This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（...This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.展开更多
A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the bounda...A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the boundary value problems are obtained.展开更多
This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditio...This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditions, solutions of the problem exist. The interesting point is that p（t） is a general function.展开更多
Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance ...Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.展开更多
As the stiffness of the elastic support varies with the physical-chemical erosion and mechanical friction, model catastrophe of a single degree-of-freedom(DOF) isolation system may occur. A 3-DOF four-point-elastic-su...As the stiffness of the elastic support varies with the physical-chemical erosion and mechanical friction, model catastrophe of a single degree-of-freedom(DOF) isolation system may occur. A 3-DOF four-point-elastic-support rigid plate(FERP) structure is presented to describe the catastrophic isolation system. Based on the newly-established structure, theoretical derivation for stiffness matrix calculation by free response(SMCby FR) and the method of stiffness identification by stiffness matrix disassembly(SIby SMD)are proposed. By integrating the SMCby FR and the SIby SMD and defining the stiffness assurance criterion(SAC), the procedures for stiffness identification of a FERP structure(SIFERP) are summarized. Then, a numerical example is adopted for the SIFERP validation, in which the simulated tested free response data are generated by the numerical methods, and operation for filtering noise is conducted to imitate the practical application. Results in the numerical example demonstrate the feasibility and accuracy of the developed SIFERP for stiffness identification.展开更多
This paper deals with a four-point boundary value problem [φ(u')]' = f(t, u, u'),a < t < b with u(a) - u(ao) = A, u(b) - u(bo) = B, where a < a0 <b0 < b.
This paper is concerned with the existence of solutions for a second-order four-point boundary value problem at resonance. The main methods depend on the technique of the upper and lower solutions and the coincidence ...This paper is concerned with the existence of solutions for a second-order four-point boundary value problem at resonance. The main methods depend on the technique of the upper and lower solutions and the coincidence degree theory.展开更多
基金Tutorial Scientific Research Program Foundation of Education Department of Gansu Province(0710-04).
文摘This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.
基金Sponsored by the National Natural Science Foundation of China (10671012)Doctoral Program Foundation of Education Ministry of China(20050007011)
文摘A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the boundary value problems are obtained.
基金The NSF(11271154)of Chinathe Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education+1 种基金the 985 program of Jilin Universitythe DR Fund(150152)of Henan University of Technology
文摘This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditions, solutions of the problem exist. The interesting point is that p（t） is a general function.
基金supported by NSFC(51105131)Excellent Youth Foundation of Henan Scientific Committee(124100510002)Creative Talent Foundation in University of Henan Province(2011HASTIT016)
文摘Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.
基金Project(51221462)supported by the National Natural Science Foundation of ChinaProject(20120095110001)supported by the PhD Programs Foundation of Ministry of Education of ChinaProject(CXZZ13_0927)supported by Research and Innovation Project for College Graduates of Jiangsu Province,China
文摘As the stiffness of the elastic support varies with the physical-chemical erosion and mechanical friction, model catastrophe of a single degree-of-freedom(DOF) isolation system may occur. A 3-DOF four-point-elastic-support rigid plate(FERP) structure is presented to describe the catastrophic isolation system. Based on the newly-established structure, theoretical derivation for stiffness matrix calculation by free response(SMCby FR) and the method of stiffness identification by stiffness matrix disassembly(SIby SMD)are proposed. By integrating the SMCby FR and the SIby SMD and defining the stiffness assurance criterion(SAC), the procedures for stiffness identification of a FERP structure(SIFERP) are summarized. Then, a numerical example is adopted for the SIFERP validation, in which the simulated tested free response data are generated by the numerical methods, and operation for filtering noise is conducted to imitate the practical application. Results in the numerical example demonstrate the feasibility and accuracy of the developed SIFERP for stiffness identification.
文摘This paper deals with a four-point boundary value problem [φ(u')]' = f(t, u, u'),a < t < b with u(a) - u(ao) = A, u(b) - u(bo) = B, where a < a0 <b0 < b.
文摘This paper is concerned with the existence of solutions for a second-order four-point boundary value problem at resonance. The main methods depend on the technique of the upper and lower solutions and the coincidence degree theory.
