In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o...In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.展开更多
In this paper the fixed point index problem for a class of positive operators with boundary control conditions is discussed,and some sufficient conditions for the fixed pointindex to be equal to1 or 0 are given.Moreov...In this paper the fixed point index problem for a class of positive operators with boundary control conditions is discussed,and some sufficient conditions for the fixed pointindex to be equal to1 or 0 are given.Moreover,a general fixed point theorem of expansions and compressions for cone is obtained,which generalizes and improves the corresponding results of[3,8,9].As an application,we utilize the results presented above to study the existence conditions of positive solutions of nonlinear integral equations modelling infectious diseases.展开更多
The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma ̄[2], Ihe isolated wave in transmission line ̄[3], and the isolated wave in t...The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma ̄[2], Ihe isolated wave in transmission line ̄[3], and the isolated wave in the bound-ary surface of the divided layer fluid ̄[4]. For the characteristic problem of the gene-ralized KdV equation, this paper, based on the Riemann function, designs a suitablestructure, then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding fixed point, the above integral differential equ-ation has a unique regular solution, so the characteristic problem of the generalizedKdV equation has a. unique solution. The iteration solution derived from the integraldifferential equation sequence is uniformly convegent in.展开更多
Partial differential equations(PDE)on manifolds arise in many areas,including mathematics and many applied fields.Due to the complicated geometrical structure of the manifold,it is difficult to get efficient numerical...Partial differential equations(PDE)on manifolds arise in many areas,including mathematics and many applied fields.Due to the complicated geometrical structure of the manifold,it is difficult to get efficient numerical method to solve PDE on manifold.In the paper,we propose a method called point integral method(PIM)to solve the Poisson-type equations from point clouds.Among different kinds of PDEs,the Poisson-type equations including the standard Poisson equation and the related eigenproblem of the Laplace-Beltrami operator are one of the most important.In PIM,the key idea is to derive the integral equations which approximates the Poisson-type equations and contains no derivatives but only the values of the unknown function.This featuremakes the integral equation easy to be discretized frompoint cloud.In the paper,we explain the derivation of the integral equations,describe the point integral method and its implementation,and present the numerical experiments to demonstrate the convergence of PIM.展开更多
With the rapid development of flexible interconnection technology in active distribution networks(ADNs),many power electronic devices have been employed to improve system operational performance.As a novel fully-con-t...With the rapid development of flexible interconnection technology in active distribution networks(ADNs),many power electronic devices have been employed to improve system operational performance.As a novel fully-con-trolled power electronic device,energy storage integrated soft open point(ESOP)is gradually replacing traditional switches.This can significantly enhance the controllability of ADNs.To facilitate the utilization of ESOP,device loca-tions and capacities should be configured optimally.Thus,this paper proposes a multi-stage expansion planning method of ESOP with the consideration of tie-line reconstruction.First,based on multi-terminal modular design characteristics,the ESOP planning model is established.A multi-stage planning framework of ESOP is then presented,in which the evolutionary relationship among different planning schemes is analyzed.Based on this framework,a multi-stage planning method of ESOP with consideration of tie-line reconstruction is subsequently proposed.Finally,case studies are conducted on a modified practical distribution network,and the cost-benefit analysis of device and multiple impact factors are given to prove the effectiveness of the proposed method.展开更多
文摘In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.
基金Project supported by National Natural Science Foundation of China
文摘In this paper the fixed point index problem for a class of positive operators with boundary control conditions is discussed,and some sufficient conditions for the fixed pointindex to be equal to1 or 0 are given.Moreover,a general fixed point theorem of expansions and compressions for cone is obtained,which generalizes and improves the corresponding results of[3,8,9].As an application,we utilize the results presented above to study the existence conditions of positive solutions of nonlinear integral equations modelling infectious diseases.
文摘The generalized KdV equation is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma ̄[2], Ihe isolated wave in transmission line ̄[3], and the isolated wave in the bound-ary surface of the divided layer fluid ̄[4]. For the characteristic problem of the gene-ralized KdV equation, this paper, based on the Riemann function, designs a suitablestructure, then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding fixed point, the above integral differential equ-ation has a unique regular solution, so the characteristic problem of the generalizedKdV equation has a. unique solution. The iteration solution derived from the integraldifferential equation sequence is uniformly convegent in.
基金This research was partial supported by NSFC Grant(11201257 to Z.S.,11371220 to Z.S.and J.S.and 11271011 to J.S.)National Basic Research Program of China(973 Program 2012CB825500 to J.S.).
文摘Partial differential equations(PDE)on manifolds arise in many areas,including mathematics and many applied fields.Due to the complicated geometrical structure of the manifold,it is difficult to get efficient numerical method to solve PDE on manifold.In the paper,we propose a method called point integral method(PIM)to solve the Poisson-type equations from point clouds.Among different kinds of PDEs,the Poisson-type equations including the standard Poisson equation and the related eigenproblem of the Laplace-Beltrami operator are one of the most important.In PIM,the key idea is to derive the integral equations which approximates the Poisson-type equations and contains no derivatives but only the values of the unknown function.This featuremakes the integral equation easy to be discretized frompoint cloud.In the paper,we explain the derivation of the integral equations,describe the point integral method and its implementation,and present the numerical experiments to demonstrate the convergence of PIM.
基金supported by the National Natural Science Foundation of China (51977139,52061635103)Tianjin Science Foundation for Youths (21JCQNJC00430)Science and Technology Project of State Grid Tianjin Electric Power Co. (KJ21-1-36).
文摘With the rapid development of flexible interconnection technology in active distribution networks(ADNs),many power electronic devices have been employed to improve system operational performance.As a novel fully-con-trolled power electronic device,energy storage integrated soft open point(ESOP)is gradually replacing traditional switches.This can significantly enhance the controllability of ADNs.To facilitate the utilization of ESOP,device loca-tions and capacities should be configured optimally.Thus,this paper proposes a multi-stage expansion planning method of ESOP with the consideration of tie-line reconstruction.First,based on multi-terminal modular design characteristics,the ESOP planning model is established.A multi-stage planning framework of ESOP is then presented,in which the evolutionary relationship among different planning schemes is analyzed.Based on this framework,a multi-stage planning method of ESOP with consideration of tie-line reconstruction is subsequently proposed.Finally,case studies are conducted on a modified practical distribution network,and the cost-benefit analysis of device and multiple impact factors are given to prove the effectiveness of the proposed method.