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ON THE EXISTENCE OF ZERO pointS OF A CONTINUOUS FUNCTION

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Acta Mathematica Scientia 2002年第2期22卷 171-177页

作者： J.M. SorianoDepartamento de Andlisis Matematico, Facultad de Matemdticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain Univ Sevilla Fac Matemat Dept Anal Matemat E-41080 Seville Spain

A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to... 详细信息

关键词： Zero point continuation methods banach fixed point theorem homotopy topological direct sum isomorphism k-contractive mapping

INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL

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Acta Mathematica Scientia 2020年第2期40卷 529-542页

作者： Xueke PU Boling GUO School of Mathematics and Information Science Guangzhou UniversityGuangzhou 510006China Institute of Applied Physics and Computational Mathematics P.O.Box 8009Beijing 100088China

This article studies the initial-boundary value problem for a three dimensional magnetic-curvature-driven Rayleigh-Taylor *** first obtain the global existence of weak solutions for the full model equation by employing the Galerkin’s approximation ***,for a slightly simplified model,we show the existence and uniqueness of global strong solutions via the banach’s fixed point theorem and vanishing viscosity method.

关键词： Magnetic-curvature-driven Rayleigh-Taylor model weak solutions strong solutions banach fixed point theorem vanishing viscosity method

Analytic Solutions of an Iterative Differential Equation under Brjuno Condition

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Acta Mathematica Sinica,English Series 2009年第9期25卷 1469-1482页

作者： Jian LIU Jian Guo SI School of Science University of Ji'nan Ji'nan 250022 P.R. China School of Mathematics Shandong University Ji'nan 250100 P.R. China

In this paper, the differential equation involving iterates of the unknown function,x＇（z）=[a^2-x^2（z）]x^[m]（z）with a complex parameter a, is investigated in the complex field C for the existence of analytic solutions. First of all, we discuss the existence and the continuous dependence on the parameter a of analytic solution for the above equation, by making use of banach fixed point theorem. Then, as well as in many previous works, we reduce the equation with the SchrSder transformation x（z） = y（αy^-1（z）） to the following another functional differential equation without iteration of the unknown functionαy＇（αz）=[a^2-y^2（αz）]y＇（z）y（α^mz）,which is called an auxiliary equation. By constructing local invertible analytic solutions of the auxiliary equation, analytic solutions of the form y（αy^-1 （z）） for the original iterative differential equation are obtained. We discuss not only these α given in SchrSder transformation in the hyperbolic case 0 〈｜α｜〈 1 and resonance, i.e., at a root of the unity, but also those α near resonance （i.e., near a root of the unity） under Brjuno condition. Finally, we introduce explicit analytic solutions for the original iterative differential equation by means of a recurrent formula, and give some particular solutions in the form of power functions when a = 0.

关键词： iterative differential equation analytic solution banach fixed point theorem resonance Diophantine condition Brjuno condition

Re ned rigorous perturbation bounds for the SR decomposition

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Applied Mathematics(A Journal of Chinese Universities) 2021年第4期36卷 537-553页

作者： Mahvish Samar Aamir Farooq Department of Mathematics Shantou UniversityShantou 515063China College of Mathematics and Statistics Chongqing UniversityChongqing 401331China

In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are ***,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation *** and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.

关键词： SR decomposition Rigorous perturbation bound Lyapunov majorant function banach fixed point theorem Mixed and componentwise condition numbers

Existence and controllability results to second order neutral differential equation with non-instantaneous impulses

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Journal of Control and Decision 2020年第3期7卷 286-308页

作者： Muslim Malik Avadhesh Kumar School of Basic Sciences Indian Institute of Technology MandiMandiIndia

In this paper,existence and uniqueness of the solutions of the second order neutral differential equation with non-instantaneous impulses in a Hilbert space X are *** is followed by a brief discussion on the exact and trajectory ***,the strongly continuous cosine family of linear operators and banach fixed point theorem are used to establish the ***,an example is given to illustrate the analytical findings.

关键词： Non-instantaneous impulsive system neutral differential equations deviated argument banach fixed point theorem controllability

On controllability for a class of second order semilinear stochastic systems

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Journal of Control and Decision 2016年第4期3卷 211-222页

作者： S.Karthikeyan K.Balachandran J.-H.Kim Department of Mathematics Periyar UniversitySalemIndia Department of Mathematics Bharathiar UniversityCoimbatoreIndia Department of Mathematics Yonsei UniversityYonseiSouth Korea

Many dynamical systems are modeled as second order differential *** this paper we address the problem of controllability for second order semilinear stochastic systems in finite dimensional *** criteria for the complete controllability are formulated under some appropriate *** results are obtained by using the banach fixed point *** an illustrative example is provided.

关键词： Complete controllability second order stochastic system semilinear system banach fixed point theorem

EXISTENCE OF STABLE EQUILIBRIUM FOR A CLASS OF MULTI-SPECIES ECOSYSTEM

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Annals of Differential Equations 1998年第2期14卷 304-308页

作者：余国栋贵州教育学院

In this paper, we discuss the existence of the stable equilibrium in multispecies Scheoner ecosystem. By means of banach fixed point theorem, we obtain a sufficent condition for the system to have a unique positive eq... 详细信息

关键词： banach fixed point theorem M-matrix global stability.

EXISTENCE OF MILD SOLUTIONS TO SEMILINEAR FRACTIONAL ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

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Annals of Differential Equations 2011年第3期27卷 318-322页

作者： Heping Jiang(Dept. of Math.,Huangshan University,Huangshan 245041,Anhui) Wei Jiang(School of Mathematical Science,University of Anhui,Hefei 230039)

In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a banach space.

关键词： mild solutions fractional order functional differential equations banach fixed point theorem analytic semigroup

Existence and Controllability Result for Nonlinear Neutral Evolution Integrodifferential Systems

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Northeastern Mathematical Journal 2008年第1期24卷 54-62页

作者：吕悦刘明姬吕显瑞 School of Mathematics Jilin University Changchun 130012

In this paper, we establish sufficient conditions for existence and controllability of nonlinear neutral evolution integroditferential systems in banach spaces. The result is obtained by using the resolvent operators ... 详细信息

关键词： mild solution controllability resolvent operator neutral evolution integrodifferential system banach fixed point theorem