the steady states of a non cooperative model arising in reactor dynamics in this work we investigate the existence and stability of coexistence states of a reaction diffusion model originated by the theory of nuclear reactors by converting it to an equivalent system with linear cooperative part we obtain the necessary and sufficient conditions for the existence of coexistence states via lower and upper solutions method in addition stability results and a criterion are also given to enrich and complement those available in the literature

a quasilinear parabolic system arising in modelling of catalytic reactors a system of four quasilinear parabolic equations arising in modelling of catalytic reactors is studied the system is coupled in a nonstandard way we prove that the system has unique global solution the asymptotic behavior as t is studied

differential geometric methods in variable structure control this article presents a differential geometric approach for the design of sliding modes in non linear variable structure feedback systems coordinate free characterizations of local existence conditions for sliding regimes and a geometric reformulation of some of its most salient features are presented the approach uses basic notions from differential geometry involving vector fields distributions and 1 forms both single and multiple input cases are treated with some illustrative examples

on the uniqueness and ordering of steady states of predator prey systems this paper discusses the relationship between the uniqueness and the ordering of strictly positive solutions of elliptic predator prey interacting systems if v and u v are two such solutions with u or v v then u v v when the positive solutions are numerically close to the extreme case the solution is unique

on the commuting isometries abstract the paper summarizes clarifies and supplements results on decompositions and a model for pairs of commuting isometries the geometrical model is given whenever it is possible the remaining problem of describing the model for completely non compatible pairs of isometries is reduced to completely non compatible pairs of unilateral shifts moreover subspaces generating incompatibility are determined

wold slocinski decompositions for commuting isometric triples abstract extending two remarkable results by von neumann halmos wold for isometric operators and slocinski for pairs of commuting isometries we discuss the possibility to decompose a given commuting triple v v 1 v 2 v 3 of isometric operators acting on a hilbert space h into the direct sum between commuting triples consisting of unitary operators and or unilateral shifts we prove that such a decomposition exists if and only if the pairs v 1 v 2 v 3 v 2 v 3 v 1 and v 1 v 3 v 2 have decompositions of wold slocinski type if only two of these pairs are supposed to have such a decomposition then the wold slocinski decomposition associated to v has seven summands several structure results of geometric type for these summands are also presented examples and counterexamples are used for illustrative purposes certain results are presented in full generality i e for commuting isometric n tuples

brief sliding mode control for two time scale systems stability issues the paper presents some results on global exponential stability of linear time invariant systems with different time scales the full system is decomposed in two reduced ones by means of singular perturbations and a smooth approximation of a variable structure control is synthesized for each of them using reaching law approach the global closed loop stability is then proved for the whole system using lyapunov methods and a particular state space decomposition moreover a literal form for e a parameter which measures the minimum separation between time scales is derived

compatible pairs of commuting isometries abstract the paper is devoted to pairs of commuting isometries a unique decomposition of such pairs into a compatible and a completely non compatible part is constructed the compatible part is fully described

on wold type decomposition abstract the main result of this paper is some new equivalent condition for a contraction to be a direct sum of a unitary operator and a c 0 completely nonunitary contraction called wold type decomposition it is applied for p k quasihyponormal k paranormal k paranormal and of class q operators this decomposition is connected with the putnam fuglede property additionally we show an example of operator of class q with norm 1 but without svep so not paranormal finally we remark that each k paranormal operator is k 1 paranormal

some remarks on the supersolution subsolution method for superlinear elliptic equations au f x u o x e r 1 where a is the n dimensional laplacian n 3 3 and f u is a locally holder continuous with exponent 8 e 0 1 function on r x 0 co which is locally lipschitz in u because of the importance of 1 in differential geometry and in various applications there has been a growing interest in studying the existence and asymptotic behavior of positive entire solutions of 1 see for example the papers l 12 14 191 by an entire solution of 1 we here mean a function u e cfoz r which satisfies 1 at every point of r by now it is well known that the supersolution subsolution method or the method of barriers is an extremely powerful tool for establishing the existence of positive solutions of 1 this method is based on

global existence for reaction diffusion systems with mass control and critical growth with respect to the gradient abstract in this paper we study the existence of global weak solutions for 2 2 reaction diffusion systems for which two main properties hold the positivity of the solutions and the total mass of the components are preserved with time moreover we suppose that the non linearities have critical growth with respect to the gradient the technique we use here in order to prove global existence is in the same spirit of the method developed by boccardo murat and puel for a single equation

asymptotic behavior of global solutions for a chemical reaction model this paper deals with a system of reaction diffusion equations modeling a chemical reaction process involving three substances the mathematical system consists of three semilinear partial differential equations of parabolic type with homogenous neumann boundary conditions the goal is to determine whether each substance has a positive asymptotic limit by the method of upper and lower solutions

persistence in a periodic competitor competitor mutualist diffusion system in this paper we investigate the existence and the asymptotic behavior of periodic solutions for a periodic reaction diffusion system of a competitor competitor mutualist model under dirichlet boundary conditions we shall prove that under certain conditions this system is persistent and under some other conditions it exhibits extinction or more exactly the species of mutualist extincts

second order elliptic differential inequalities in banach spaces we derive monotonicity results for solutions of partial differential inequalities of elliptic type in ordered normed spaces with respect to the boundary values as a consequence we get an existence theorem for the dirichlet boundary value problem by means of a variant of tarski s fixed point theorem

positive solutions of the second order differential systems in reactor dynamics abstract in this paper we are concerned with the existence of positive solutions of the second order cooperative system u u u g t f u t 0 1 u t 0 1 u 0 u 1 0 0 1 0 where 2 is a constant 0 is a parameter g 0 1 0 is continuous and g 0 on any subinterval of 0 1 f 0 0 is continuous and f s 0 for s 0 under some suitable conditions on the nonlinearity f we show that above system has at least one positive solution for any 0 the proof of our main results is based upon bifurcation techniques

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

monotone iterative methods for finite difference system of reaction diffusion equations this paper presents an existence comparison theorem and an iterative method for a nonlinear finite difference system which corresponds to a class of semilinear parabolic and elliptic boundary value problems the basic idea of the iterative method for the computation of numerical solutions is the monotone approach which involves the notion of upper and lower solutions and the construction of monotone sequences from a suitable linear discrete system using upper and lower solutions as two distinct initial iterations two monotone sequences from a suitable linear system are constructed it is shown that these two sequences converge monotonically from above and below respectively to a unique solution of the nonlinear discrete equations this formulation leads to a well posed problem for the nonlinear discrete system applications are given to several models arising from physical chemical and biological systems numerical results are given to some of these models including a discussion on the rate of convergence of the monotone sequences

sliding observer based feedback control for flexible joints manipulator abstract high precision measurements of joint displacements and elastic forces are available on a flexible joints manipulator in contrast velocity measurements and elastic forces derivative are in many cases contaminated by noise or unavailable technical or economical constraint it is therefore interesting to investigate the possibility of controlling robot dynamics by only using position and elastic force measurements this paper presents a singular perturbation approach for trajectory tracking control combined with non linear sliding state observer the stability of the closed loop system is investigated

feedback control of two time scale nonlinear systems this article concerns a class of two time scale single input single output nonlinear systems for such systems combination of singular perturbation and geometric methods is employed to synthesize well conditioned static state feedback laws that induce a well characterized input output behaviour and guarantee stability of the closed loop system the developed control laws are applied to two nonlinear chemical processes with time scale multiplicity and their performance is evaluated through simulations

a monotone iterative scheme for nonlinear reaction diffusion systems having nonmonotone reaction terms abstract a monotone scheme is proposed for the solution of weakly coupled systems of reaction diffusion equations without any monotonicity property of the nonlinear reaction terms the considerations are taken within the framework of weak solutions

s shaped global bifurcation curve and hopf bifurcation of positive solutions to a predator prey model where d is a bounded domain in r n 1 with smooth boundary d and a b c d m are positive constants problem 1 0 is known as the predator prey model with holling tanner type interactions where u and v represent the densities of the prey and predator respectively hence we are only interested in positive solutions by which we mean that both u and v are positive in d it is easy to see that a 1 is necessary for the existence of positive solutions to 1 0 and we shall also assume that d 1 the case d 1 is rather different and will not be discussed here we are mainly interested in studying the number of positive solutions of 1 0 and the stability of these solutions in particular we shall show that when b d c and m fall into certain range the solution set u v a of 1 0 forms a s shaped smooth curve and that hopf bifurcation occurs along this curve this not only confirms rigorously similar numerical observations on 1 0 made in 4 but also shows that the corresponding parabolic system

unbounded positive entire solutions of semilinear elliptic equations on etudie l existence et le comportement asymptotique des solutions positives non bornees d equations elliptiques semilineaires du type u f x u dans r n on etablit des resultats globaux

a diffusive competition model with a protection zone this paper is concerned with a two species diffusive competition model with a protection zone for the weak competitor our mathematical results imply that when the protection zone is above a certain critical patch size determined by the birth rate of the weak competitor the weak species almost always survives but it cannot survive when the protection zone is below the critical size and its competitor is strong enough while this is the main feature of the model the actual dynamical behavior of the reaction diffusion system is more complicated the key to reveal the main feature of the system lies in a detailed analysis of the attracting regions of its steady state solutions our mathematical analysis shows that compared with the predator prey model discussed in yihong du junping shi a diffusive predator prey model with a protect zone j differential equations 226 2006 63 91 the protection zone has some essentially different effects on the fine dynamics of the competition model

on nonlinear coupled reaction diffusion equations this paper is concerned with the existence and uniqueness of solutions of reaction diffusion equations arising in many applications and often coupled our approach to the problem is based on converting the coupled equations into a system of volterra fredholm type integral equations by means of the green s function representation and using the banach fixed point theorem an application to nonlinear second order evolution equations is also indicated

fuzzy self organizing controller and its application for dynamic processes abstract this paper deals with a self organizing controller used in real time and its application for dynamic processes the control policy of the controller is able to develop and improve automatically a new self organizing control algorithm which modifies the fuzzy control decision table is presented in this paper the control algorithm needs much less computation time and memory of the computer this paper provides two examples of the fuzzy self organizing control a set of experiment results is described it shows that the controller can be applied to some processes such as processes with time lag and non linearity or one whose parameter or running conditions are varied which were usually not controlled very well with a conventional controller

on positive solutions of a nonlinear equilibrium boundary value problem abstract we give necessary and sufficient conditions for the existence of positive solutions to a nonlinear elliptic system arising from mathematical ecology with the dirichlet boundary data assigned by the equilibria of the corresponding ode system the main result is theorem 1 the tools are dancer fixed point index and degree theory

wold decomposition for doubly commuting isometries abstract in this paper we obtain a complete description of the class of n tuples n 2 of doubly commuting isometries in particular we present a several variables analogue of the wold decomposition for isometries on hilbert spaces our main result is a generalization of m slocinski s wold type decomposition of a pair of doubly commuting isometries

a reaction diffusion system of a competitor competitor mutualist model we investigate the homogeneous dirichlet problem and neumann problem to a reactiondiffusion system of a competitor competitor mutualist model the existence uniqueness and boundedness of the solutions are established by means of the comparison principle and the monotonicity method for the dirichlet problem we study the existence of trivial and nontrivial nonnegative equilibrium solutions and their stabilities for the neumann problem we analyze the contant equilibrium solutions and their stabilities the main method used in studying of the stabilities is the spectral analysis to the linearized operators the o d e problem to the same model was proposed and studied by b rai h i freedman and j f addicott

characterization and computation for the bound e in linear time variantsingularly perturbed systems abstract this paper gives a complete solution to the bound problem in a linear time invariant singularly perturbed system a criterion is presented to determine the existence of the bound

variable structure control of synchronous generator singularly perturbed analysis synchronous generators have a natural different time scale dynamics that is why for modelling and control design in such systems the methods of singular perturbations are widely used in this paper the possibilities of sliding mode control design for synchronous generators are analysed with this aim the concept of singular perturbation is revised in order to use it for relay control systems the obtained results are used for sliding mode control of synchronous generator

existence of coupled quasi solutions of systems of nonlinear reaction diffusion equations systems of nonlinear parabolic initial boundary value problems arise in many applications such as epidemies ecology biochemistry biology chemical and nuclear engineering constructive methods of proving existence results for such problems which can also provide numerical procedures for the computation of solutions are of greater value than theoretical existence results the method of upper and lower solutions coupled with monotone iterative technique has been employed successfully to prove existence of multiple solutions of nonlinear reaction diffusion equations in special cases by various authors 335 10 11 15 181 recently in 6 171 weakly coupled systems of reaction diffusion equations when the nonlinear terms are independent of gradient terms are discussed and some special type of results are obtained we in this paper investigate general systems of nonlinear reaction diffusion problems when the nonlinear terms possess a mixed quasi monotone property we discuss a very general situation and obtain coupled extremal quasi solutions which in special cases reduce to minimal and maximal solutions we shall also indicate how one step cyclic monotone iterative schemes can be generated which yield accelerated rate of convergence of iterates this work is in the spirit of our recent paper 12 for elliptic systems

the role of algebraic structure in the invariant subspace theory abstract following a recent work of authors 1 we establish the algebraic analogs of three major decomposition theorems of nagy foias langer halmos wallen and fishel in baer rings this approach not only provides purely algebraic and shorter proofs of these decomposition theorems but also suggests the possibility of eliminating the role of analytic structure in results related to the invariant subspace theory

on nonlinear reaction diffusion systems abstract this paper presents a qualitative analysis for a coupled system of two reaction diffusion equations under various boundary conditions which arises from a number of physical problems the nonlinear reaction functions are classified into three basic types according to their relative quasi monotone property for each type of reaction functions an existence comparison theorem in terms of upper and lower solutions is established for the time dependent system as well as some boundary value problems three concrete physical systems arising from epidemics biochemistry and engineering are taken as representatives of the basic types of reacting problems through suitable construction of upper and lower solutions various qualitative properties of the solution for each system are obtained these include the existence and bounds of time dependent solutions asymptotic behavior of the solution stability and instability of nontrivial steady state solutions estimates of stability regions and finally the blowing up property of the solution special attention is given to the homogeneous neumann boundary condition

singular perturbation analysis of linear systems with scalar quantized control abstract the effect of a scalar quantized control input on an otherwise linear singularly perturbed control system is analyzed the cases of open loop and closed loop control are studied analytical techniques are derived that allow the decoupling of such systems into fast and slow subsystems for analysis and design the results of a numerical example are given to demonstrate these techniques

a shimorin type analytic model on an annulus for left invertible operators and applications abstract a new analytic model for left invertible operators which extends both shimorin s analytic model for left invertible and analytic operators and gellar s model for bilateral weighted shift is introduced and investigated we show that a left invertible operator t which satisfies certain conditions can be modeled as a multiplication operator m z on a reproducing kernel hilbert space of vector valued analytic functions on an annulus or a disc a similar result for composition operators in l 2 spaces is established

periodic solutions of coupled semilinear parabolic boundary value problems the study of periodic solutions to parabolic differential systems goes back to j fourier who investigated the linear heat equation for the determination of temperature oscillation on earth cf 141 in recent years attention has been given to nonlinear parabolic boundary value problems cf l 2 4 6 7 15 16 however most of the discussions in the literature are concerned with a single parabolic equation under dirichlet type boundary condition due to the recent development in the biochemical and biological fields there arise various types of reactiondiffusion systems e g see lo 121 an interesting problem in some of these systems such as the belousov zhabotinskii reaction model is an understanding of the oscillating nature of the solution in this paper we investigate periodic solutions for a coupled system of parabolic boundary value problems in a one dimensional domain under various boundary conditions specifically the equations under consideration are given by

numerical solutions for some coupled systems of nonlinear boundary value problems in the well known volterra lotka model concerning two competing species with diffusion the densities of the species are governed by a coupled system of reaction diffusion equations the aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems this iterative scheme is based on the method of upper lower solutions which leads to two monotone sequences from some uncoupled linear systems it is shown that each of the two sequences converges to a nontrivial solution of the discrete equations the model under consideration may have one two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration numerical results are given for these solutions under both the dirichlet boundary condition and the mixed type boundary condition

numerical methods for coupled systems of nonlinear parabolic boundary value problems abstract a system of nonlinear finite difference equations corresponding to a class of coupled parabolic equations in a bounded domain is investigated using the method of upper lower solutions we construct two monotone sequences for the finite difference equations it is shown that when the reaction function is quasimonotone nondecreasing nonincreasing or mixed quasimonotone these two sequences converge monotonically to a unique solution of the finite difference system this monotone convergence leads to an existence comparison theorem as well as iterative numerical algorithms for the computation of the solution it also gives error estimates for the finite difference solution in each iteration without explicit knowledge of the solution moreover the monotone convergence property is used to prove the convergence of the finite difference solution to the corresponding solution of the differential system as the mesh size decreases to zero

the global existence and blowing up property of solutions for a nuclear model abstract in this paper we study the global existence and blowing up property of solutions for a coupled system of two reaction diffusion equations under the neumann conditions which arises from nuclear reactor dynamics the estimates of stability regions obtained are the best at the moment for constant initial data representations of solutions are given for a solution blowing up in finite time an upper bound and a lower bound on the blowing up time are povided

slow periodic motions with internal sliding modes in variable structure systems singularly perturbed relay systems sprs in which the reduced systems have the stable periodic motions with internal sliding modes are studied the slow motion integral manifold of such systems consists of the parts which correspond to the different values of relay control and the solutions may contain the jumps from one part of the slow manifold to another for such systems a theorem about existence and stability of the periodic solutions is proved an algorithm of asymptotic representation for this periodic solutions using boundary layer method is presented it is proved that in the neighbourhood of the break away point the asymptotic representation starts with the first order boundary layer function

existence of steady state solutions to predator prey equations in a heterogeneous environment is considered here x t e 52 x r where 52 is a bounded domain in ky u u u urn is an m tuple of functions d is a constant positive definite matrix and the a are continuous matrix valued functions in 4 it is shown that if this system admits a bounded invariant region in r and a certain quantity 0 is positive then the solution of the initial boundary value problem with initial condition u x 0 u x and homogeneous neumann boundary condition will converge to its own spatial average exponentially in l or l as t co this result implies that when the diffusion is sufficiently strong any spatially nonconstant steady state solution of the parabolic system above is unstable

global bifurcation of positive radial solutions for an elliptic system in reactor dynamics in this paper we are concerned with the existence of positive radial solutions of the elliptic system email protected email protected f x u r 1 0 is a constant m 0 is a parameter and 0 0 is continuous and f t s 0 for all t s r 1 r 2 x 0 under some appropriate conditions on the nonlinearity f we show that the above system possesses at least one positive radial solution for any email protected 0 the proof of our main results is based upon bifurcation techniques

global existence and blow up for a nonlinear reaction diffusion system abstract we consider the nonlinear reaction diffusion system u t u u m 1 v n 1 v t v u m 2 v n 2 subject to dirichlet boundary conditions andm2 m1 1 n1 n2 1 we prove that ifm1 1 n2 1 andm2n1 1 m1 1 n2 all nonnegative solutions are global while ifm1 1 orn2 1 orm2n1 1 m1 1 n2 both global existence and finite time blow up coexist

quasi steady state approximation for a reaction diffusion system with fast intermediate abstract we consider a prototype reaction diffusion system which models a network of two consecutive reactions in which chemical components a and b form an intermediate c which decays into two products p and q such a situation often occurs in applications and in the typical case when the intermediate is highly reactive the species c is eliminated from the system by means of a quasi steady state approximation in this paper we prove the convergence of the solutions in l 2 as the decay rate of the intermediate tends to infinity for all bounded initial data even in the case of initial boundary layers the limiting system is indeed the one which results from formal application of the qssa the proof combines the recent l 2 approach to reaction diffusion systems having at most quadratic reaction terms with local l bounds which are independent of the decay rate of the intermediate we also prove existence of global classical solutions to the initial system

invariant subspaces of h2 t2 and l2 t2 preserving compatibility abstract operators of multiplication by independent variables on the space of square summable functions over the torus and its hardy subspace are considered invariant subspaces where the operators are compatible are described

compensation of measurable disturbances for two time scale nonlinear systems this paper deals with a class of two time scale nonlinear systems with time varying disturbances modeled within the framework of singular perturbations systems in both standard and nonstandard form are considered for these systems we synthesize well conditioned control laws that utilize feedback of the full state vector and feedforward compensation of disturbances to exponentially stabilize the fast dynamics and enforce a pre specified input output behavior independently of the disturbances in the closed loop slow subsystem singular perturbation methods are employed to establish that the discrepancy between the output of the closed loop full order system and the output of the closed loop slow subsystem is proportional to the value of the singular perturbation parameter the stability of the closed loop system is analyzed using lyapunov s direct method and precise conditions that guarantee boundedness of the trajectories for sufficiently small values of the singular perturbation parameter are derived the application of the developed methodology is illustrated through a catalytic continuous stirred tank reactor example modeled as a singularly perturbed system in nonstandard form

a unified texture model based on a 2 d wold like decomposition a unified texture model that is applicable to a wide variety of texture types found in natural images is presented this model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters the texture field is assumed to be a realization of a regular homogeneous random field which is characterized in general by a mixed spectral distribution the texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component the deterministic component is further orthogonally decomposed into a harmonic component and a generalized evanescent component both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component the model is very efficient in terms of the number of parameters required to faithfully represent textures reconstructed textures are practically indistinguishable from the originals

texture coding using a wold decomposition model a novel approach for coding textured images is presented the texture field is assumed to be a realization of a regular homogeneous random field which can have a mixed spectral distribution on the basis of a two dimensional 2 d wold like decomposition the field is represented as a sum of a purely indeterministic harmonic and countable number of evanescent fields we present an algorithm for estimating and coding the texture model parameters and show that the suggested algorithm yields high quality reconstructions at low bit rates the model and the resulting coding algorithm are seen to be applicable to a wide variety of texture types found in natural images

variable structure control for singularly perturbed linear continuous systems with matched disturbances a variable structure system can be studied using the singular perturbation theory the discontinuous control that leads to a finite time reaching of the sliding surface creates fast time transients analogous to the stable boundary layer dynamics of a singularly perturbed system as the sliding mode is attained the slow time dynamics prevails just as that of a singularly perturbed system after the boundary layer dynamics fades away in this technical note the problem of sliding mode control for singularly perturbed systems in the presence of matched bounded external disturbances is investigated a composite sliding surface is constructed from solutions of algebraic lyapunov equations which are derived from both the fast and the slow subsystems the resultant sliding motion ensures lyapunov stability with disturbance rejection two proposed schemes that ensure the asymptotic stability of the system are presented the effectiveness of the proposed methods is demonstrated in a numerical example of a magnetic tape control system

sliding mode control for singularly perturbed systems this paper addresses the design of sliding mode controllers for singularly perturbed systems the full order system is separated into slow and fast subsystems and a sliding mode controller is designed for each subsystem a composite of these controls is then implemented on the full order system it is shown that if specific reaching conditions are satisfied for the reduced order models and an additional condition is met then the reaching conditions are also satisfied for the full order model furthermore sufficient conditions are derived which guarantee that the approximation error between the controlled reduced order response and the controlled full order model response is small a numerical example is given which successfully demonstrates the techniques developed in this paper

coexistence theorems of steady states for predator prey interacting systems on donne des conditions necessaires et suffisantes pour l existence des solutions positives des etats stationnaires pour des systemes predateur proie sous des conditions aux limites de dirichlet sur r n

asymptotic behavior and positive solutions of a chemical reaction diffusion system abstract this paper is concerned with some qualitative analysis for a coupled system of three reaction diffusion equations which arises from certain chemical reactions first discovered by belousov and zhabotinskii the analysis includes the existence of a bounded global time dependent solutions the stability and instability of the zero solution and the existence and nonexistence of a positive steady state solution including a global attractor of the system the global existence and stability problem is determined by the method of upper and lower solutions and the existence of a positive steady state solution is based on the fixed point index and bifurcation theory this analysis leads to a necessary and sufficient condition for the existence and nonexistence of a positive steady state solution in relation to the various physical parameters of the system

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods

positive solutions of systems of semilinear elliptic equations the pendulum method abstract conditions are formulated which guarantee the existence of positive solutions for simultaneous systems on an open domain with each constant is a positive measure the main tools used are probabilistic potential theory markov processes and an iterative scheme which is not a generalization of the one used for quasi monotone systems quasi monotonicity is not assumed and new results are obtained