This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive soluti...This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.展开更多
In this paper, by using the Leray-Schauder continuation theorem, we establish the existence and uniqueness theorems of solutions of two-point boundary value problems for 2nth-order nonlinear differential equations wit...In this paper, by using the Leray-Schauder continuation theorem, we establish the existence and uniqueness theorems of solutions of two-point boundary value problems for 2nth-order nonlinear differential equations with nonlinear growth.展开更多
In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the correspondin...In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the corresponding result on the second order de-layed differential equation. Our proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.展开更多
针对快速随机扩展树(Rapidly-Exploring Random Trees,RRT)算法在规划路径中随机性较大、扩展效率较低且规划的路径不利于机器人移动等缺点,提出一种改进的RRT算法。首先,加入目标偏向策略和自适应步长策略,减小RRT的随机性,增强路径规...针对快速随机扩展树(Rapidly-Exploring Random Trees,RRT)算法在规划路径中随机性较大、扩展效率较低且规划的路径不利于机器人移动等缺点,提出一种改进的RRT算法。首先,加入目标偏向策略和自适应步长策略,减小RRT的随机性,增强路径规划的鲁棒性和算法的探索能力;其次,引入改进的人工势场法,使算法扩展方向更偏向目标点,提高算法的搜索效率;然后,去除改进RRT算法规划路径的冗余节点,使得生成的路径更加简短和高效;最后,使用n阶贝塞尔曲线对路径进行平滑处理,使规划的路径更有利于机器人移动。实验结果表明,与传统RRT算法、RRT*算法和另外一种已有的改进方法相比,改进的RRT算法在路径规划时间、路径长度、路径节点以及迭代次数等方面效果都更好,路径更加平滑且更短。展开更多
基金Research supported by the National Natural Science Foundation of China (10871116)the Natural Science Foundation of Shandong Province of China (ZR2010AM005)the Doctoral Program Foundation of Education Ministry of China (200804460001)
文摘This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.
文摘In this paper, by using the Leray-Schauder continuation theorem, we establish the existence and uniqueness theorems of solutions of two-point boundary value problems for 2nth-order nonlinear differential equations with nonlinear growth.
基金National Natural Science Foundation of China (10671069)Shanghai LeadingAcademic Discipline Project (B407).
文摘In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the corresponding result on the second order de-layed differential equation. Our proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.
文摘针对快速随机扩展树(Rapidly-Exploring Random Trees,RRT)算法在规划路径中随机性较大、扩展效率较低且规划的路径不利于机器人移动等缺点,提出一种改进的RRT算法。首先,加入目标偏向策略和自适应步长策略,减小RRT的随机性,增强路径规划的鲁棒性和算法的探索能力;其次,引入改进的人工势场法,使算法扩展方向更偏向目标点,提高算法的搜索效率;然后,去除改进RRT算法规划路径的冗余节点,使得生成的路径更加简短和高效;最后,使用n阶贝塞尔曲线对路径进行平滑处理,使规划的路径更有利于机器人移动。实验结果表明,与传统RRT算法、RRT*算法和另外一种已有的改进方法相比,改进的RRT算法在路径规划时间、路径长度、路径节点以及迭代次数等方面效果都更好,路径更加平滑且更短。
