In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results a...In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.展开更多
The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sido...The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.展开更多
In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are ob...In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.展开更多
By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous ...By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .展开更多
In this paper,we construct an infinite family of approximate inertial manifolds for the Navier-Stokes equations.These manifolds provide higher and higher order approximations to the attractor.Our manifolds are constru...In this paper,we construct an infinite family of approximate inertial manifolds for the Navier-Stokes equations.These manifolds provide higher and higher order approximations to the attractor.Our manifolds are constructed by contraction principle and therefore can be easily approximated by simple explicit functions in real computations.展开更多
对Rademacher级数sum(±u_n)from n=1 to ∞的性质进行了研究,结果表明:Rademacher级数所具有的确界原理可推导出收缩原理,而更为一般的随机级数sum(ξ_nu_n)from n=1 to ∞也可以满足确界原理,因而将收缩原理推广到了更为一般的随...对Rademacher级数sum(±u_n)from n=1 to ∞的性质进行了研究,结果表明:Rademacher级数所具有的确界原理可推导出收缩原理,而更为一般的随机级数sum(ξ_nu_n)from n=1 to ∞也可以满足确界原理,因而将收缩原理推广到了更为一般的随机级数sum(ξ_nu_n)from n=1 to ∞,从而得到了更好的结果.展开更多
文摘In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.
文摘The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.
文摘In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.
文摘By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .
文摘In this paper,we construct an infinite family of approximate inertial manifolds for the Navier-Stokes equations.These manifolds provide higher and higher order approximations to the attractor.Our manifolds are constructed by contraction principle and therefore can be easily approximated by simple explicit functions in real computations.
文摘对Rademacher级数sum(±u_n)from n=1 to ∞的性质进行了研究,结果表明:Rademacher级数所具有的确界原理可推导出收缩原理,而更为一般的随机级数sum(ξ_nu_n)from n=1 to ∞也可以满足确界原理,因而将收缩原理推广到了更为一般的随机级数sum(ξ_nu_n)from n=1 to ∞,从而得到了更好的结果.
