In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the ...In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the bifurcation result,we determine the intervals ofλfor the existence,nonexistence,and exact multiplicity of one-sign solutions for this problem.展开更多
this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al....this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.展开更多
基金Supported by the National Natural Science Foundation of China(11561038)。
文摘In this paper,we study the following Kirchhoff type problem:{-M(∫_(R^(N))|▽u|^(2)dx)△u=λa(x)f(u),x∈R^(N),u=0 as|x|→+∞.Unilateral global bifurcation result is established for this problem.As applications of the bifurcation result,we determine the intervals ofλfor the existence,nonexistence,and exact multiplicity of one-sign solutions for this problem.
基金Supported in part by NSFC(No.11961011)Guangxi Science and Technology Base and Talents Special Project(No.2021AC06001).
文摘this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.
