)uβ on Rn (n?3) where 0<α?1, 0<β?1, and p and q are nonnegative continuous functions has a nonnegative entire radial solution satisfying lim|x|→∞u(x)=lim|x|→∞v(x)=∞ if and only if the functions p and q satisfy
3.
R. Sakai 《Journal of Approximation Theory》1998,93(3):441-449
We consider the “Freud weight”W2Q(x)=exp(−Q(x)). let 1<p<∞, and letL*n(f) be a modified Lagrange interpolation polynomial to a measurable functionf∈{f; ess supx∈ |f(x)| WQ(x)(1+|x|)α<∞},α>0. Then we have limn→∞ ∫∞−∞ [|f(x)−L*n(f; x)| WQ(x)(1+|x|)−Δ]p dx=0, whereΔis a constant depending onpandα. 相似文献
4.
Let V(x) be a non-negative, bounded potential in RN, N?3 and p supercritical, . We look for positive solutions of the standing-wave nonlinear Schrödinger equation Δu−V(x)u+up=0 in RN, with u(x)→0 as |x|→+∞. We prove that if V(x)=o(−2|x|) as |x|→+∞, then for N?4 and this problem admits a continuum of solutions. If in addition we have, for instance, V(x)=O(|x|−μ) with μ>N, then this result still holds provided that N?3 and . Other conditions for solvability, involving behavior of V at ∞, are also provided. 相似文献
5.
Soohyun Bae 《Journal of Differential Equations》2007,237(1):159-197
We establish that for n?3 and p>1, the elliptic equation Δu+K(x)up=0 in Rn possesses a continuum of positive entire solutions with logarithmic decay at ∞, provided that a locally Hölder continuous function K?0 in Rn?{0}, satisfies K(x)=O(σ|x|) at x=0 for some σ>−2, and 2|x|K(x)=c+O([log|x|]−θ) near ∞ for some constants c>0 and θ>1. The continuum contains at least countably many solutions among which any two do not intersect. This is an affirmative answer to an open question raised in [S. Bae, T.K. Chang, On a class of semilinear elliptic equations in Rn, J. Differential Equations 185 (2002) 225-250]. The crucial observation is that in the radial case of K(r)=K(|x|), two fundamental weights, and , appear in analyzing the asymptotic behavior of solutions. 相似文献
6.
Yulian An 《Journal of Mathematical Analysis and Applications》2006,322(2):1071-1082
In this article, we consider uniqueness of positive radial solutions to the elliptic system Δu+a(|x|)f(u,v)=0, Δv+b(|x|)g(u,v)=0, subject to the Dirichlet boundary condition on the open unit ball in RN (N?2). Our uniqueness results applies to, for instance, f(u,v)=uqvp, g(u,v)=upvq, p,q>0, p+q<1 or more general cases. 相似文献
7.
Pei-Kee Lin 《Journal of Mathematical Analysis and Applications》2005,312(1):138-147
Let (X,F,μ) be a complete probability space, B a sub-σ-algebra, and Φ the probabilistic conditional expectation operator determined by B. Let K be the Banach lattice {f∈L1(X,F,μ):‖Φ(|f|)‖∞<∞} with the norm ‖f‖=‖Φ(|f|)‖∞. We prove the following theorems:
- (1)
- The closed unit ball of K contains an extreme point if and only if there is a localizing set E for B such that supp(Φ(χE))=X.
- (2)
- Suppose that there is n∈N such that f?nΦ(f) for all positive f in L∞(X,F,μ). Then K has the uniformly λ-property and every element f in the complex K with is a convex combination of at most 2n extreme points in the closed unit ball of K.
8.
Zhu Ning 《高校应用数学学报(英文版)》1998,13(3):241-250
ANOTEONTHEBEHAVIOROFBLOW┐UPSOLUTIONSFORONE┐PHASESTEFANPROBLEMSZHUNINGAbstract.Inthispaper,thefolowingone-phaseStefanproblemis... 相似文献
9.
Hong Li 《Journal of Mathematical Analysis and Applications》2010,365(1):338-333
Under the simple conditions on f and g, we show that entire positive radial solutions exist for the semilinear elliptic system Δu=p(|x|)f(v), Δv=q(|x|)g(u), x∈RN, N?3, where the functions are continuous. 相似文献
10.
11.
Jie Xiao 《Journal of Differential Equations》2006,224(2):277-295
Let u(t,x) be the solution of the heat equation (∂t-Δx)u(t,x)=0 on subject to u(0,x)=f(x) on Rn. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t2,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞). 相似文献
12.
Atsushi Murase 《Mathematische Annalen》2010,347(3):529-543
Let f be a holomorphic cusp form of weight l on SL2(Z) and Ω an algebraic Hecke character of an imaginary quadratic field K with Ω((α)) = (α/|α|) l for ${\alpha\in K^{\times}}Let f be a holomorphic cusp form of weight l on SL2(Z) and Ω an algebraic Hecke character of an imaginary quadratic field K with Ω((α)) = (α/|α|)
l
for a ? K×{\alpha\in K^{\times}}. Let L(f, Ω; s) be the Rankin-Selberg L-function attached to (f, Ω) and P(f, Ω) an “Ω-averaged” sum of CM values of f. In this paper, we give a formula expressing the central L-values L(f, Ω; 1/2) in terms of the square of P(f, Ω). 相似文献
13.
Smail Djebali 《Journal of Mathematical Analysis and Applications》2007,333(2):863-870
In this note we investigate the existence of positive solutions vanishing at +∞ to the elliptic equation Δu+f(x,u)+g(|x|)x⋅∇u=0, |x|>A>0, in Rn (n?3) under mild restrictions on the functions f, g. 相似文献
14.
We establish that the elliptic equation Δu+K(x)up+μf(x)=0 in Rn has infinitely many positive entire solutions for small μ?0 under suitable conditions on K, p, and f. 相似文献
15.
Zongming Guo 《Journal of Differential Equations》2005,211(1):187-217
The structure of positive boundary blow-up solutions to quasi-linear elliptic problems of the form −Δpu=λf(u), u=∞ on ∂Ω, 1<p<∞, is studied in a bounded smooth domain , for a class of nonlinearities f∈C1((0,∞)?{z2})∩C0[0,∞) satisfying f(0)=f(z1)=f(z2)=0 with 0<z1<z2, f<0 in (0,z1)∪(z2,∞), f>0 in (z1,z2). Large, small and intermediate solutions are obtained for λ sufficiently large. It is known from Part I (see Structure of boundary blow-up solutions for quasilinear elliptic problems, part (I): large and small solutions, preprint), that the large solution is the unique large solution to the problem. We will see that the small solution is also the unique small solution to the problem while there are infinitely many intermediate solutions. Our results are new even for the case p=2. 相似文献
16.
Positive definite dot product kernels in learning theory 总被引:1,自引:0,他引:1
In the classical support vector machines, linear polynomials corresponding to the reproducing kernel K(x,y)=xy are used. In many models of learning theory, polynomial kernels K(x,y)=l=0Nal(xy)l generating polynomials of degree N, and dot product kernels K(x,y)=l=0+al(xy)l are involved. For corresponding learning algorithms, properties of these kernels need to be understood. In this paper, we consider their positive definiteness. A necessary and sufficient condition for the dot product kernel K to be positive definite is given. Generally, we present a characterization of a function f:RR such that the matrix [f(xixj)]i,j=1m is positive semi-definite for any x1,x2,...,xmRn, n2.
Supported by CERG Grant No. CityU 1144/01P and City University of Hong Kong Grant No. 7001342.AMS subject classification 42A82, 41A05 相似文献
17.
In this paper, we consider one-dimensional nonlinear Schrödinger equation iut−uxx+V(x)u+f(2|u|)u=0 on [0,π]×R under the boundary conditions a1u(t,0)−b1ux(t,0)=0, a2u(t,π)+b2ux(t,π)=0, , for i=1,2. It is proved that for a prescribed and analytic positive potential V(x), the above equation admits small-amplitude quasi-periodic solutions corresponding to d-dimensional invariant tori of the associated infinite-dimensional dynamical system. 相似文献
18.
This paper deals with the second term asymptotic behavior of large solutions to the problems Δu=b(x)f(u), x∈Ω, subject to the singular boundary condition u(x)=∞, x∈∂Ω, where Ω is a smooth bounded domain in RN, and b(x) is a non-negative weight function. The absorption term f is regularly varying at infinite with index ρ>1 (that is limu→∞f(ξu)/f(u)=ξρ for every ξ>0) and the mapping f(u)/u is increasing on (0,+∞). Our analysis relies on the Karamata regular variation theory. 相似文献
19.
M. Bloznelis 《Journal of Theoretical Probability》1996,9(3):541-560
LetX={X(t), t[0, 1]} be a stochastically continuous cadlag process. Assume that thek dimensional finite joint distributions ofX are in the domain of normal attraction of strictlyp-stable, 0<p<2, measure onR
k
for all 1k<. For functionsf, g such that
p
(|X(x–X(u)|) >g(u–s) and
p
(|X(s–X(t|)|X(t)–X(u|)>f(u–s), 0 s t u 1, conditions are found which imply that the distributions –(n
–1/p
(X
1+···+X
n )),n1, converge weakly inD[0, 1] to the distribution of ap-stable process. HereX
1,X
2, ... are independent copies ofX and
p
(Z)=sup
t<0
t
pP{|Z|<t} denotes the weakpth moment of a random variable Z. 相似文献
20.
We consider functionals of the calculus of variations of the form F(u)= ∝01 f(x, u, u′) dx defined for u ε W1,∞(0, 1), and we show that the relaxed functional
with respect to weak W1,1(0, 1) convergence can be written as
, where the additional term L(u), called the Lavrentiev term, is explicitly identified in terms of F. 相似文献
Full-size image