In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imp...In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.展开更多
The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the co...The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.展开更多
The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit form...The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.展开更多
This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the ...This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.展开更多
By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive soluti...By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.展开更多
In this paper, a fractional multi-point boundary value problem is considered. By using the fixed point index theory and Krein-Rutman theorem, some results on existence are obtained.
In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(...In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.展开更多
为研究惯容系统位置对调谐质量阻尼器(tuned mass damper,TMD)减振性能的影响,首先基于动力学原理,采用定点理论对惯质调谐质量阻尼器(TMD-inerter,TMDI)进行参数优化,得到最优频率比和最优阻尼比解析解;其次讨论了频率比及阻尼比对结...为研究惯容系统位置对调谐质量阻尼器(tuned mass damper,TMD)减振性能的影响,首先基于动力学原理,采用定点理论对惯质调谐质量阻尼器(TMD-inerter,TMDI)进行参数优化,得到最优频率比和最优阻尼比解析解;其次讨论了频率比及阻尼比对结构振动特性的影响;最后对TMDI鲁棒性进行研究。结果表明:惯容系统连接位置对阻尼器吸振能力影响显著,与传统TMD和非接地TMDI相比,接地TMDI使主结构动力放大系数分别减小约8.4%、16.5%;接地TMDI调频宽度相比传统TMD提高约6%;在阻尼摄动范围内,接地TMDI减振系统动力放大系数增幅约1.5倍;接地TMDI具有更良好的鲁棒性,可为设计新型TMDI模型提供理论参考。展开更多
We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we confine ourselves to several topics on fixed points of self-maps on...We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we confine ourselves to several topics on fixed points of self-maps on manifolds and polyhedra. Special attention is paid to connections with geometric group theory and dynamics, as well as some formal approaches.展开更多
文摘In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.
文摘The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.
文摘The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.
文摘This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.
文摘By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.
文摘In this paper, a fractional multi-point boundary value problem is considered. By using the fixed point index theory and Krein-Rutman theorem, some results on existence are obtained.
基金Supported by the Foundation of the Office of Science and Technology of Henan(122102310373)Supported by the NSF of Education Department of Henan Province(12B110025)
文摘In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.
文摘为研究惯容系统位置对调谐质量阻尼器(tuned mass damper,TMD)减振性能的影响,首先基于动力学原理,采用定点理论对惯质调谐质量阻尼器(TMD-inerter,TMDI)进行参数优化,得到最优频率比和最优阻尼比解析解;其次讨论了频率比及阻尼比对结构振动特性的影响;最后对TMDI鲁棒性进行研究。结果表明:惯容系统连接位置对阻尼器吸振能力影响显著,与传统TMD和非接地TMDI相比,接地TMDI使主结构动力放大系数分别减小约8.4%、16.5%;接地TMDI调频宽度相比传统TMD提高约6%;在阻尼摄动范围内,接地TMDI减振系统动力放大系数增幅约1.5倍;接地TMDI具有更良好的鲁棒性,可为设计新型TMDI模型提供理论参考。
基金Supported by NSF of China(Grant Nos.11131008,11431009)
文摘We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we confine ourselves to several topics on fixed points of self-maps on manifolds and polyhedra. Special attention is paid to connections with geometric group theory and dynamics, as well as some formal approaches.
