共查询到20条相似文献,搜索用时 15 毫秒
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The semilinear elliptic eigenvalue problem with superlinearpure power nonlinearity is considered. This problem is treatedfrom the standpoint of L2-theory and the precise asymptoticformula for the eigenvalue parameter = () as is established,where is the L2-norm of the solution u associated with . 2000Mathematics Subject Classification 35P30 (primary), 35J60 (secondary). 相似文献
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利用上下解方法,锥理论,Schauder不动点定理,Amann不动点定理以及映射度理论研究Sturm—Liouville边值问题(SL.ρ),在某些特定条件下,得到了有多重非负解的存在性结论.从而一定程度上推广和改进了最近的相关结果. 相似文献
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利用M(o)nch不动点定理,在更广泛的的条件下,证明了Banach空间中Sturm-Liouville问题解的存在性. 相似文献
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奇异非线性Sturm-Liouville问题的正解 总被引:12,自引:0,他引:12
本文研究奇异非线性Sturm-Liouville问题其中(Lφ)(x)=(p(x)φ′(x))′+g(x)φ(x),并且允许h(x)在x=0和x=1奇异。应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下获得了正解的存在性结果,本质地推广和改进了文献[1-9]中的主要结论。 相似文献
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Inverse SturmLiouville problems with eigenparameter-dependentboundary conditions are considered. Theorems analogous to thoseof both Hochstadt and Gelfand and Levitan are proved. In particular, let ly = (1/r)((py')'+qy), ,
where det = > 0, c 0, det > 0, t 0 and (cs + dr au tb)2 < 4(cr ta)(ds ub). Denoteby (l; ; ) the eigenvalue problem ly = y with boundary conditionsy(0)cos+y'(0)sin = 0 and (a+b)y(1) = (c+d)(py')(1). Define (; ; ) as above but with l replacedby . Let wn denote the eigenfunctionof (l; ; ) having eigenvalue n and initial conditions wn(0)= sin and pw'n(0) = cos and let n = awn(1)+cpw'n(1).Define n and n similarly. As sample results, it is proved that if (l; ; ) and (; ; ) have the same spectrum, and (l;; ) and (; ; ) have the samespectrum or for all n, thenq/r = /. 相似文献
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本文采用一个改进的单调迭代技巧 ,获得了二阶非线性脉冲微分方程的 Sturm-L iouville边值问题的极解 相似文献
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利用拓扑方法讨论了一类非线性Sturm-Liouville边值问题-u″=λf(x,u),0≤x≤1,α_0u(0)+β_0u′(0)=0,α_1u(1)+β_1u′(1)=0.研究了上述问题的正解的全局结构,在非线性项f(x,u)不满足条件f(x,u)≥0(u≥0)时获得了正解的存在性. 相似文献
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T. N. Harutyunyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2016,51(4):173-181
We prove a new asymptotic formula for the eigenvalues of Sturm-Liouville problem with summable potential. The obtained result extends and make more precise previously known formulas, and takes into account the smooth dependence of the spectral data on boundary conditions. 相似文献
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设{X_n.n≥1}是一非退化的i.i.d.随机变量序列,U_n是以二维Borel可测对称函数h(x,y)为核函数的U-统计量.记U_n=2/(n(n-1))Σ_≤i≤j≤nh(X_i,X_j).本文分别在核函数h(x,y)只有4/3阶矩或4/3+δ,0<δ≤1的情况下,对非常广泛的一类权函数(x)与边界函数b(x)得到了如下关于U-统计量U_n的精致渐近性:不仅使得已有的结果成为我们的特况,还大大降低了其中的矩条件. 相似文献
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Robert S. Strichartz 《Journal of Fourier Analysis and Applications》2012,18(3):626-659
We discuss two heuristic ideas concerning the spectrum of a Laplacian, and we give theorems and conjectures from the realms of manifolds, graphs and fractals that validate these heuristics. The first heuristic concerns Laplacians that do not have discrete spectra: here we discuss the notion of ??spectral mass?? closely related to the ??integrated density of states??, an average of the diagonal of the kernel of the spectral projection operator, and show that this can serve as a substitute for the eigenvalue counting function. The second heuristic is an ??asymptotic splitting law?? that describes the proportions of the spectrum that transforms according to the irreducible representations of a finite group that acts as a symmetry group of the Laplacian. For this to be valid we require the existence of a fundamental domain with relatively small boundary. We also give a version in the case that the symmetry group is a compact Lie group. Many of our results are reformulations of known results, and some are merely conjectures, but there is something to be gained by looking at them together with a unified perspective. 相似文献
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该文利用拓扑方法讨论一类非线性Sturm-Liouville边值问题\[\left\{\begin{array}{lcl}-u'=\lambda f(x, u),\\\alpha_0 u(0)+\beta_0 u'(0)=0,\ \ \alpha_1 u(1)+\beta_1 u'(1)=0;\end{array}\right.\]作者在非线性项不奇异和奇异两种情况下研究了上述问题正解解集的全局结构,在非线性项$f$不满足条件f(x,u)≥0(u≥0)时 获得了正解的存在性. 相似文献
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Let {X(t), t ≥ 0} be a Lévy process with EX(1) = 0 and EX
2(1) < ∞. In this paper, we shall give two precise asymptotic theorems for {X(t), t ≥ 0}. By the way, we prove the corresponding conclusions for strictly stable processes and a general precise asymptotic proposition
for sums of i.i.d. random variables.
This work is supported by the National Natural Science Foundation (Grant No. 10671188) and Special Foundation of USTC 相似文献
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We study a linked system of nonlinear Sturm-Liouville equations in which the linking occurs via the spectral parameters. The system is the multiparameter analog of an equation recently discussed by R. E. L. Turner. We present an existence theorem for continua of solutions of the system—the solutions being required to have specified nodal properties. 相似文献
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Galliano Valent 《Mediterranean Journal of Mathematics》2006,3(2):327-345
In the field of orthogonal polynomials theory, the classical Markov theorem shows that for determinate moment problems the
spectral measure is under control of the polynomials asymptotics.
The situation is completely different for indeterminate moment problems, in which case the interesting spectral measures are
to be constructed using Nevanlinna parametrization. Nevertheless it is interesting to observe that some spectral measures
can still be obtained from weaker forms of the Markov theorem.
The exposition will be illustrated by orthogonal polynomials related to elliptic functions: in the determinate case by examples
due to Stieltjes and some of their generalizations and in the indeterminate case by more recent examples. 相似文献
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Jesús Rodriguez 《Journal of Mathematical Analysis and Applications》2005,308(1):380-391
In this paper we study nonlinear boundary value problems of the form
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This paper gives one-term componentwise asymptotics for theM and spectral matrices of a self-adjoint realisation of aneven-order ordinary differential expression. The underlyinginterval is assumed to have at least one regular endpoint, andthe boundary conditions are supposed to be separated. Furthermore,the weight function and the reciprocal of the highest-ordercoefficient are supposed to be of regular variation at the regularendpoint, in the sense of Bingham, Goldie and Teugels. 1991Mathematics Subject Classification: 34B24, 34E05. 相似文献