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本文研究了一个四阶椭圆方程解的存在性问题.利用山路定理和喷泉定理,结合变分方法,获得了该问题弱解的几个存在性定理,推广了现有的一些结果. 相似文献
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<正> 自从五十年代以来,有很多文献(例如见[1—8])研究了一致椭圓和抛物型方程广义解的性质.广义解的Holder连续性、存在性和唯一性都解决得很好.对一致椭圆型方程作出的许多结果也平行地推广到非一致椭圆型方程的广义解.但是对非一致抛物型方程仍很少讨论,本文将就这一论题作一点讨论. 下面证明的定理1保证了非一致抛物型方程广义解的有界性;定理2和3分别给出 相似文献
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本文研究了一类分数次薛定谔方程解的存在性问题.利用喷泉定理,得到了在超线性增长条件下方程存在无穷多非平凡解,并且证明了相应解的能量是无界的.本文中非线性项不满足AmbrosettiRabinowitz条件,推广了文献[12]中的结果. 相似文献
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本文是[1]的继续.在本文中我们对非线性随机Volterra积分方程给出了解的另一存在性准则,极值解的存在性定理和随机积分不等式的比较定理,这些定理分别推广了Vaughan[2,3]和Lakshmikantham[4,5]的相应结果. 相似文献
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二阶抛物方程混合边值问题解之极值原理 总被引:1,自引:0,他引:1
张功安 《数学的实践与认识》1990,(1)
本文应用截断函数证明二阶一致抛物方程和退缩抛物方程混合边值问题解之极值原理,给出同一问题解之最大值模和积分模估计式。建立退缩抛物和椭圆方程混合边值问题解之强极值性质。 相似文献
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含有Sobolev-Hardy临界指数的拟线性椭圆方程解的存在性和多重性 总被引:1,自引:0,他引:1
本文研究了一类含有Sobolev-Hardy临界指数的拟线性奇异椭圆方程解的存在性和多重性.利用Ekeland变分原理和Clark临界点定理证明了该问题非平凡解和无穷多解的存在性,推广了已有结果. 相似文献
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本文应用上下解的概念及schauder不动点定理,在较广泛的条件下,解决了半线性抛物型泛函数微分方程周期解的存在性问题.所得结果推广了文献[3]的定理1.2. 相似文献
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在本文中,我们对非线性随机Volterra积分方程在Banach空间的弱拓扑下的随机解证明了几个存在定理.然后作为应用,我们得到了随机微分方程的弱随机解的存在定理.还得到了这些随机方程的极值随机解的存在性和随机比较定理.我们的定理改进和推广了[4,5,10,11,12]中的相应结果. 相似文献
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一类非线性抛物型方程整体解的存在性和衰减估计 总被引:2,自引:1,他引:1
本文讨论了一类拟线性抛物型方程初边值问题整体解的存在性和衰减性估计.所得结果改进并推广了文献[1],[3]和[7]的相应结果. 相似文献
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Xin Ke 《Random Structures and Algorithms》1993,4(1):85-97
The size Ramsey number r?(G, H) of graphs G and H is the smallest integer r? such that there is a graph F with r? edges and if the edge set of F is red-blue colored, there exists either a red copy of G or a blue copy of H in F. This article shows that r?(Tnd, Tnd) ? c · d2 · n and c · n3 ? r?(Kn, Tnd) ? c(d)·n3 log n for every tree Tnd on n vertices. and maximal degree at most d and a complete graph Kn on n vertices. A generalization will be given. Probabilistic method is used throught this paper. © 1993 John Wiley Sons, Inc. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(12):1377-1380
We prove that the solution of the oblique derivative parabolic problem in a noncylindrical domain ΩT belongs to the anisotropic Holder space C2+α, 1+α/2(gwT) 0 < α < 1, even if the nonsmooth “lateral boundary” of ΩT is only of class C1+α, (1+α)/2). As a corollary, we also obtain an a priori estimate in the Hölder space C2+α(Ω0) for a solution of the oblique derivative elliptic problem in a domain Ω0 whose boundary belongs only to the classe C1+α. 相似文献
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For x and y vertices of a connected graph G, let TG(x, y) denote the expected time before a random walk starting from x reaches y. We determine, for each n > 0, the n-vertex graph G and vertices x and y for which TG(x, y) is maximized. the extremal graph consists of a clique on ?(2n + 1)/3?) (or ?)(2n ? 2)/3?) vertices, including x, to which a path on the remaining vertices, ending in y, has been attached; the expected time TG(x, y) to reach y from x in this graph is approximately 4n3/27. 相似文献
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We represent a graph by assigning each vertex a finite set such that vertices are adjacent if and only if the corresponding sets have at least two common elements. The 2-intersection number θ2(G) of a graph G is the minimum size of the union of sets in such a representation. We prove that the maximum order of a path that can be represented in this way using t elements is between (t2 - 19t + 4)/4 and (t2 - t + 6)/4, making θ2(Pn) asymptotic to 2√n. We also show the existence of a constant c depending on ? such that, for any tree T with maximum degree at most d, θ2(T) ≤ c(√n)1+?. When the maximum degree is not bounded, there is an n-vertex tree T with θ2(T) > .945n2/3. © 1995 John Wiley & Sons, Inc. 相似文献
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Nguyen Thanh Long Pham Ngoc Dinh Alain 《Mathematical Methods in the Applied Sciences》1993,16(4):281-295
We study the following initial and boundary value problem: In section 1, with u0 in L2(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L2(0, T; H ∩ H2) ∩ L∞(0, T; H) if we assume u0 in H and f in C1(?,?). Numerical results are given for these two cases. 相似文献
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Let 0<a<1/2,Ta,2(x)=ax and T0,2(x)=ax+1-a, and let Ka be a unique nomepty compact subset of R satisfying Ka=Ta,1(Ka)∪Ta,2(Ka). If 1/4<a<1/2, then the Hausdorff measure of Ka×Ka is strictly less than 2 - loga 22^{ - log_a 2} . If0<a≤1/4, then the Hausdorff measure of Ka×Ka is equal to 2 - loga 22^{ - log_a 2} . 相似文献
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LAIR Alan v 《Applicable analysis》2013,92(3-4):177-189
We show that the initial boundary value problem for the diffusion equation uL ?(ux)x with bounded Neumann boundary conditions has at most one smooth solutions on the infinite cylinder provided the nonmonotonic function ? is piecewise continuously differentiable on the reals has at most finitely many extreme values on any bounded interval,satisfies the coercivity condition s?(s) ≤ cs2, c < 0 and has a derivative which is nonzero almost everywhere. In particular this result provides uniquencess for the model cubic ?(s)=s3 /3-3s2/2+2s proposed by Hölling and Nohel 相似文献
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In this paper, we determine all functions ?, defined on a field K (belonging to a certain class) and taking values in an abelian group, such that the quadratic difference ?(x + y) + ?(x ? y) ? 2?(x) ? 2?(y) depends only on the product xy for all x, y ∈ K. Using this result, we find the general solution of the functional equation ?1(x + y) + ?2(x ? y) = ?3(x) + ?4(y) + g(xy). 相似文献
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Albert Milani 《Mathematische Nachrichten》1999,199(1):115-144
We prove that C2+α,1+α/2 (Q?) solutions of problem (1.6) below are in a subspace Hcm+2(Q) of Hm+2,(m+2)/2(Q) for all m ∈ ?, if f and the coefficients are in Hcm(Q)∪Cα,α/2 (Q?). We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below. 相似文献
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Mary F. Wheeler J. R. Whiteman 《Numerical Methods for Partial Differential Equations》1994,10(3):271-294
Superconvergent error estimates in l2(H1) and l∞(H1) norms are derived for recovered gradients of finite difference in time/piecewise linear Galerkin approximations in space for linear and quasinonlinear parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context, and covers problems in regions with nonsmooth boundaries under certain assumptions on the regularity of the solutions. © 1994 John Wiley & Sons, Inc. 相似文献