In this paper, we study the existence of solution of a critical fractional equation;we will use a variational approach to find the solution. Firstly, we will find a suitable functional to our problem;next, by using th...In this paper, we study the existence of solution of a critical fractional equation;we will use a variational approach to find the solution. Firstly, we will find a suitable functional to our problem;next, by using the classical concept and properties of the genus, we construct a mini-max class of critical points.展开更多
In this paper we introduce a minimax model for network connection problems with interval parameters. We consider how to connect given nodes in a network with a path or a spanning tree under a given budget, where each ...In this paper we introduce a minimax model for network connection problems with interval parameters. We consider how to connect given nodes in a network with a path or a spanning tree under a given budget, where each link is associated with an interval and can be established at a cost of any value in the interval. The quality of an individual link （or the risk of link failure, etc.） depends on its construction cost and associated interval. To achieve fairness of the network connection, our model aims at the minimization of the maximum risk over all links used. We propose two algorithms that find optimal paths and spanning trees in polynomial time, respectively. The polynomial solvability indicates salient difference between our minimax model and the model of robust deviation criterion for network connection with interval data, which gives rise to NP-hard optimization problems.展开更多
文摘In this paper, we study the existence of solution of a critical fractional equation;we will use a variational approach to find the solution. Firstly, we will find a suitable functional to our problem;next, by using the classical concept and properties of the genus, we construct a mini-max class of critical points.
基金Supported by the National Natural Science Foundation of China(No.10531070,10771209,10721101,70631001)Chinese Academy of Sciences under Grant No.kjcx-yw-s7
文摘In this paper we introduce a minimax model for network connection problems with interval parameters. We consider how to connect given nodes in a network with a path or a spanning tree under a given budget, where each link is associated with an interval and can be established at a cost of any value in the interval. The quality of an individual link （or the risk of link failure, etc.） depends on its construction cost and associated interval. To achieve fairness of the network connection, our model aims at the minimization of the maximum risk over all links used. We propose two algorithms that find optimal paths and spanning trees in polynomial time, respectively. The polynomial solvability indicates salient difference between our minimax model and the model of robust deviation criterion for network connection with interval data, which gives rise to NP-hard optimization problems.
