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11.
Gabriele Bonanno 《Journal of Global Optimization》1998,12(1):101-104
In this note we introduce a suitable class of functionals, including the class of integral functionals, and prove that any (strict) local minimum of a functional of this class, defined on a decomposable space, is a (strict) global minimum. So, the recent result obtained by Giner in [1] is specified and extended. 相似文献
12.
A globally convergent Newton method for solving strongly monotone variational inequalities 总被引:14,自引:0,他引:14
Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method. 相似文献
13.
Existence of positive solution is established for boundary value problems of non-singular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the nonlinear alternative of Leray-Schauder method. 相似文献
14.
Tatsien Li 《Mathematical Methods in the Applied Sciences》2006,29(13):1543-1553
By means of a direct and constructive method based on the theory of semi‐global C2 solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
15.
Jean-Franç ois Coulombel Thierry Goudon 《Transactions of the American Mathematical Society》2007,359(2):637-648
We construct global smooth solutions to the multidimensional isothermal Euler equations with a strong relaxation. When the relaxation time tends to zero, we show that the density converges towards the solution to the heat equation.
16.
三种群食物链交错扩散模型的整体 总被引:1,自引:0,他引:1
本文应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性,该系统是带自扩散和交错扩散项的三种群Lotka-Volterra食物链模型.通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件. 相似文献
17.
Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions. 相似文献
18.
We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour
hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check
the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization
problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and
the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located
by the new technique. 相似文献
19.
Hua Nie Jian-hua Wu 《应用数学学报(英文版)》2006,22(2):257-264
This paper is concerned with the unstirred chemostat model with two-species and one non-reproducingresource.The global attractivity of the positive steady-state solutions of the original system is established.Moreover,the effects of the growth rate on the unique positive equilibrium of the single population model arestudied. 相似文献
20.
Stephen Pankavich 《Mathematical Methods in the Applied Sciences》2007,30(5):529-548
A collisionless plasma is modelled by the Vlasov–Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as ∣x∣ → ∞. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behaviour are shown to exist locally in time, and criteria for the continuation of these solutions are established. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献