共查询到18条相似文献,搜索用时 250 毫秒
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本文定义了非线性算子的Lip数,它从数值上刻画了在强等价距离意义下非线性算子的最小Lipschitz常数.基于所引进的Lip数,我们证明了线性算子Neumann引理及扰动引理的非线性推广.我们也给出了Lip数的两个极有意义的估值定理. 相似文献
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针对非线性Black-Scholes方程,基于quasi-Shannon小波函数给出了一种求解非线性偏微分方程的自适应多尺度小波精细积分法.该方法首先利用插值小波理论构造了用于逼近连续函数的多尺度小波插值算子,利用该算子可以将非线性Black-Scholes方程自适应离散为非线性常微分方程组;然后将用于求解常微分方程组的精细积分法和小波变换的动态过程相结合,并利用非线性处理技术(如同伦分析技术)可有效求解非线性Black-Scholes方程.数值结果表明了该方法在数值精度和计算效率方面的优越性. 相似文献
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Banach空间的Lipschitz对偶及其应用 总被引:3,自引:0,他引:3
本文引进Banach空间E的一个全新对偶空间概念—Lipschitz对偶空间,并证明:任何Banach空间的Lipschitz对偶空间是某个包含E的Banach空间的线性对偶空间,以所引进的新对偶空间为框架,本文定义了非线性Lipschitz算子的Lipshitz对偶算子,证明:任何非线性Lipschitz算子的Lipschitz对偶算子是有界线性算子.所获结果为推广线性算子理论到非线性情形(特别,运用线性算子理论研究非线性算子的特性)开辟了一条新的途径.作为例证,我们应用所建立的理论证明了若干新的非线性一致Lipschitz映象遍历收敛性定理. 相似文献
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非线性Lipschitz算子的Lipschitz对偶算子及其应用 总被引:3,自引:0,他引:3
在文山中我们对非线性Lipschitz算子定义了其Lipschitz对偶算子,并证明了任意非线性Lipschitz算子的Lipschitz对偶算子是一个定义在Lipschitz对偶空间上的有界线性算子.本文还进一步证明:设C为 Banach空间 X的闭子集,C*L为C的 Lipschitz对偶空间,U为 C*L上的有界线性算子,则当且仅当 U为 w*-w*连续的同态变换时,存在Lipschitz连续算子T,使U为T的Lipschitz对偶算子.这一结论的理论意义在于:它表明一个非线性Lipschitz算子的可逆性问题可转化为有界线性算子的可逆性问题.作为应用,通过引入一个新概念──PX-对偶算子,在一般框架下给出了非线性算子半群的生成定理. 相似文献
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本文主要给出了Banach空间中非线性压缩算子半群存在不交流的充要条件,并且在C*-代数及Hilbert空间中刻划了正非线性压缩算子半群的特征. 相似文献
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利用随机拓扑度理论研究随机非线性凝聚算子,在一定条件下得到随机算子方程A(w,x)=μx的随机解和随机算子不动点的存在性,所得结论减弱了已知文献中相应定理的条件. 相似文献
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根据Beylin-Coifman-Rokhlin和Yang的观点,用合适的小波基可以刻画性地研究C.Z算子或拟微分算子,这样就可以用小波来计算算子,比如可以从奇异积分算子的B-C-R算法刻画出发,用小波限制紧算子进行逼近,本文旨在计算作为原算子与逼近算子的差的误差算子的H1到L1的连续性范数的最佳衰减速度和在Lp上的连续性范数的衰减速度的范围。 相似文献
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Ljubomir B. Ćirić Jeong Sheok Ume Siniša N. Ješić Marina M. Arandjelović-Milovanović 《Numerical Functional Analysis & Optimization》2013,34(11-12):1231-1243
In this paper, we modify the Ishikawa iteration process and show that such process, associated with a nonlinear Lipschitzian generalized strongly pseudo-contractive operator with a fixed point in a (not necessarily uniformly smooth) Banach space, converges strongly to the unique fixed point of this operator. 相似文献
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G. Botelho D. Pellegrino J. Santos J.B. Seoane-Sepúlveda 《Journal of Mathematical Analysis and Applications》2015
In this paper we prove a general version of the extrapolation theorem for absolutely summing nonlinear operators. It is explicitly shown that this result encompasses the previous old and recent, linear and nonlinear extrapolation theorems as particular cases. One of the steps of the proof provides another nonlinear extrapolation theorem of independent interest. 相似文献
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In this paper we consider two quasilinear boundary value problems. The first is vector valued and has periodic boundary conditions.
The second is scalar valued with nonlinear boundary conditions determined by multivalued maximal monotone maps. Using the
theory of maximal monotone operators for reflexive Banach spaces and the Leray-Schauder principle we establish the existence
of solutions for both problems. 相似文献
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Hilbert空间中余弦值不为1的非线性算子构成了一类广泛的特殊的非线性算子.研究了这类非线性算子的满射性,并给出了其成立的几个充分条件. 相似文献
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Andrade Doherty 《偏微分方程(英文版)》1999,12(4):337-344
In this work we are concerned with the existence of integral solution for a nonlinear abstract viscoelastic problem in Banach space, where the operator is accretive dependent on time. 相似文献
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Sophia Th. Kyritsi Nikolaos Matzakos Nikolaos Papageorgiou 《Czechoslovak Mathematical Journal》2005,55(3):545-579
In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a
maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator
of the form x ↦ a(x, x′)′. In this problem the maximal monotone term is required to be defined everywhere in the state space ℝN. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ↦ (a(x)x′)′. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential
variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of
solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side. 相似文献
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Eigenproblem for p-Laplacian and nonlinear elliptic equation with nonlinear boundary conditions 下载免费PDF全文
In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalue problem as simplicity, isolation and its strict monotonicity. Afterward, we character also the second eigenvalue and its strictly partial monotony. On the other hand, in some sense, we establish the non-resonance below the first and furthermore between the first and second eigenvalues of nonlinear Steklov–Robin. 相似文献
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1.引言首先研究线性方程Au=f (1.1)的求解问题,其中A是H→H的连续线性算子,H是可分Hilbert空间,U,f∈H,||f||=1.利用得到的结论,研究一类非线性算子方程AuBu+Cu=f(1.2) 相似文献