In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such si...In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq（R3） for all q 1. The condition on the integral kernels is known to be optimal.展开更多
The aim of the present study is to design a new fifth order system of Emden–Fowler equations and related four types of the model.The standard second order form of the Emden–Fowler has been used to obtain the new mod...The aim of the present study is to design a new fifth order system of Emden–Fowler equations and related four types of the model.The standard second order form of the Emden–Fowler has been used to obtain the new model.The shape factor that appear more than one time discussed in detail for every case of the designed model.The singularity atη=0 at one point or multiple points is also discussed at each type of the model.For validation and correctness of the new designed model,one example of each type based on system of fifth order Emden–Fowler equations are provided and numerical solutions of the designed equations of each type have been obtained by using variational iteration scheme.The comparison of the exact results and present numerical outcomes for solving one problem of each type is presented to check the accuracy of the designed model.展开更多
This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singula...This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.展开更多
基金Supported by the NSFC (10771054, 10971141, 11071200)the NFS of Beijing (1092004)the NFS of Fujian Province (2010J01013)
文摘In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L（log＋L）ε（Sm-1 × Sn-1） （ε = 1 or 2） supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq（R3） for all q 1. The condition on the integral kernels is known to be optimal.
文摘The aim of the present study is to design a new fifth order system of Emden–Fowler equations and related four types of the model.The standard second order form of the Emden–Fowler has been used to obtain the new model.The shape factor that appear more than one time discussed in detail for every case of the designed model.The singularity atη=0 at one point or multiple points is also discussed at each type of the model.For validation and correctness of the new designed model,one example of each type based on system of fifth order Emden–Fowler equations are provided and numerical solutions of the designed equations of each type have been obtained by using variational iteration scheme.The comparison of the exact results and present numerical outcomes for solving one problem of each type is presented to check the accuracy of the designed model.
基金supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
