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31.
Samir AL-Sadder Raid A. Othman AL-Rawi 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,75(8-9):459-473
An efficient scheme, called quasi-linearization finite differences, is developed for large-deflection analysis of prismatic
and non-prismatic slender cantilever beams subjected to various types of continuous and discontinuous external variable distributed
and concentrated loads in horizontal and vertical global directions. Simultaneous equations of highly nonlinear and linear
terms are obtained when casting the derived exact highly nonlinear governing differential equation using central finite differences
on the nodes along the beam. A quasi-linearization scheme is used to solve these equations based on successive corrections
of the nonlinear terms in the simultaneous equations. The nonlinear terms in the simultaneous equations are assumed constant
during each correction (iteration). Several representative numerical examples of prismatic and non-prismatic slender cantilever
beams with different loading conditions are analyzed to illustrate the merits of the adopted numerical scheme as well as its
validity, accuracy and efficiency. The results of the present scheme are checked using large-displacement finite element analysis
by the MSC/NASTRAN program. A comparison between the present secheme, MSC/NASTRAN and available results from the literature
reveals excellent agreement. The advantage of the new scheme is that the load can be applied in one step with few iterations
(3–6 iterations). 相似文献
32.
Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18 , 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks. 相似文献
33.
The paper studies differential equations of the form u′(x) = f(x, u(x), λ(x)), u(x0) = u0, where the right‐hand side is merely measurable in x. In particular sufficient conditions for the continuous and the differentiable dependence of solution u on the data and on the parameter λ are stated. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
34.
We consider generalized potential operators with the kernel on bounded quasimetric measure space (X, μ, d) with doubling measure μ satisfying the upper growth condition μB(x, r) ? KrN, N ∈ (0, ∞). Under some natural assumptions on a(r) in terms of almost monotonicity we prove that such potential operators are bounded from the variable exponent Lebesgue space Lp(?)(X, μ) into a certain Musielak‐Orlicz space Lp(X, μ) with the N‐function Φ(x, r) defined by the exponent p(x) and the function a(r). A reformulation of the obtained result in terms of the Matuszewska‐Orlicz indices of the function a(r) is also given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
35.
Kazuaki Taira 《Mathematische Nachrichten》2011,284(1):105-123
The purpose of this paper is to study a class of semilinear elliptic boundary value problems with degenerate boundary conditions which include as particular cases the Dirichlet problem and the Robin problem. The approach here is based on the super‐sub‐solution method in the degenerate case, and is distinguished by the extensive use of an Lp Schauder theory elaborated for second‐order, elliptic differential operators with discontinuous zero‐th order term. By using Schauder's fixed point theorem, we prove that the existence of an ordered pair of sub‐ and supersolutions of our problem implies the existence of a solution of the problem. The results extend an earlier theorem due to Kazdan and Warner to the degenerate case. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
36.
We consider some functional Banach algebras with multiplications as the usual convolution product * and the so‐called Duhamel product ?. We study the structure of generators of the Banach algebras (C(n)[0, 1], *) and (C(n)[0, 1], ?). We also use the Banach algebra techniques in the calculation of spectral multiplicities and extended eigenvectors of some operators. Moreover, we give in terms of extended eigenvectors a new characterization of a special class of composition operators acting in the Lebesgue space Lp[0, 1] by the formula (Cφf)(x) = f(φ(x)). 相似文献
37.
This article addresses nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping. The presence of a nonlinear boundary source alone is known to pose a significant difficulty since the linear Neumann problem for the wave equation is not, in general, well‐posed in the finite‐energy space H1(Ω) × L2(?Ω) with boundary data in L2 due to the failure of the uniform Lopatinskii condition. Further challenges stem from the fact that both sources are non‐dissipative and are not locally Lipschitz operators from H1(Ω) into L2(Ω), or L2(?Ω). With some restrictions on the parameters in the model and with careful analysis involving the Nehari Manifold, we obtain global existence of a unique weak solution, and establish exponential and algebraic uniform decay rates of the finite energy (depending on the behavior of the dissipation terms). Moreover, we prove a blow up result for weak solutions with nonnegative initial energy. 相似文献
38.
It is shown that the exponent of convergence λ(f) of any solution f of with entire coefficients A0(z), …, Ak?2(z), satisfies λ(f) ? λ ∈ [1, ∞) if and only if the coefficients A0(z), …, Ak?2(z) are polynomials such that for j = 0, …, k ? 2. In the unit disc analogue of this result certain intersections of weighted Bergman spaces take the role of polynomials. The key idea in the proofs is W. J. Kim’s 1969 representation of coefficients in terms of ratios of linearly independent solutions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
39.
We investigate the asymptotic behavior of the eigenvalues and the eigenfunctions of q‐Sturm‐Liouville eigenvalue problems. For this aim we study the asymptotic behavior of q‐trigonometric functions as well as fundamental sets of solutions of the associated second order q‐difference equation. As in classical Sturm‐Liouville theory, the eigenvalues behave like zeros of q‐trigonometric functions and the eigenfunctions behave like q‐trigonometric functions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
40.
In this paper we develop elements of the global calculus of Fourier integral operators in ${{\mathbb R}^n}$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L2 estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of weighted estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions. 相似文献