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991.
《Numerical Functional Analysis & Optimization》2013,34(2):229-247
ABSTRACT The existence of a countable set of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated by some variational methods based on the idea of the Fenchel conjugate. As a consequence of a duality developed here, we obtain the existence of a countable set of solutions for our problem that are minimizers to a certain integral functional. We derive (also in the superlinear case) a measure of a duality gap between primal and dual functional for approximate solutions. 相似文献
992.
John T. Conway 《Integral Transforms and Special Functions》2017,28(6):443-459
Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the independent variable u is the argument of Jacobian elliptic function theory. This allows a limitless number of indefinite integrals with respect to the amplitude to be derived for these three elliptic integrals. Sample results are given, including the integrals derived from powers of the 12 Glaisher elliptic functions. New recurrence relations and integrals are also given for the 12 Glaisher elliptic functions. 相似文献
993.
994.
995.
Z. Yosibash M. Arad A. Yakhot G. Ben-Dor 《Numerical Methods for Partial Differential Equations》1998,14(3):281-296
A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is “pollution” free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 281–296, 1998 相似文献
996.
A. V. Arutyunov D. Yu. Karamzin 《Computational Mathematics and Mathematical Physics》2007,47(3):349-360
The abnormal minimization problem with a finite-dimensional image and geometric constraints is examined. In particular, inequality constraints are included. Second-order necessary conditions for this problem are established that strengthen previously known results. 相似文献
997.
A.B.J. Kuijlaars P.M.J. Tibboel 《Journal of Computational and Applied Mathematics》2009,233(3):775-785
We consider orthogonal polynomials on the real line with respect to a weight and in particular the asymptotic behaviour of the coefficients an,N and bn,N in the three-term recurrence xπn,N(x)=πn+1,N(x)+bn,Nπn,N(x)+an,Nπn−1,N(x). For one-cut regular V we show, using the Deift-Zhou method of steepest descent for Riemann-Hilbert problems, that the diagonal recurrence coefficients an,n and bn,n have asymptotic expansions as n→∞ in powers of 1/n2 and powers of 1/n, respectively. 相似文献
998.
François Delarue 《Journal of Differential Equations》2010,248(4):924-1574
We here establish an a priori Hölder estimate of Krylov and Safonov type for the viscosity solutions of a degenerate quasilinear elliptic PDE of non-divergence form. The diffusion matrix may degenerate when the norm of the gradient of the solution is small: the exhibited Hölder exponent and Hölder constant only depend on the growth of the source term and on the bounds of the spectrum of the diffusion matrix for large values of the gradient. In particular, the given estimate is independent of the regularity of the coefficients. As in the original paper by Krylov and Safonov, the proof relies on a probabilistic interpretation of the equation. 相似文献
999.
An initial-value method is given for second-order singularly perturbed boundary-value problems with a boundary layer at one endpoint. The idea is to replace the original two-point boundary value problem by two suitable initial-value problems. The method is very easy to use and to implement. Nontrivial text problems are used to show the feasibility of the given method, its versatility, and its performance in solving linear and nonlinear singularly perturbed problems.This work was supported in part by the Consiglio Nazionale delle Ricerche, Contract No. 86.02108.01, and in part by the Ministero della Pubblica Istruzione. 相似文献
1000.
Twin solutions to singular boundary value problems 总被引:5,自引:0,他引:5
Ravi P. Agarwal Donal O'Regan 《Proceedings of the American Mathematical Society》2000,128(7):2085-2094
In this paper we establish the existence of two nonnegative solutions to singular and singular focal boundary value problems. Our nonlinearity may be singular at , and/or .