摘要：
In this paper, we investigate the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems. By using fountain theorem due to Zou, we obtain two new criteria for guaranteeing that second order Hamiltonian systems have infinitely many homoclinic solutions. Recent results in the literature are generalized and significantly improved.
作者：
Kelley, Carl T.*;Qi, Liqun;Tong, Xiaojiao;Yin, Hongxia
期刊：
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2011年7(2):497-521 ISSN：1547-5816
通讯作者：
Kelley, Carl T.
作者机构：
[Kelley, Carl T.] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA.;[Qi, Liqun] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China.;[Tong, Xiaojiao] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421002, Peoples R China.;[Yin, Hongxia] Minnesota State Univ Mankato, Dept Math & Stat, Mankato, MN 56001 USA.;[Kelley, Carl T.] N Carolina State Univ, Dept Math, Box 8205, Raleigh, NC 27695 USA.
通讯机构：
[Kelley, Carl T.] N;N Carolina State Univ, Dept Math, Box 8205, Raleigh, NC 27695 USA.
关键词：
System of nonlinear equations;stable solutions;saddle-node bifurcation;Hopf bifurcation;stability functions;smoothing Newton method
摘要：
In this paper, we present a new approach for finding a stable solution of a system of nonlinear equations arising from dynamical systems. We introduce the concept of stability functions and use this idea to construct stability solution models of several typical small signal stability problems in dynamical systems. Each model consists of a system of constrained semismooth equations. The advantage of the new models is twofold. Firstly, the stability requirement of dynamical systems is controlled by nonlinear inequalities. Secondly, the semismoothness property of the stability functions makes the models solvable by efficient numerical methods. We introduce smoothing functions for the stability functions and present a smoothing Newton method for solving the problems. Global and local quadratic convergence of the algorithm is established. Numerical examples from dynamical systems are also given to illustrate the efficiency of the new approach.
作者机构：
[刘燕; 杨洁] School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;[李龙] Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang 421008, China;[刘燕] School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China
通讯机构：
[Liu, Y.] S;School of Mathematical Sciences, Dalian University of Technology, China
