In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further result...In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further results in a particular case where qi = qi.展开更多
The growth of entire functions under the q-difference operators is studied inthis paper, and then some properties of Julia set of entire functions under the higher orderq-difference operators are obtained.
In this paper, we discussed the problem of nonlocal value for nonlinear fractional q-difference equation. The classical tools of fixed point theorems such as Krasnoselskii’s theorem and Banach’s contraction principl...In this paper, we discussed the problem of nonlocal value for nonlinear fractional q-difference equation. The classical tools of fixed point theorems such as Krasnoselskii’s theorem and Banach’s contraction principle are used. At the end of the manuscript, we have an example that illustrates the key findings.展开更多
We consider the properties on solutions of some q-difference equations of the form ∑ n j=0 aj（z）f（qj z）=an＋1（z）, where a0（z）,..., an＋1（z） are meromorphic functions, a0（z）an（z） ≠ 0 and q ∈ C such th...We consider the properties on solutions of some q-difference equations of the form ∑ n j=0 aj（z）f（qj z）=an＋1（z）, where a0（z）,..., an＋1（z） are meromorphic functions, a0（z）an（z） ≠ 0 and q ∈ C such that 0 〈 ｜q｜ ≤ 1. We give estimates on the upper bound for the length of the gap in the power series of entire solutions of （＊） when the coefficients a0（z）,..., an＋1（z） are polynomials and 0 〈 ｜q｜ 〈 1. For some special cases, we give estimates of growth of f（z）. And we also show that the case 0 〈 ｜q｜ 〈 1 is different from the case ｜q｜=1.展开更多
In this paper, we consider the value distribution of meromorphic solutions of order zero of some kind of q-difference equations and examples are also given to elaborate our results.
In this paper, automorphisms of the algebra of q-difference operators, as an associative algebra for arbitrary q and as a Lie algebra for q being not a root of unity, are determined.
This is a set of lecture notes for the first author’s lectures on the difference equations in2019 at the Institute of Advanced Study for Mathematics at Zhejiang University.We focus on explicit computations and exampl...This is a set of lecture notes for the first author’s lectures on the difference equations in2019 at the Institute of Advanced Study for Mathematics at Zhejiang University.We focus on explicit computations and examples.The convergence of local solutions is discussed.展开更多
In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions ...In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.展开更多
By using the basic(or q)-Calculus many subclasses of analytic and univalent functions have been generalized and studied from different viewpoints and perspectives.In this paper,we aim to define certain new subclasses ...By using the basic(or q)-Calculus many subclasses of analytic and univalent functions have been generalized and studied from different viewpoints and perspectives.In this paper,we aim to define certain new subclasses of an analytic function.We then give necessary and sufficient conditions for each of the defined function classes.We also study necessary and sufficient conditions for a function whose coefficients are probabilities of q-Poisson distribution.To validate our results,some known consequences are also given in the form of Remarks and Corollaries.展开更多
In this paper, we apply the iterative technology to establish the existence of solutions for a fractional boundary value problem with q-difference. Explicit iterative sequences are given to approxinate the solutions a...In this paper, we apply the iterative technology to establish the existence of solutions for a fractional boundary value problem with q-difference. Explicit iterative sequences are given to approxinate the solutions and the error estimations are also given.展开更多
基金supported by the National Natural Science Foundation of China (11171119,11126145,11026096)the Nature Science Foundation of Jiangxi Province in China(20114BAB211003)
文摘In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further results in a particular case where qi = qi.
基金supported by the National Natural Science Foundation of China(11571049,11101048)
文摘The growth of entire functions under the q-difference operators is studied inthis paper, and then some properties of Julia set of entire functions under the higher orderq-difference operators are obtained.
文摘In this paper, we discussed the problem of nonlocal value for nonlinear fractional q-difference equation. The classical tools of fixed point theorems such as Krasnoselskii’s theorem and Banach’s contraction principle are used. At the end of the manuscript, we have an example that illustrates the key findings.
基金Supported by National Natural Science Foundation of China (Grant No. 10871076)
文摘We consider the properties on solutions of some q-difference equations of the form ∑ n j=0 aj（z）f（qj z）=an＋1（z）, where a0（z）,..., an＋1（z） are meromorphic functions, a0（z）an（z） ≠ 0 and q ∈ C such that 0 〈 ｜q｜ ≤ 1. We give estimates on the upper bound for the length of the gap in the power series of entire solutions of （＊） when the coefficients a0（z）,..., an＋1（z） are polynomials and 0 〈 ｜q｜ 〈 1. For some special cases, we give estimates of growth of f（z）. And we also show that the case 0 〈 ｜q｜ 〈 1 is different from the case ｜q｜=1.
基金Supported by the National Natural Science Foundation of China (Grant No.10871076)the Youth Science Foundation of Education Bureau of Jiangxi Province (Grant No.GJJ11072)the Natural Science Foundation of Jiangxi Province (Grant No.2009GQS0013)
文摘In this paper, we consider the value distribution of meromorphic solutions of order zero of some kind of q-difference equations and examples are also given to elaborate our results.
文摘In this paper, automorphisms of the algebra of q-difference operators, as an associative algebra for arbitrary q and as a Lie algebra for q being not a root of unity, are determined.
基金supported by a KIAS Individual Grant(MG083901)at Korea Institute for Advanced Studya POSCO Science fellowship。
文摘This is a set of lecture notes for the first author’s lectures on the difference equations in2019 at the Institute of Advanced Study for Mathematics at Zhejiang University.We focus on explicit computations and examples.The convergence of local solutions is discussed.
文摘In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.
文摘By using the basic(or q)-Calculus many subclasses of analytic and univalent functions have been generalized and studied from different viewpoints and perspectives.In this paper,we aim to define certain new subclasses of an analytic function.We then give necessary and sufficient conditions for each of the defined function classes.We also study necessary and sufficient conditions for a function whose coefficients are probabilities of q-Poisson distribution.To validate our results,some known consequences are also given in the form of Remarks and Corollaries.
文摘In this paper, we apply the iterative technology to establish the existence of solutions for a fractional boundary value problem with q-difference. Explicit iterative sequences are given to approxinate the solutions and the error estimations are also given.
