高阶线性微分方程的解及其解的导数的不动点

研究了复域齐次和非齐次线性微分方程的解及其解的导数的不动点与超级问题,得到了整函数系数的齐次和非齐次线性微分方程的解及其解的导数的不动点的两个结果,所得结果推广了一些相关结果.     

亚纯函数系数微分方程的解和小函数的关系

研究了一类亚纯函数为系数的二阶非齐次线性微分方程的解及其微分多项式和小函数的关系,并得到了这类微分方程解以及解的一阶,二阶导数与微分多项式的不动点性质.     

二阶线性微分方程亚纯解的不动点与超级

本文研究了以亚纯函数为系数的二阶线性微分方程的解及其一阶和二阶导数的不动点及超级问题，得到：二阶线性微分方程亚纯解及其一阶和二阶导数的不动点性质，由于受到微分方程的限制，与一般亚纯函数的不动点性质相比是十分有趣的，事实上，它们与解的增长性密切相关。     

二阶线性微分方程解与不动点的关系

使用Nevanlinna值分布的基本理论和方法,研究了几类二阶线性微分方程解及解的导数与其不动点之间的关系,得到了方程解及其导数的不动点的不同点收敛指数为无穷和二级收敛指数等于解的超级的精确结果.     

高阶线性微分方程解的二阶导数的不动点

研究了以整函数为系数的高阶线性微分方程解的二阶导数的不动点,得到的两个结果推广了一些相关结论.     

一类二阶非齐次微分方程解的增长性与不动点[英文]

研究方程f''+A(z)f'' B(z)f=F解的增长性与解及其导数的不动点问题,其中A(z),B(z),F(z)(不恒等于0)是整函数,F的级为无穷,得到了方程解的超级、二级不同零点收敛指数,方程解及其一阶和二阶导数的二级不动点收敛指数等的精确估计.     

一类二阶非齐次微分方程解的增长性与不动点(英文)

本文研究方程f′′+A(z)f′+B(z)f=F解的增长性、解及其导数的不动点问题,其中A(z),B(z)(不恒等于0),F(z)(不恒等于0)是整函数,F的级为无穷.得到方程解的超级、二级不同零点收敛指数、方程解及其一阶和二阶导数的二级不动点收敛指数等的精确估计.     

一类微分方程的解及其解的导数与不动点的关系

研究了一类亚纯系数微分方程的复振问题,通过应用亚纯函数的分解和模的增长估计,得到了该类方程的级的精确估计,同时对方程的解及其一阶导数与不动点间的关系进行了研究,指出由于受到微分方程的制约,该类方程的不动点密度与解的增长性有着密切的关系.     

含有变量阶导数及一个参数的非线性分数阶微分方程初值问题

该文利用Schauder不动点定理研究了含有变量阶导数的非线性分数阶微分方程初值问题解的存在性.     

单位圆内二阶线性微分方程的解与小函数的关系

讨论了系数是单位圆内解析函数的二阶齐次和非齐次线性微分方程的解及其一阶导数和二阶导数与小函数之间的关系,并得到了它们之间的精确估计.     

亚纯函数系数高阶复域微分方程解的不动点

研究了一类亚纯函数系数的高阶线性微分方程的解的不动点问题,应用值分布的理论和方法,得到了复域微分方程亚纯解的不动点性质.     

Blowups of complex-valued solutions for some hydrodynamic models

We study complex-valued blowups of solutions for several hydrodynamic models. For complex-valued initial conditions, smooth local solutions can have finite-time singularities since the energy inequality does not hold. By using some version of the renormalization group method, we derive the equations for corresponding fixed points and analyze the spectrum of the linearized operator. We describe the open set of initial conditions for which blowups at finite time can occur.     

Brownian motion and exposed solutions of differential inclusions

We present a research program designed by A. Bressan and some partial results related to it. First, we construct a probability measure supported on the space of solutions to a planar differential inclusion, where the right-hand side is a Lipschitz continuous segment. Such measure assigns probability one to solutions having derivatives a.e. equal to one of the endpoints of the segment. Second, for a class of planar differential inclusions with Hölder continuous right-hand side F, we prove existence of solutions whose derivatives are exposed points of F. Finally, we complete the research program if the right-hand side of the differential inclusion does not depend on the state and prove a result on the Lipschitz continuity of an auxiliary map. The proofs rely on basic properties of Brownian motion.     

Fixed point solutions of generalized equilibrium problems for nonexpansive mappings

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a generalized equilibrium problem in a real Hilbert space. Then, strong convergence of the scheme to a common element of the two sets is proved. As an application, problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem is solved. Moreover, solution is given to the problem of finding a common element of fixed points set of nonexpansive mappings and the set of solutions of a variational inequality problem.     

On the Growth and Fixed Points of Solutions of Second Order Differential Equations with Meromorphic Coefficients

In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain that the exponents of convergence of these fixed points are all equal to the order of growth.     

Positive solutions for a system of coupled fractional boundary value problems

We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations, subject to multipoint boundary conditions that contain fractional derivatives, by using some theorems from the fixed point index theory.     

Optimum solutions for a system of differential equations via measure of noncompactness

New classes of mappings, called cyclic (noncyclic) condensing operators, are introduced and used to investigate the existence of best proximity points (best proximity pairs) with the help of a suitable measure of noncompactness. In this way, we obtain some real generalizations of Schauder and Darbo’s fixed point theorems. In the last section, we apply such results to study the existence of optimum solutions to a system of differential equations.     

Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems

In this paper, we present an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of an infinite family of nonexpansive mappings and the set of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters.