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Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to further study the properties of boundary value problems for fractional differential equations with non-linear terms,we discusses the existence of positive solutions for eigenvalue problems of (n-1,1) fractional differential equations with sign-changing nonlinear terms, where the fractional derivative is Riemann-Liouville. First we use the Green function for a given boundary value problem and convert the differential equation into an equivalent integral equation. Then, under the condition that the nonlinear term f(t, x) satisfies Caratheodory conditions (that is to say, the non-linear term f(t,x) is measurable function when the variable x was chosen arbitrarily, and the non-linear term f(t,x) is continuous function of x when the variable t was fixed). By constructing a suitable Banach space, we use the cone-stretching and compression fixed point theorem and Leray-Schauder nonlinear selection to obtain the sufficient conditions for the existence of positive solutions of boundary value problems.The results show that the nonlinear term f(t,x) can be singular at any point t. At the same time, the range of the eigenvalue which makes the solution of the boundary value problem exist was changed.The results lay a foundation for further study of the existing conclusions.

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Hebei University of Science & Technology is the property of Hebei University of Science & Technology, Journal of Hebei University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Dalian University of Technology / Dalian Ligong Daxue Xuebao is the property of Journal of Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Dalian University of Technology / Dalian Ligong Daxue Xuebao is the property of Journal of Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Transactions of Beijing Institute of Technology is the property of Beijing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Perturbation of (p,Y) -operator Bessel sequences, (p, Y)-operator frames and (p, Y)-operator Riesz bases in Banach space are mainly studied. Inequality form perturbation condition of Hilbert space frames, obtained by Casazza and Christensen, is generalized to Banach space by using the operator theory and algebraic method. Inequality form perturbation conditions of (p, Y)-operator Bessel sequences, (p, Y)-operator frames and (p,Y)-operator Riesz bases are proved. Some equivalence perturbation conditions are also investigated. [ABSTRACT FROM AUTHOR]

Let H be a Hilbert space. ... (H) denotes the Banach space of all bounded linear operators of H into H. A class of analytic operator-valued functions in three-dimensional Hilbert space is introduced, ... = {f/(Ζ) : f(Ζ) = ... is analytic on the unit disk |Ζ|≤ 1, where the coefficients An are compact positive Hermitian operators of H into H and I denote the identity operator on H,...≤1 for any χ ∈H with || χ|| =1}. Using the convexity techniques of functional analysis and operator theory, the extreme points of ... are researched in suitable conditions. [ABSTRACT FROM AUTHOR]

In this paper, Xd-Bessel sequences, Xd-frames and Xd-Riesz basis for a Banach space are discussed. A necessary and sufficient condition of Xd-frame and Xd-Riesz basis is given in Banach space. Also it is proved that when Xd is a BK-space, Bx(Xd) is isometrically isomorphism with B(X, Xd) which means Bx (Xd) is a Banach space. When Xd is a reflective BK-space with the basis {ei }iε^, then independent Xd-frames and Xd-Riesz basis for a Banach space X are the same. [ABSTRACT FROM AUTHOR]