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multiplicity in Continuous Adiabatic MSMPR Reactive Precipitators

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Chinese Journal of Chemical Engineering 1998年第2期6卷 48-58页

作者：尹秋响 Department of Chemical Engineering Tianjin University

The possibility of both concentration and temperature multiplicities has bcen studied for the case of acontinuous adiabatic mixed suspension mixed product removal(MSMPR)reactive precipitaior.A Process in-volving homogeneous chemical reaction in first order reaction kinetics with respect to each of the reactive compo-nents and subsequent crystallization described by conventional power law growth and power law magma depen-dent nucleation models is *** temperature dependency of each of these kinetics is described by Ar-rhenius *** regions are determined in which multiple steady states *** linear stability ofthese steady states is analyzed by using the Routh criterion approach.

关键词： multiplicity MSMPR crystallizer reactive precipitation stability

multiplicity of Periodic Bouncing Solutions for Sublinear Damped Variation Systems via Nonsmooth Variational Methods

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Acta Mathematica Sinica,English Series 2023年第7期39卷 1332-1350页

作者： Si Qi WANG Fei GUO School of Mathematics Tianjin UniversityTianjin 300354China Tianjin Key Laboratory of Brain-Inspired Intelligence Technology Tianjin 300354China

Two results about the multiplicity of nontrivial periodic bouncing solutions for sublinear damped vibration systems-x=g(t)x+f(t,x) are obtained via the Generalized Nonsmooth Saddle Point Theorem and a technique established by Wu Xian and Wang *** of them imply the condition "f≥0" required in some previous papers can be weakened,furthermore,one of them also implies the condition about ■F(t,x)/■t required in some previous papers,such as "|■F(t,x)/■t|=σ_(0)F(t,x)" and "|■F(t,x)/■t|≤C(1+F(t,x))", is unnecessary,where F(t,x):=∫_(0)~xf(t,x)ds,and σ_(0),C are positive constants.

关键词： Damped vibration systems generalized Nonsmooth Saddle Point Theorem sublinear conditions periodic bouncing solutions multiplicity

multiplicity OF PERIODIC SOLUTIONS FOR SECOND ORDER HAMILTONIAN SYSTEMS WITH MIXED NONLINEARITIES

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Acta Mathematica Scientia 2021年第2期41卷 371-380页

作者： Mingwei WANG Fei GUO School of Mathematics Tianjin UniversityTianjin 300354China

The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this *** via the Symmetric Mountain Pass Lemma,two results about i... 详细信息

关键词： multiplicity periodic solutions second order Hamiltonian systems Symmetric Mountain Pass Lemma

multiplicity of Periodic Solutions for Second Order Hamiltonian Systems with Asymptotically Quadratic Conditions

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Acta Mathematica Sinica,English Series 2020年第1期36卷 55-65页

作者： Peng LIU Fei GUO School of Mathematics Tianjin University

A class of second order non-autonomous Hamiltonian systems with asymptotically quadratic conditions is considered in this *** Fountain Theorem,one multiplicity result of periodic solutions is obtained,which improves s... 详细信息

关键词： Second order Hamiltonian systems asymptotically quadratic conditions Fountain Theorem periodic solution multiplicity

multiplicity of Homoclinic Solutions for Second Order Hamiltonian Systems with Local Conditions at the Origin

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Acta Mathematica Sinica,English Series 2022年第4期38卷 735-744页

作者： Peng LIU Fei GUO School of Mathematics Tianjin UniversityTianjin 300354P.R.China Tianjin Key Laboratory of Brain-Inspired Intelligence Technology Tianjin 300354P.R.China

In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L∈C(R,RN×N)is symmetric but non-periodic,W∈C1(R×RN,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.

关键词： Second order non-autonomous Hamiltonian systems Homoclinic solutions multiplicity new symmetric mountain pass lemma

multiplicity OF SOLUTIONS OF WEIGHTED(p, q)-LAPLACIAN WITH SMALL SOURCE

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Acta Mathematica Scientia 2018年第2期38卷 419-428页

作者：宋慧娟尹景学王泽佳 College of Mathematics and Informational Science Jiangxi Normal University School of Mathematical Sciences South China Normal University

In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system -div（h1（x）｜△u｜p-2△u）=d（x）｜u｜r-2u＋Gu（x,u,v） in Ω -div（h2（x）｜△u｜q-2△v）=f（x）｜v｜s-2v＋Gv（x,u,v） in Ω, u=v=0 on δΩ where Ω is a bounded domain in RN with smooth boundary δΩ, N ≥ 2, 1 〈 r 〈 p ∞, 1〈 s 〈 q 〈 ∞; h1（x） and h2（x） are allowed to have ＂essential＂ zeroes at some points in Ω; d（x）｜u｜r-2u and f（x）｜v｜s-2v are small sources with Gu（x,u,v）, Gv（x,u,v） being their high-order perturbations with respect to （u, v） near the origin, respectively.

关键词： Weighted (p q)-Laplacian small sources multiplicity

multiplicity results for the unstirred chemostat model with general response functions

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Science China Mathematics 2013年第10期56卷 2035-2050页

作者： NIE Hua WU JianHua College of Mathematics and Information Science Shaanxi Normal University

We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single smooth solution curve, whose properties determine the multiplicity of positive steady state solutions. The key point of our analysis is to study the ＂turning points＂ on this positive steady state solution curve, and to prove that any nontrivial solution to the associated linearized problem is one of sign by constructing a suitable test function. The main tools used here include bifurcation theory, monotone method, mountain passing lemma and Sturm comnarison theorem.

关键词： chemostat general response function multiplicity bifurcation theory Sturm comparison theorem

multiplicity Distribution of Evaporated Fragments in Relativistic Nucleus-Nucleus Collisions

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Chinese journal of nuclear physics 1995年第1期17卷 17-20页

作者： Liu, Fuhu Inst of High Energy Physics Chinese Acad of Sciences Beijing China

The multiplicity distribtuion of evaporated fragments in relativistic nucleus-nucleus collisions are *** calculated results are in agreement with the exper-imental data in the energy range from 3.7 to 200 GeV/N.

关键词： Relativistic nucleus-nucleus collisions Evaporated fragment, multiplicity distribution

Analyses of multiplicity and Stability Patterns of Agglomeration Controlled Precipitation with Both Primary and Secondary Nucleations

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Chinese Journal of Chemical Engineering 2002年第2期10卷 202-207页

作者：尹秋响张美景王静康 School of Chemical Engineering and Technology Tianjin University Tianjin 300072 China

The possibility of multiplicity in an isothermal continuous mixed suspension-mixed product removalcrystallizer is explored using the bifurcation theory. A process involving agglomeration controlled precipitationis considered in which secondary nucleation occurs simultaneously with primary nucleation. The determinantequations for the existence of multiple steady states are developed and the multiplicity boundaries dependent on thephysical and kinetic properties and operational parameters of the process are obtained by resolving these determinantequations. The number of steady states in the precipitator for various multiplicity regions is determined and thelinear stability of these steady states is analyzed by using the Routh criterion.

关键词： precipitation mixed suspension-mixed product removal crystallizer agglomeration multiplicity sta- bility