continuous dependence for impulsive functional dynamic equations involving variable time scales using a known correspondence between the solutions of impulsive measure functional differential equations and the solutions of impulsive functional dynamic equations on time scales we prove that the limit of solutions of impulsive functional dynamic equations over a convergent sequence of time scales converges to a solution of an impulsive functional dynamic equation over the limiting time scale

generalized differential equations differentiability of solutions with respect to initial conditions and parameters abstract we show that under certain assumptions solutions of generalized ordinary differential equations are differentiable with respect to initial conditions and parameters this result unifies and extends several existing theorems for other types of equations such as impulsive differential equations or dynamic equations on time scales

local superlinearity and sublinearity for the p laplacian we study the existence nonexistence and multiplicity of positive solutions for a family of problems updelta p u f lambda x u u in w 0 1 p upomega where is a bounded domain in mathbb r n n p and 0 is a parameter the family we consider includes the well known nonlinearities of ambrosetti brezis cerami type in a more general form namely lambda a x u q b x u r where 0 leqslant q p 1 r leqslant p 1 here the coefficient a x is assumed to be nonnegative but b x is allowed to change sign even in the critical case preliminary results of independent interest include the extension to the p laplacian context of the brezis nirenberg result on local minimization in w 0 1 p text and c 0 1 a c 1 alpha estimate for equations of the form updelta p u h x u with h of critical growth a strong comparison result for the p laplacian and a variational approach to the method of upper lower solutions for the p laplacian

pattern formation in the brusselator system in the paper we deal with a reaction diffusion system well known as the brusselator model and some improved results for the steady states of this model are presented we first give an a priori estimates positive upper and lower bounds of positive steady states then we obtain the non existence and existence of positive non constant steady states as the parameters and b are varied which means some certain conditions under which the pattern formation occurs or not

on normal subgroups which are direct products now that the classification of finite simple groups is complete it is logical to look at the extension problem an important special case to consider is when m is a minimal normal subgroup of g and both g m and m are known groups if m is abelian various techniques have been used to derive information about g indeed almost the entire theory of finite solvable groups can be said to rest upon these techniques the motivation behind the present paper was to develop techniques for dealing with the situation when m is not abelian specifically we consider the following problems 1 determine the structure of g from the structure of g m and some subgroup or subgroups of g 2 find subgroups h in g such that g hm and in particular determine whether m has a complement in g 3 determine when two subgroups h and h found in 2 are conjugate in g if m is a non abelian minimal normal subgroup of a finite group g then

turing patterns in the lengyel epstein system for the cima reaction the first experimental evidence of the turing pattern was observed by de kepper and her associates 1990 on the cima reaction in an open unstirred gel reactor almost 40 years after turing s prediction lengyel and epstein characterized this famous experiment using a system of reaction diffusion equations in this paper we report some fundamental analytic properties of the lengyel epstein system our result also indicates that if either of the initial concentrations of the reactants the size of the reactor or the effective diffusion rate are not large enough then the system does not admit nonconstant steady states a priori estimates are fundamental to our approach for this nonexistence result the degree theory was combined with the a priori estimates to derive existence of nonconstant steady states

dynamics in a diffusive predator prey system with ratio dependent predator influence abstract a diffusive predator prey system with predator functional response subject to neumann boundary conditions is considered existence nonexistence and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation hopf and steady state bifurcation analyses are carried out in detail these results provide theoretical evidences to the complex spatio temporal dynamics found by numerical simulation

existence of nonoscillatory solutions to neutral dynamic equations on time scales abstract in this paper we give an analogue of the arzela ascoli theorem on time scales then we establish the existence of nonoscillatory solutions to the neutral dynamic equation x t p t x g t f t x h t 0 on a time scale to dwell upon the importance of our results three interesting examples are also included

dynamics of two compartment gray scott equations abstract in this work the existence of a global attractor is proved for the solution semiflow of the coupled two compartment gray scott equations with the homogeneous neumann boundary condition on a bounded domain of space dimension n 3 the grouping estimation method combined with a new decomposition approach is introduced to overcome the difficulties in proving the absorbing property and the asymptotic compactness of this four component reaction diffusion systems with cubic autocatalytic nonlinearity and linear coupling the finite dimensionality of the global attractor is also proved

on representing finite lattices as intervals in subgroup lattices of finite groups let mnbe the lattice of length 2 withn 1 atoms it is an open problem to decide whether or not every such lattice or indeed whether or not every finite lattice can be represented as an interval in the subgroup lattice of some finite group we complete the work of the second author lucchini by reducing this problem to a series of questions concerning the finite non abelian simple groups

averaging dynamic equations on time scales abstract the aim of this paper is to generalize the classical theorems on averaging of differential equations we focus on dynamic equations on time scales and prove both periodic and nonperiodic version of the averaging theorem as well as a related theorem on the existence of periodic solutions

mesa type patterns in the one dimensional brusselator and their stability the brusselator is a generic reaction diffusion model for a tri molecular chemical reaction we consider the case when the input and output reactions are slow in this limit we show the existence of k periodic spatially bi stable structures mesas and study their stability using singular perturbation techniques we find a threshold for the stability of k mesas this threshold occurs in the regime where the exponentially small tails of the localized structures start to interact by comparing our results with turing analysis we show that in the generic case a turing instability is followed by a slow coarsening process whereby logarithmically many mesas are annihilated before the system reaches a steady equilibrium state we also study a breather type instability of a mesa which occurs due to a hopf bifurcation full numerical simulations are shown to confirm the analytical results in 1952 turing proposed that the formation of spatial patterns during morphogenesis could be explained in terms of the instability of a homogeneous steady state solution of a reaction diffusion network describing the evolution of a set of morphogens 31 turing himself illustrated his ideas on two chemical models turing s original work is primarily concerned with the stability analysis of the homogeneous steady state solution of the rate equations for the interacting morphogens 22 the main point of biological interest however is whether stable spatial structures may be generated beyond the instability i e whether the rate equations admit stable and positive inhomogeneous solutions exhibiting the most characteristic features of morphogenetic patterns this point has been taken up seriously in the early seventies more systematic numerical studies of turing s model have been performed showing irregular spatial structures 4 this led to serious reservations about the relevance of turing s theory in developmental biology particularly its ability to generate regular patterns but these criticisms originate from a somewhat unfortunate choice of turing s example and they do not touch the essential points of turing s theory more specifically the obvious requirement that the rate equations must admit positive and bounded solutions is not satisfied in turing s example 11

asymptotically autonomous semiflows chain recurrence and lyapunov functions from the work of c conley it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set here we improve a result of l markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow in the special case that there is a lyapunov function for the limiting semiflow sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the lyapunov function

massera s theorems for various types of equations with discontinuous solutions abstract we present new massera type theorems for various types of equations with periodic right hand sides we deal with generalized ordinary differential equations measure differential equations impulsive equations all of which might have discontinuous solutions as well as dynamic equations on time scales for scalar nonlinear equations we find sufficient conditions guaranteeing that each bounded solution is asymptotic to a periodic solution for linear systems we show that the existence of a bounded solution implies the existence of a periodic solution we include some examples to illustrate our results

non periodic averaging principles for measure functional differential equations and functional dynamic equations on time scales involving impulses abstract we present a non periodic averaging principle for measure functional differential equations and using the correspondence between solutions of measure functional differential equations and solutions of functional dynamic equations on time scales see federson et al 2012 8 we obtain a non periodic averaging result for functional dynamic equations on time scales moreover using the relation between measure functional differential equations and impulsive measure functional differential equations we get a non periodic averaging theorem for these equations also it is a known fact that we can relate impulsive measure functional differential equations and impulsive functional dynamic equations on time scales see federson et al 2013 9 therefore applying this correspondence to our averaging principle we obtain a non periodic averaging theorem for impulsive functional dynamic equations on time scales

boundedness of solutions of measure differential equations and dynamic equations on time scales abstract in this paper we investigate the boundedness results for measure differential equations in order to obtain our results we use the correspondence between these equations and generalized odes furthermore we prove our results concerning boundedness of solutions for dynamic equations on time scales using the fact that these equations represent a particular case of measure differential equations

controllability of linear and nonlinear systems governed by stieltjes differential equations abstract in this manuscript controllability of vector valued g derivative stieltjes differential system is considered for linear system explicit solution of homogeneous case is obtained by constructing a generalized matrix exponential function and nonhomogeneous solution is achieved with transferring the corresponding problem into a class of stieltjes impulsive differential equations based on the analysis techniques of linear system theory the gramian criterion and the rank criterion for linear case are established respectively existence of local and global solution for nonlinear system are presented by the well knonw banach contraction principle and the controllability result for nonlinear systems is shown by krasnoselskii s fixed point theorem simulations for linear and nonlinear systems are tackled respectively to verify the efficiency of theoretical results

turing pattern of the oregonator model abstract the oregonator model is the mathematical dynamics which describes the field koros noyes mechanics of the famous belousov zhabotinskii reaction in this work we establish some fundamental analytic properties of this dynamics and its corresponding steady state under various conditions on the parameters and the size of the reactor we examine the existence and non existence of non constant steady states in particular for some properly chosen parameter ranges we prove the occurrence of the turing pattern generated by this oregonator model our results exhibit interesting and very different roles of the diffusion rates and the reactor in the formation of the turing pattern our mathematical analysis mainly relies on a priori estimates and the topological degree argument

stability and instability for dynamic equations on time scales in this paper we examine the stability and instability of the equilibrium solution x 0 to the first order system of dynamic equations x d f t x t t 0 x d r n where t is from a so called time scale t with t 0 tand d is a compact set our methods involve the existence of a positive definite liapunov function v such that its delta derivative v d satisfies certain integral definite or semidefinite sign properties finally we use liapunov functions to develop an invariance principle regarding solutions to the above dynamic equation

monodromy groups of hurwitz type problems abstract we solve the hurwitz monodromy problem for degree 4 covers that is the hurwitz space h 4 g of all simply branched covers of p 1 of degree 4 and genus g is an unramified cover of the space p 2 g 6 of 2 g 6 tuples of distinct points in p 1 we determine the monodromy of 1 p 2 g 6 on the points of the fiber this turns out to be the same problem as the action of 1 p 2 g 6 on a certain local system of z 2 vector spaces we generalize our result by treating the analogous local system with z n coefficients 3 n in place of z 2 this in turn allows us to answer a question of ellenberg concerning families of galois covers of p 1 with deck group z n 2 s 3

instabilities and patterns in coupled reaction diffusion layers we study instabilities and pattern formation in reaction diffusion layers that are diffusively coupled for two layer systems of identical two component reactions we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem there are eight possible primary bifurcation scenarios including a turing turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling for systems of n component layers and nonidentical layers the linear problem s block form allows approximate decomposition into lower dimensional linear problems if the coupling is sufficiently weak as an example we apply these results to a two layer brusselator system the competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system selecting a sqrt 2 1 length scale ratio produces an unusual steady square pattern

lyapunov stability for measure differential equations and dynamic equations on time scales abstract in this paper we prove the stability results for measure differential equations considering more general conditions under the lyapunov functionals and concerning the functions f and g moreover we prove these stability results for the dynamic equations on time scales using the correspondence between the solutions of these last equations and the solutions of the measure differential equations

henstock kurzweil delta and nabla integrals we will study the henstock kurzweil delta and nabla integrals which generalize the henstock kurzweil integral many properties of these integrals will be obtained these results will enable time scale researchers to study more general dynamic equations the henstock kurzweil delta nabla integral contains the riemann delta nabla and lebesque delta nabla integrals as special cases c 2005 elsevier inc all rights reserved

stationary solutions of a volume filling chemotaxis model with logistic growth and their stability in this paper we derive the conditions for the existence of stationary solutions i e nonconstant steady states of a volume filling chemotaxis model with logistic growth over a bounded domain subject to homogeneous neumann boundary conditions at the same time we show that the same system without the chemotaxis term does not admit pattern formations moreover based on an explicit formula for the stationary solutions which is derived by asymptotic bifurcation analysis we establish the stability criteria and find a selection mechanism of the principal wave modes for the stable stationary solution by estimating the leading term of the principal eigenvalue we show that all bifurcations except the one at the first location of the bifurcation parameter are unstable and if the pattern is stable then its principal wave mode must be a positive integer which minimizes the bifurcation parameter for a special case where the carrying capacity is one half we find a necessary and sufficient condition for th

spatiotemporal pattern formation of a diffusive bimolecular model with autocatalysis and saturation law in this paper a reaction diffusion bimolecular model with autocatalysis and saturation law is investigated firstly we provide some conditions for the stability turing instability of the constant positive solution then we mainly consider hopf bifurcations and steady state bifurcations which bifurcate from the unique constant positive solution of the system our results suggest the existence of spatially non homogeneous periodic orbit and non constant positive steady state solutions which implies the possibility of rich spatiotemporal patterns in this diffusive bimolecular model numerical examples are presented to support our theoretical analysis furthermore non existence of non constant steady state is investigated in terms of parameters

general existence principles for stieltjes differential equations with applications to mathematical biology abstract stieltjes differential equations which contain equations with impulses and equations on time scales as particular cases simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function in this paper we prove new existence results for functional and discontinuous stieltjes differential equations and we show that such general results have real world applications specifically we show that stieltjes differential equations are specially suitable to study populations which exhibit dormant states and or very short impulsive periods of reproduction in particular we construct two mathematical models for the evolution of a silkworm population our first model can be explicitly solved as it consists on a linear stieltjes equation our second model more realistic is nonlinear discontinuous and functional and we deduce the existence of solutions by means of a result proven in this paper

periodic averaging theorems for various types of equations abstract we prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem we also present a periodic averaging theorem for a large class of retarded equations

growth of solutions for measure differential equations and dynamic equations on time scales abstract in this paper we investigate the asymptotic behavior for measure differential equations and dynamic equations on time scales via generalized ordinary differential equations generalized odes for short at first we establish new results that guarantee the existence of unbounded solutions for generalized odes and after that using the known correspondence between generalized odes and measure differential equations also between measure differential equations and dynamic equations on time scales we obtain similar results for these equations finally we present an application to illustrate our main results

measure functional differential equations and functional dynamic equations on time scales abstract we study measure functional differential equations and clarify their relation to generalized ordinary differential equations we show that functional dynamic equations on time scales represent a special case of measure functional differential equations for both types of equations we obtain results on the existence and uniqueness of solutions continuous dependence and periodic averaging

groups satisfying a strong complement property abstract let g n h be a finite group where n is normal in g and h is a complement of n in g for a given generating sequence h 1 h d of h we say that n h 1 h d satisfies the strong complement property if h 1 x 1 h d x d is a complement of n in g for all x 1 x d n when d is the minimal number of elements needed to generate h and n h 1 h d satisfies the strong complement property for every generating sequence h 1 h d with length d then we say that n h satisfies the strong complement property in the case when n and h are coprime we show that n h can only satisfy the strong complement property if h is cyclic or if h acts trivially on n we give on the other hand a number of examples that show this does not need to be the case when considering the strong complement property of n h 1 h d for a given fixed generating sequence in the case when n and h are not of coprime order we give examples where n h satisfies the strong complement property and where h is not cyclic and does not act trivially on n

automorphisms of induced extensions suppose m is a normal subgroup of the group g and m is a direct product of subgroups li 1 1 the objective of the present paper is to show that the problem of finding the automorphisms of g may be reduced to that of finding certain isomorphisms of the groups g m and n k if n 1 then n k g and our theorems are trivialities thus our results are really concerned with the case when n 1 suppose si is an automorphism of g if m n and k are the images under a of m n and k respectively then a induces an isomorphism of g m onto g m and an isomorphism y of nfk onto n ik further b maps the subgroup n m onto n m 7 maps m k onto m fk and and 7 induce the same mapping of n m onto n m here we identify n m and n m with n k f mik and n k m k respectively thus the previous statement simply means that if y kn k n for ne n and n en then mn m n the thrust of the present paper is to reverse the above namely suppose fl is an isomorphism of g m onto g m for some normal subgroup m and suppose y is an isomorphism of n k onto n jk for some subgroups n and k with k a normal subgroup of n assume that k m n fl maps kim onto n m y maps m k onto m k and i and 7 induce the same mapping of n m onto n m if certain other hypotheses are satisfied the other assumptions basically stating that m n and k are like m n and k we show that there is an automorphism u of g such that z induces both i and 7

superlinear problems without ambrosetti and rabinowitz growth condition superlinear elliptic boundary value problems without ambrosetti and rabinowitz growth condition are considered existence of nontrivial solution result is established by combining some arguments used by struwe and tarantello and schechter and zou also by wang and wei firstly by using the mountain pass theorem due to ambrosetti and rabinowitz is constructed a solution for almost every parameter by varying the parameter then it is considered the continuation of the solutions

bifurcation and spatiotemporal patterns in a homogeneous diffusive predator prey system abstract a diffusive predator prey system with holling type ii predator functional response subject to neumann boundary conditions is considered hopf and steady state bifurcation analysis are carried out in details in particular we show the existence of multiple spatially non homogeneous periodic orbits while the system parameters are all spatially homogeneous our results and global bifurcation theory also suggest the existence of loops of spatially non homogeneous periodic orbits and steady state solutions these results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulation

qualitative analysis of a predator prey model with holling type ii functional response incorporating a prey refuge abstract we study a predator prey model with holling type ii functional response incorporating a prey refuge under homogeneous neumann boundary condition we show the existence and non existence of non constant positive steady state solutions depending on the constant m 0 1 which provides a condition for protecting 1 m u of prey u from predation moreover we investigate the asymptotic behavior of spacially inhomogeneous solutions and the local existence of periodic solutions

almost automorphic solutions of dynamic equations on time scales abstract in the present work we introduce the concept of almost automorphic functions on time scales and present the first results about their basic properties then we study the nonautonomous dynamic equations on time scales given by x t a t x t f t and x t a t x t g t x t t t where t is a special case of time scales that we define in this article we prove a result ensuring the existence of an almost automorphic solution for both equations assuming that the associated homogeneous equation of this system admits an exponential dichotomy also assuming that the function g satisfies the global lipschitz type condition we prove the existence and uniqueness of an almost automorphic solution of the nonlinear dynamic equation on time scales further we present some applications of our results for some new almost automorphic time scales finally we present some interesting models in which our main results can be applied

a priori estimates and existence for elliptic systems via bootstrap in weighted lebesgue spaces we present a new general method to obtain regularity and a priori estimates for solutions of semilinear elliptic systems in bounded domains this method is based on a bootstrap procedure used alternatively on each component in the scale of weighted lebesgue spaces lp lp x dx where x is the distance to the boundary using this method we significantly improve the known existence results for various classes of elliptic systems

equations in groups that are virtually direct products abstract in this note we show that the satisfiability of equations and inequations with recognisable constraints is decidable in groups that are virtually direct products of finitely many hyperbolic groups

dynamic equations on time scales and generalized ordinary differential equations abstract the aim of this paper is to show that dynamic equations on time scales can be treated in the framework of generalized ordinary differential equations as introduced by j kurzweil we also use some known results for generalized ordinary differential equations to obtain new theorems related to stability and continuous dependence on parameters for dynamic equations on time scales

existence of a positive solution and numerical solution for some elliptic superlinear problem abstract in this paper we prove the existence of positive solutions of an elliptic superlinear problem also we are interested here in getting results concerning the existence of positive solutions for the discrete formulation of our problem therefore in order to do it we employ the radial solutions of the elliptic superlinear problem obtaining a second order dynamic equation on time scales which encompasses discrete continuous and hybrid formulations of our problem this unified equation allows us to present numerical simulations which give us a more precise analysis and description concerning the behavior of the solution according to the parameters

diffusion self diffusion and cross diffusion u1 x 0 u 1 0 x u2 x 0 u 2 0 x i n 0 where 2 n 1 2 x 2 is the laplace operator 0 is a bounded smooth domain of r n with n1 0 and 0 are the boundary and the closure of 0 respectively 0t 0 0 t and 0t 0 0 t for some t 0 is the outward unit normal vector on 0 di ai bi ci i 1 2 are all positive constants while ij i j 1 2 denote non negative constants the initial values u1 0 and u2 0 are non negative smooth func tions which are not identically zero the mathematical model 1 1 was proposed by shigesada et al 27 in their study of spatial segregation of interacting species where u1 and u2 represent the densities of two competing species d1 and d2 are their diffu sion rates a1 and a2 denote the intrinsic growth rates b1 and c2 account for intra specific competitions b2 and c1 are the coefficients of inter specific competitions 11 and 22 are usually referred as self diffusion pressures and 12 and 21 are cross diffusion pressures an interesting feature of 1 1 is that the movements of these two competing species are affected by the population pressures due to the mutual interference between the individuals and it was hoped that the nonlinear dispersive force due to the

extremal solutions of measure differential equations abstract we investigate the existence of the least and greatest solutions to measure differential equations as well as the relation between the extremal solutions and lower or upper solutions along the way we prove a fairly general local existence theorem and an analogue of peano s uniqueness theorem for measure differential equations finally we show that the general theory is applicable in the study of differential equations with impulses or dynamic equations on time scales

generalized elementary functions abstract we use the theory of generalized linear differential equations to introduce new definitions of the exponential hyperbolic and trigonometric functions we derive some basic properties of these generalized functions and show that the time scale elementary functions with lebesgue integrable arguments represent a special case of our definitions

on superlinear problems without the ambrosetti and rabinowitz condition abstract existence and multiplicity results are obtained for superlinear p laplacian equations without the ambrosetti and rabinowitz condition to overcome the difficulty that the palais smale sequences of the euler lagrange functional may be unbounded we consider the cerami sequences our results extend the recent results of miyagaki and souto o miyagaki m souto superlinear problems without ambrosetti and rabinowitz growth condition j differential equations 245 2008 3628 3638

on global bifurcation for quasilinear elliptic systems on bounded domains general second order quasilinear elliptic systems with nonlinear boundary conditions on bounded domains are formulated into nonlinear mappings between sobolev spaces it is shown that the linearized mapping is a fredholm operator of index zero this and the abstract global bifurcation theorem of jacobo pejsachowicz patrick j rabier degree theory for c1 fredholm mappings of index 0 j anal math 76 1998 289 319 allow us to carry out bifurcation analysis directly on these elliptic systems at the abstract level we establish a unilateral global bifurcation result that is needed when studying positive solutions finally we supply two examples of cross diffusion population model and chemotaxis model to demonstrate how the theory can be applied

basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling abstract this article investigates both basic qualitative and basic quantitative properties of solutions to first and higher order dynamic equations on time scales and thus provides a foundation and framework for future advanced nonlinear studies in the field particular focus lies in the existence uniqueness dependency approximation and explicit representation of solutions to nonlinear initial value problems the main tools used are from modern areas of nonlinear analysis including the fixed point theorems of banach and schafer the method of successive approximations a novel definition of measuring distance in metric spaces and normed spaces and a separation of variables technique is introduced to the general time scale setting the new results compliment and extend those of stefan hilger s seminal paper of 1990 as an application of the new results we present and analyse a simple model from economics known as the keynesian cross model with lagged income in the general time scale environment ideas suggesting further applications and possible new directions for the novel results are also presented

hopf bifurcation analysis in the 1 d lengyel epstein reaction diffusion model abstract the lengyel epstein model with diffusion and homogeneous neumann boundary condition is considered in this paper we give the existence of multiple spatially non homogeneous periodic solutions though all the parameters of the system are spatially homogeneous

dynamics and pattern formation in a diffusive predator prey system with strong allee effect in prey abstract the dynamics of a reaction diffusion predator prey system with strong allee effect in the prey population is considered nonexistence of nonconstant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as nonconstant steady state solutions are studied these results show that the impact of the allee effect essentially increases the system spatiotemporal complexity

on summability multipliability product integrability and parallel translation abstract in this paper we provide necessary and sufficient conditions for the existence of the kurzweil mcshane and riemann product integrals of step mappings with well ordered steps and for right regulated mappings with values in banach algebras our basic tools are the concepts of summability and multipliability of families in normed algebras indexed by well ordered subsets of the real line these concepts also lead to the generalization of some results from the usual theory of infinite series and products finally we present two applications of product integrals first we describe the relation between stieltjes type product integrals haahti products and parallel translation operators second we provide a link between the theory of strong kurzweil product integrals and strong solutions of linear generalized differential equations

a priori bounds and global existence of solutions of the steady state sel kov model we consider the system of reaction diffusion equations known as the sel kov model this model has been applied to various problems in chemistry and biology we obtain a priori bounds on the size of the positive steady state solutions of the system defined on bounded domains in r n 1 n 3 this is the physically relevant case previously such bounds had been obtained in the case n 1 under more restrictive hypotheses we also obtain regularity results on the smoothness of such solutions and show that non trivial solutions exist for a wide range of parameter values

variation of lyapunov s method for dynamic systems on time scales abstract a new comparison theorem that connects the solutions of perturbed and unperturbed dynamic systems in a manner useful to the theory of perturbations is given and this comparison theorem is employed as a stability criterion to compare the asymptotic behaviors of perturbed and unperturbed systems it is further shown by means of both theory and numerical computation that time scales do offer a unification in order to emphasize the better asymptotic behavior of perturbed systems in both continuous and discrete cases

well posedness results for abstract generalized differential equations and measure functional differential equations abstract in the first part of the paper we consider nonlinear generalized ordinary differential equations whose solutions take values in infinite dimensional banach spaces and prove new theorems concerning the existence of solutions and continuous dependence on initial values and parameters in the second part we apply these results in the study of nonlinear measure functional differential equations and impulsive functional differential equations with infinite delay

pattern formation of a coupled two cell brusselator model abstract in this paper we study the stationary problems for the coupled two cell brusselator model as follows d 1 u 1 b 1 u b u 2 v c w u in d 2 v u u 2 v in d 1 w 1 b 1 w b w 2 z c u w in d 2 z w w 2 z in u v w z 0 on we first study the stability of the unique positive constant solution u v w z 1 1 1 1 then we give a priori estimate positive upper and lower bounds to the positive solution at last we obtain the non existence and existence of positive non constant solutions as parameters d 1 d 2 and b varied

global bifurcation analysis and pattern formation in homogeneous diffusive predator prey systems abstract the dynamics of a general diffusive predator prey system is considered existence and nonexistence of non constant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as non constant steady state solutions are studied

qualitative analysis of steady states to the sel kov model in this work we are concerned with a reaction diffusion system well known as the sel kov model which has been used for the study of morphogenesis population dynamics and autocatalytic oxidation reactions we derive some further analytic results for the steady states to this model in particular we show that no nonconstant positive steady state exists if 0 1 and large where nonconstant positive steady states can occur thus these conclusions indicate that the parameter p plays a crucial role in leading to spatially nonhomogeneous distribution of the two reactants the a priori estimates are fundamental to our mathematical approaches

maximal subgroups in composite finite groups the purpose of this paper is to present a method for translating the problem of finding all maximal subgroups of finite groups into questions concerning groups that are nearly simple a finite group is called nearly simple if it has only one minimal normal subgroup and that it nonabelian and simple in view of the recently announced classification of all finite simple groups this seems to be a useful reduction though it must be acknowledged see e g scott 6 that there are still enormous obstacles on the way to understanding even just the maximal subgroups of the simple groups let g be a finite group and m a minimal normal subgroup of g the maximal subgroups of g containing m are of course in bijective correspondence with the maximal subgroups of the smaller group g m and so we need not concern ourselves with those if m is abelian the maximal subgroups of g not containing m are precisely the complements of m in g the number of conjugacy classes of these is 0 or the order of the first cohomology group g m the case of a4 nona lian and nonsimple is the principal part of this paper if neither reduction is applicable then all minimal normal subgroups of g are nonabelian simple groups this is dealt with in the entirely straightforward penultimate section of the paper these reductions are all canonical or natural in a sense which could perhaps be expressed in the language of categories and functors but here we prefer to stay with older conventions in particular we usually do not distinguish between a homomorphism and that obtained from it by restricting the codomain nevertheless the interested reader will observe that much of the strength of the results lies precisely in their canonical nature implicit as it may remain in this exposition while i do not know of any explicit statement of this reduction 114 002 l 8693 86 ie3 00

non constant positive steady states of the sel kov model abstract this paper deals with the reaction diffusion system known as the sel kov model with the homogeneous neumann boundary condition this model has been applied to various problems in chemistry and biology we first give a priori estimates positive upper and lower bounds of positive steady states and then study the non existence bifurcation and global existence of non constant positive steady states as the parameters and are varied