<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the ...<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0＜α≤b_n+c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~'+c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.展开更多
This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, B...This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）展开更多
This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to ...This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.展开更多
In this paper, necessary and sufficient conditions for a closed range composition operator CФ on the general family of holomorphic function spaces F（p,q,s） and more generally on α-Besov type spaces F（p,αp-2,s） ...In this paper, necessary and sufficient conditions for a closed range composition operator CФ on the general family of holomorphic function spaces F（p,q,s） and more generally on α-Besov type spaces F（p,αp-2,s） are given. We give a Carleson measure characterization on F （p, αp - 2, s） spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of CФ on F（p,q,s） and F（p,αp- 2,s） spaces.展开更多
In this paper,we study the existence of the reflexive,reflexive selfadjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual(P,Q).We derive necessary...In this paper,we study the existence of the reflexive,reflexive selfadjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual(P,Q).We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.展开更多
The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued L p -spaces are studied. To obtain the uniform maximal regularity and the Carlem...The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued L p -spaces are studied. To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations, the sufficient conditions are founded. By using these facts, the unique continuation properties are established. In the application part, the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.展开更多
Based on Mansevich-Mawhin continuation theorem and some analysis skill, some new sufficient conditions for the existence of periodic solutions to a duffing type p-Laplacian differential equation with several p-Laplaci...Based on Mansevich-Mawhin continuation theorem and some analysis skill, some new sufficient conditions for the existence of periodic solutions to a duffing type p-Laplacian differential equation with several p-Laplacian operators are obtained. Moreover, we construct an example to illustrate the feasibility of our results.展开更多
In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point ...In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point theorem on the cone.展开更多
In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
In this paper, we＇ll prove new representation theorems for a kind of second order stochastic integral- differential operator by stochastic differential equations （SDEs） and backward stochastic differential equatio...In this paper, we＇ll prove new representation theorems for a kind of second order stochastic integral- differential operator by stochastic differential equations （SDEs） and backward stochastic differential equations （BSDEs） with jumps, and give some applications.展开更多
This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has ...This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has different singularity （vanishing in finite time）.展开更多
The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mo...The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.展开更多
One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a（au/at）, studied in this paper, where the item au/at which makes it more general. The...One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a（au/at）, studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2（O, T; L2 （Ω）） is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.展开更多
The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and ...The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.展开更多
基金This work was supported partially by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions by Ministry of Educationthe Department Fund of Science and Technology in Shanghai Higher Education Institutionsthe Special Funds for Major Specialities by the Shanghai Education Committee.
文摘<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0＜α≤b_n+c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~'+c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.
基金Supported in part by the National Natural Science Foundation of China(11271359)the Fundamental Research Funds for the Central Universities(2014-Ia-037and 2015-IVA-069)
文摘This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）
基金Supported by the National Natural Science Foundation of China (10771064)the Natural Science Foundation of Zhejiang province (Y6090036+1 种基金Y7080197,Y606197)the Foundation of Department of Education of Zhejiang Province (20070482)
文摘This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.
文摘In this paper, necessary and sufficient conditions for a closed range composition operator CФ on the general family of holomorphic function spaces F（p,q,s） and more generally on α-Besov type spaces F（p,αp-2,s） are given. We give a Carleson measure characterization on F （p, αp - 2, s） spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of CФ on F（p,q,s） and F（p,αp- 2,s） spaces.
文摘In this paper,we study the existence of the reflexive,reflexive selfadjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual(P,Q).We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.
文摘The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued L p -spaces are studied. To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations, the sufficient conditions are founded. By using these facts, the unique continuation properties are established. In the application part, the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.
基金sponsored by the National Natural Science Foundation of China (11071001)NSF of Education Bureau of Anhui Province (KJ2009A005Z+2 种基金KJ2010ZD022010SQRL159)Anhui Provincial Natural Science Foundation (1208085MA13)
文摘Based on Mansevich-Mawhin continuation theorem and some analysis skill, some new sufficient conditions for the existence of periodic solutions to a duffing type p-Laplacian differential equation with several p-Laplacian operators are obtained. Moreover, we construct an example to illustrate the feasibility of our results.
基金supported financially by the National Natural Science Foundation of China(10971179)the Foundation for Outstanding Middle-Aged and Young Scientists of Shandong Province(BS2010SF004)a Project of Shandong Province Higher Educational Science and Technology Program(No.J10LA53)
文摘In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point theorem on the cone.
文摘In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
基金Supported by the National Natural Science Foundation of China(No.11171186)the"111"project(No.B12023)
文摘In this paper, we＇ll prove new representation theorems for a kind of second order stochastic integral- differential operator by stochastic differential equations （SDEs） and backward stochastic differential equations （BSDEs） with jumps, and give some applications.
基金Partially supported by the NSF(11271154)of China the 985 program of Jilin University
文摘This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has different singularity （vanishing in finite time）.
基金supported by the Bulgarian National Science Fund under Project DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution”, 2017。
文摘The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.
基金supported by the National Natural Science Foundation of China(11071053)Natural Science Foundation of Hebei Province(A2014207010)+1 种基金Key Project of Science and Research of Hebei Educational Department(ZD2016024)Key Project of Science and Research of Hebei University of Economics and Business(2015KYZ03)
文摘One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a（au/at）, studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2（O, T; L2 （Ω）） is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.
文摘The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.
