In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper...The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper presents a new approach to rank the alternatives by G1-coefficient of variation method.The focus of this approach is the use of the combination weighing,which is able to compensate for the deficiencies in the method of evaluation index single weighing.In the case study,an appropriate evaluation index system was established to determine the evaluation value of each ventilation mode.Then the proposed approach was used to select the best development face ventilation mode.The result shows that the proposed approach is able to rank the alternative development face ventilation mode reasonably,the combination weighing method had the advantages of both subjective and objective weighing methods in that it took into consideration of both the experience and wisdom of experts,and the new changes in objective conditions.This approach provides a more reasonable and reliable procedure to analyse and evaluate different ventilation modes.展开更多
In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence resul...In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence results of the coupled Dirac systems are obtained for nonlinearity with superquadratic growth rates.The results obtained by GONG and LU(2017)are extended to the case of chiral boundary condition.展开更多
Slip of a composite box beam may reduce its stiffness, enlarge its deformation and affect its performance. In this work, the governing differential equations and boundary conditions of composite box beams were establi...Slip of a composite box beam may reduce its stiffness, enlarge its deformation and affect its performance. In this work, the governing differential equations and boundary conditions of composite box beams were established. Analytic solutions of combined differential equations were also established. Partial degree of freedom was adopted to establish a new FEA element of three-dimensional beam, taking into account the slip effect. Slip and its first-order derivative were introduced into the nodes of composite box beams as generalized degree of freedom. Stiffness matrix and load array of beam elements were established. A three-dimensional nonlinear calculation program was worked out. The results show that the element is reliable and easy to divide and is suitable for special nonlinear analysis of large-span composite box beams.展开更多
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
基金Projects(51504286,51374242)supported by the National Natural Science Foundation of ChinaProject(2015M572270)supported by China Postdoctoral Science FoundationProject(2015RS4004)supported by the Science and Technology Plan of Hunan Province,China
文摘The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper presents a new approach to rank the alternatives by G1-coefficient of variation method.The focus of this approach is the use of the combination weighing,which is able to compensate for the deficiencies in the method of evaluation index single weighing.In the case study,an appropriate evaluation index system was established to determine the evaluation value of each ventilation mode.Then the proposed approach was used to select the best development face ventilation mode.The result shows that the proposed approach is able to rank the alternative development face ventilation mode reasonably,the combination weighing method had the advantages of both subjective and objective weighing methods in that it took into consideration of both the experience and wisdom of experts,and the new changes in objective conditions.This approach provides a more reasonable and reliable procedure to analyse and evaluate different ventilation modes.
基金Supported by the National Natural Science Foundation of China(11801499)。
文摘In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence results of the coupled Dirac systems are obtained for nonlinearity with superquadratic growth rates.The results obtained by GONG and LU(2017)are extended to the case of chiral boundary condition.
基金Project(50708112) supported by the National Natural Science Foundation of ChinaProject(IRT1296) supported by the Program for Changjiang Scholars and Innovative Research Team in University
文摘Slip of a composite box beam may reduce its stiffness, enlarge its deformation and affect its performance. In this work, the governing differential equations and boundary conditions of composite box beams were established. Analytic solutions of combined differential equations were also established. Partial degree of freedom was adopted to establish a new FEA element of three-dimensional beam, taking into account the slip effect. Slip and its first-order derivative were introduced into the nodes of composite box beams as generalized degree of freedom. Stiffness matrix and load array of beam elements were established. A three-dimensional nonlinear calculation program was worked out. The results show that the element is reliable and easy to divide and is suitable for special nonlinear analysis of large-span composite box beams.
