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Coincidence Points and Invariant Approximation Results for Multimaps

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Acta Mathematica Sinica,English Series 2007年第9期23卷 1601-1610页

作者： Donal O'regan Naseer SHAHZAD Department of Mathematics National University of IrelandGalwayIreland Department of Mathematics King Abdul Aziz University

Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either e... 详细信息

关键词： coincidence point weak commutativity best approximant

Positive and Nontrivial Solutions for the Urysohn Integral Equation

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1745-1750页

作者： Daniel FRANCO Gennaro INFANTE Donal O'regan Departamentode Matemática Aplicada Universidad Nacional de Educación a Distancia Dipartimentodi Matematica Universitàdella Calabria Department of Mathematics National University of Ireland

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.

关键词： Urysohn integral equation positive solutions eigenvalues

Generalized I-Contractions and Pointwise R-Subweakly Commuting Maps

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Acta Mathematica Sinica,English Series 2007年第8期23卷 1505-1508页

作者： D.O'regan N.HUSSAIN Department of Mathematics National University of IrelandGalwayIreland Department of Mathematics King Abdul Aziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia

The existence of common fixed points and invariant approximations for pointwise R- subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class... 详细信息

关键词： common fixed point pointwise R-subweakly commuting maps tangential maps diminishing orbital diameters invariant approximation

Asymptotical consensus of fractional-order multi-agent systems with current and delay states

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Applied Mathematics and Mechanics(English Edition) 2019年第11期40卷 1677-1694页

作者： Xuhui WANG Xuesong LI Nanjing HUANG D.O'regan Department of Mathematics Sichuan UniversityChengdu 610064China School of Mathematics Statistics and Applied MathematicsNational University of IrelandGalwayIreland

In this paper,we study some new fractional-order multi-agent systems with current and delay states (FMASCD).Using the generalized Nyquist's stability criterion and Gerschgorin's circle theorem,we obtain the bounded input-bounded output (BIBO) stability and asymptotical consensus of the FMASCD under mild ***,we give some numerical examples to illustrate our main results.

关键词： fractional-order multi-agent system (FMAS) asymptotical consensus current state delay state

An Upper and Lower Solution Theory for the Problem(G′(y))′+f(t,y)=0 on Finite and Infinite Intervals

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Acta Mathematica Sinica,English Series 2006年第3期22卷 827-832页

作者： Ravi P.AGARWAL Donal O'regan Svatoslav STANEK Department of Mathematical Sciences Florida Institute of TechnologyMelbourneFlorida 32901-6975USA Department of Mathematics National University of IrelandGalwayIreland Department of Mathematical Analysis Faculty of SciencePalack University

A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative,... 详细信息

关键词： alternative upper and lower solutions infinite interval diagonalization process Leray-Schauder alternative

In situ Assemblies of Bacteria and Nutrient Dynamics in Response to an Ecosystem Engineer,Marine Clam Scapharca subcrenata,in the Sediment of an Aquaculture Bioremediation System

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Journal of Ocean University of China 2020年第6期19卷 1447-1460页

作者： NICHOLAUS regan LUKWAMBE Betina YANG Wen ZHU Jinyong ZHENG Zhongming School of Marine Sciences Ningbo UniversityNingbo 315832China Department of Natural Sciences Mbeya University of Science and TechnologyMbeya 53000Tanzania Department of Food Science and Technology University of Dar es SalaamDar es Salaam 35091Tanzania

The relationships between nutrient dynamics,microbial community,and macrofauna are important in bioremediation *** this study,we examined the effects of marine clam Scapharca subcrenata sedimentary activities on the microbial assemblages,benthic nutrient chemistry,and its subsequent remediation impacts on organic effluent in the sediment of an aquaculture wastewater bioremediation *** results showed that microbial community composition differed significantly in the clam area(ANOSIM,R=0.707,P=0.037).Pyrosequencing of bacterial 16S rRNA gene revealed a total of 48 unique phyla,79 classes,107 orders,197 families,and 321 genera amongst all *** most dominant bacterial assemblages were Proteobacteria,Bacteroidetes,Acidobacteria,Firmicutes,Verrucomicrobia,and Actinobacteria,with Bacteroidetes and Firmicutes significantly higher in all treatment samples than control(P<0.001).All dominant phyla in the list were shared across all samples and accounted for 89%(control)and 97%(treatment)of the total 16S *** nutrient flux rates from the sediments into the water(treatment group)were 51%(ammonium),88%(nitrate),77%(nitrite)and 45%(phosphate)higher,relative to the control implying increased mineralization,degradability,and mobility of the benthic ***,significantly increased oxygen consumption rates were evident in the clam area signifying improved oxygen distribution within the *** organic effluent contents associated with total-organic matter,carbon,nitrogen,and,phosphate were lower among the clam treatments relative to the *** results describe the potential roles and mechanisms contributed by marine bivalve *** on benthic-bacterial-community assembly,nutrient balance,and effluent reduction in the sediments of aquaculture wastewaters bioremediation system.

关键词： Scapharca subcrenata effluents bioturbation:sediment chemistry bioremediation nutrient dynamics

NON-INSTANTANEOUS IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS WITH STATE DEPENDENT DELAY AND PRACTICAL STABILITY

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Acta Mathematica Scientia 2021年第5期41卷 1699-1718页

作者： Ravi AGARWAL Ricardo ALMEIDA Snezhana HRISTOVA Donal O'regan Department of Mathematics Texas A&M University-KingsvilleKingsvilleTX 78363USA Distinguished University Professor of Mathematics Florida Institute of TechnologyMelbourneFL 32901USA Center for Research and Development in Mathematics and Applications Department of MathematicsUniversity of AveiroPortugal Department of Applied Mathematics and Modeling University of Plovdiv Paisii HilendarskiPlovdivBulgaria School of Mathematics Statistics and Applied MathematicsNational University of IrelandGalwayIreland

Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state *** case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are *** stability properties,based on the modified Razumikhin method are *** examples are given in this paper to illustrate the results.

关键词： non-instantaneous impulses Caputo fractional differential equations practical stability

Positive Solutions to Singular Boundary Value Problems with Sign Changing Nonlinearities on the Half-Line via Upper and Lower Solutions

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Acta Mathematica Sinica,English Series 2007年第8期23卷 1447-1456页

作者： Bao Qiang YAN Donal O'regan Ravi P. AGARWAL Department of Mathematics Shandong Normal University Ji'nan 250014 P. R. China Department of Mathematics National University of Ireland Galway Ireland Department of Mathematical Science Florida Institute of Technology Melbourne FL32901 USA

This paper presents a lower and upper solution technique for singular second order boundary value problems on the half line.

关键词： boundary value problems lower and upper solutions Schauder's fixed point theorem

Nonexistence and Existence of Multiple Positive Solutions for Superlinear Three-point Boundary Value Problems via Index Theory

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 529-540页

作者： Bao-qiang Yan Donal O'regan Ravi P. Agarwal Department of Mathematics Shandong Normal University Jinan 250014 China Department of Mathematics National University of Ireland Galway Ireland Department of Mathematical Science Florida Institute of Technology Melbourne Florida 32901 USA

This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.

关键词： Three-point boundary value problems cone fixed point index