initial value problems for systems of integrodifferential equations in banach spaces in this paper by the use of new comparison results and mixed monotone iterative techniques the existence of solutions of initial value problems for systems of integrodifferential equations in banach spaces is discussed the results obtained in this paper generalize and improve the results corresponding to those obtained by others our result is new even in finite dimensional spaces

monotone method for equations describing transport phenomena in a banach space in this paper monotone methods have been developed for equations arising in transport processes in a banach space this method proves the existence of extremal solutions for such equations the advantage of the method for such type of equations is that the successive iterates are solutions of the corresponding initial value problems

fixed points and approximate solutions for nonlinear operator equations we study a nonlinear operator equation and obtain a sequence of approximate solutions by extending the monotone iterative technique to new situations some examples and applications are presented

quasi solutions vector lyapunov functions and monotone method the notion of quasi solution which was introduced earlier has been developed in this paper further the notion of coupled quasi solutions and coupled maximal and minimal solutions has been introduced it is shown that the idea of quasi solutions leads to isolated subsystems and has obtained error estimates between solutions and quasi solutions also monotone iterative techniques have been developed to obtain coupled maximal and minimal quasi solutions

antiperiodic boundary value problem for first order impulsive ordinary differential equations this paper discusses the antiperiodic boundary value problem for first order impulsive ordinary differential equations we establish several existence results by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique

existence theorems for a class of functional differential systems in recent papers 2 6 the authors have established existence and comparison theorems for the well known cauchy problem for ordinary diferential equations without using the monotone property on the given system these results are obtained under the conditions of the type which have been considered in the classical paper of miiller 8 1 the interesting feature of the results established in 2 6 is the fact that the solutions of the cauchy problem remain in the given sector in this paper we shall first establish existence and comparison theorems for a class of more general functional differential systems without using monotone property further we develop a monotone iterative technique to establish the existence of minimal and maximal solutions

positive solutions of operator equations on ordered banach spaces and applications this paper is concerned with an operator equation on ordered banach spaces the existence and uniqueness of its positive solutions is obtained by using the properties of cones and monotone iterative technique as applications we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for two classes of integral equations

an operator theoretic formulation of asynchronous exponential growth a strongly continuous semigroup of bounded linear operators t t t o in the banach space x has asynchronous exponential growth with intrinsic growth constant a0 provided that there is a nonzero finite rank operator p0 in x such that limr ooe x tt t po necessary and sufficient cvonditions are established for t t t o to have asynchronous exponential growth applications are made to a maturity time model of cell population growth and a transition probability model of cell population growth

on a stochastic nonlinear equation in one dimensional viscoelasticity in this paper we discuss an initial boundary value problem for a stochastic nonlinear equation arising in one dimensional viscoelasticity we propose to use a new direct method to obtain a solution this method is expected to be applicable to a broad class of nonlinear stochastic partial differential equations

strong solutions of stochastic models for viscoelastic flows of oldroyd type abstract in this work we study stochastic oldroyd type models for viscoelastic fluids in r d d 2 3 we show existence and uniqueness of strong local maximal solutions when the initial data are in h s for s d 2 d 2 3 probabilistic estimate of the random time interval for the existence of a local solution is expressed in terms of expected values of the initial data

integral boundary value problems for first order integro differential equations with deviating arguments this paper deals with first order integro differential equations of mixed type with deviating arguments we investigate the existence of solutions of such problems with integral boundary conditions by establishing a comparison result and applying the monotone iterative technique to obtain corresponding results we also discuss first order differential inequalities with deviating arguments two examples demonstrate the application of our results

well posedness and large deviations for a class of spdes with levy noise abstract in this paper a class of stochastic partial differential equations spdes with levy noise is concerned firstly the local well posedness is established by the iterative approximation then the large deviation principle ldp for the regularized spdes is obtained by the weak convergence approach to get the ldp for spdes here an exponential equivalence of the probability measures is proved the results can be applied to some types of spdes such as stochastic burgers equation stochastic b family equation stochastic modified novikov equation and stochastic hunter saxton equation

positive solutions of the three point boundary value problem for second order differential equations with an advanced argument abstract in this paper by using the fixed point index method we establish the existence of at least one or at least two positive solutions to the three point boundary value problem for a second order differential equation with an advanced argument u t a t f u h t 0 t 0 1 u 0 0 u u 1 where 0 1 0 and 1 0 as an application we also give an example to demonstrate our result

a mathematical study in the theory of dynamic population abstract this article deals with a mathematical model of an age structured proliferating cell population originally proposed by lebowitz and rubinow j math biol 1 1974 17 36 individual cells are distinguished by age and by cell cycle length the cell cycle length is considered as an inherited property determined at birth here general boundary conditions are considered by means of a linear and bounded operator k after establishing the theorem of traces we show that the model is well posed in the sense of the theory of semigroup without restriction on the boundary operator k we study the positivity and the irreducibility of the generated semigroup and we calculate its essential type the asymptotic behavior is obtained in the uniform topology

initial value problems for nonlinear second order impulsive integro differential equations in banach spaces in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of initial value problems for nonlinear second order impulsive integro differential equations in banach spaces

a multiplicity result for second order impulsive differential equations via the leggett williams fixed point theorem using the leggett williams fixed point theorem we present in this paper criteria which guarantee the existence of three nonnegative solutions to second order impulsive equations

existence and iteration of monotone positive solutions for multipoint boundary value problem with p laplacian operator in the paper we obtain the existence of monotone positive solutions and establish acorresponding iterative scheme for the following multipoint boundary value problem with p laplacian operator f p u t q t f t u t 0 0

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

extremal solutions of periodic boundary value problems for first order integro differential equations of mixed type this paper investigates the maximal and minimal solutions of periodic boundary value problems for first order nonlinear integro differential equations of mixed type by establishing a comparison result and using the monotone iterative technique

dynamics of structured populations with inherited properties abstract a mathematical model of an age structured proliferating cell population is analyzed the model allows the inheritance of cycle length from mother cells to daughter cells it is proved that the solutions have the property of asynchronous exponential growth provided the transition kernel of inheritance satisfies smoothness and positivity requirements the method of proof uses the theory of semigroups of operators and the theory of positive operators

monotone iterative technique for the elastic systems with structural damping in banach spaces in this paper we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence of mild solutions to a second order evolution equation initial value problem in an ordered banach space which can model an elastic system with structural damping under monotone condition and the noncompactness measure condition on nonlinearity we obtain the existence of extremal mild solutions and positive mild solutions moreover some applications are given to illustrate our theoretical results

a mathematical study for a rotenberg model abstract this paper deals with a mathematical model in cell dynamics population originally proposed by m rotenberg 1983 j theoret biol 103 181 199 individual cells are distinguished by their degree of maturity and maturation velocity here all biological rules are considered we bring new techniques to the discussion of this model we show that the model is well posed in the sense of the theory of semigroups we study the positivity and irreducibility of the generated semigroups and we calculate its essential type the asymptotic behavior is obtained in uniform topology

existence of multiple quasifixed points of mixed monotone operators by iterative techniques fixed point theorems of mixed monotone operators by iterative technique in a banach space with the ordering relative to cone k the notion of coupled quasi fixed points is introduced and the main result shows their existence

the asymptotic behavior of a transport equation in cell population dynamics with a null maturation velocity abstract in this paper we complete the study of rotenberg s model m rotenberg 1983 j theoret biol 103 181 199 describing the growth of a cell population and treated partially by m boulanouar and h emamirad differential integral equations 13 2000 125 144 in contrast to our previously cited treatment here we impose the condition that the maturation velocity for any cell can become null this consideration implies that the cell population never completely leaves its initial distribution because at every time we can find some cells of initial cell population that are not divided in this case the generated semigroup is not compact to surmount this difficulty after studying the irreducibility of the generated semigroup we calculate explicitly its essential type and we show the asymptotic convergence of the generated semigroup to a projection of rank 1

boundary value problems for a class of impulsive functional equations this paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions we study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times by the use of the monotone method some of the options included in this formulation are differential equations with maximum and integro differential equations in this paper we also prove that the lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval the corresponding results are established for the impulsive case the general formulation includes several types of functional dependence delay equations equations with maxima integro differential equations finally we consider the case of functional dependence which is given by nonincreasing and bounded functions

positive solutions for multipoint boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for a one dimensional p laplacian p u f t u 0 t 0 1 subject to the boundary value condition u 0 i 1 n 2 i u i u 1 i 1 n 2 i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and i i satisfy i i 0 0 i 1 n 2 i 1 and i 1 n 2 i 1 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

monotone iterative techniques of lakshmikantham for a boundary value problem for systems of differential equations with maxima abstract the monotone iterative techniques of lakshmikantham are applied to approximately finding a couple of extremal quasi solutions of a two point boundary value problem for systems of differential equations with maxima

a class of second order impulsive integro differential equations on unbounded domain in a banach space in this paper by using the cone theory and monotone iterative technique we investigate the existence of extremal solutions and unique solution of the initial value problem ivp for a class of second order impulsive integro differential equations on unbounded domain in a banach space our results improve and extend many recent results

pathwise mild solutions for quasilinear stochastic partial differential equations abstract stochastic partial differential equations spdes have become a key modeling tool in applications yet there are many classes of spdes where the existence and regularity theory for solutions is not completely developed here we contribute to this aspect and prove the existence of mild solutions for a broad class of quasilinear cauchy problems including among others cross diffusion systems as a key application our solutions are local in time and are derived via a fixed point argument in suitable function spaces the key idea is to combine in a suitable way the classical theory of deterministic quasilinear parabolic partial differential equations pdes with recent theory of evolution semigroups we also show how to apply our theory to the shigesada kawasaki teramoto skt model furthermore we provide examples of blow up and ill posed operators which can occur after finite time showing that solutions can only be local in time for general quasilinear spdes while they might be global in time for special subclasses of problems

monotone and numerical analytic methods for differential equations abstract the method of lower and upper solutions combined with monotone iterative techniques is used for ordinary differential equations with integral boundary conditions showing the existence of extremal solutions some existence results are also formulated using the numerical analytic method sufficient conditions for existence are given

positive solutions for nonlinear operator equations and several classes of applications in this paper we study a class of nonlinear operator equations x ax x 0 on ordered banach spaces where a is a monotone generalized concave operator using the properties of cones and monotone iterative technique we establish the existence and uniqueness of solutions for such equations in particular we do not demand the existence of upper lower solutions and compactness and continuity conditions as applications we study first order initial value problems and two point boundary value problems with the nonlinear term is required to be monotone in its second argument in the end applications to nonlinear systems of equations and to nonlinear matrix equations are also considered

stochastic compressible euler equations and inviscid limits abstract we prove the existence of a unique local strong solution to the stochastic compressible euler system with nonlinear multiplicative noise this solution exists up to a positive stopping time and is strong in both the pde and probabilistic sense based on this existence result we study the inviscid limit of the stochastic compressible navier stokes system as the viscosity tends to zero any sequence of finite energy weak martingale solutions converges to the compressible euler system

a fixed point theorem for convex and decreasing operators abstract in this paper we present a new fixed point theorem for noncompact convex and decreasing operators which extends the existing corresponding results as a sample we give an application of the fixed point theorem to the two point boundary value problem for a second order differential equation

monotone iterative techniques of v lakshmikantham for a boundary value problem for systems of impulsive differential difference equations by means of the monotone iterative techniques of v lakshmikantham a couple of minimal and maximal quasisolutions of a two point boundary value problem for a system of impulsive differential difference equations are constructed

a monotone method for the equation uxyz f comparison theorems for the nonlinear boundary value problem u x y z f x y z u u x u y u z u x y u y z u z x with the boundary conditions u o y z a y z u x 0 z b z x u x y 0 c x y a y 0 c 0 y a 0 z b z 0 b 0 x c x 0 are established under certain conditions then it is shown that there exist sequences of lower and upper solutions which converge uniformly and monotonically to minimal and maximal solutions respectively

two examples on the property of the noise in the systems of equations of fluid mechanics abstract in this manuscript we discuss two examples of the results on the systems of partial differential equations in fluid mechanics obtained via stochastic analysis for which deterministic case has no counterpart firstly it is well known that for a deterministic system of equations in fluid mechanics a lack of diffusion creates a significant obstacle in proving its global well posedness for a sufficiently small initial data nevertheless it may be proven that for the hall magnetohydrodynamics system forced by l e vy noise such a result may be obtained even with zero viscous diffusion secondly we may extend the classical kelvin s conservation of circulation flow as well as the cauchy s vorticity transport formula on the euler equations to show that the solution to the damped euler equations enjoys the exact same identities except with an exponential decay in time such identities are known to completely fail once we add diffusion and consider the damped navier stokes equations nevertheless discovering a stochastic lagrangian formulation we are able to show that such identities indeed do continue to hold informally on average i e via a mathematical expectation over the random ensemble at earlier time the stochastic lagrangian formulation and these identities have also been obtained for the solution to the boussinesq system these results are rigorously proven in mohan and yamazaki 0000 and yamazaki 0000 in this manuscript we will not pursue complete proofs which were in particular mostly inspired by kim 2011 and iyer 2006 but rather elaborate on motivations difficulty and remaining open problems for future works

on the stochastic quasi linear symmetric hyperbolic system abstract we establish the existence and uniqueness of a local smooth solution to the cauchy problem for a quasi linear symmetric hyperbolic system with random noise in r d when the noise is multiplicative satisfying some nondegenerate conditions and the initial data are sufficiently small we show that the solution exists globally in time in probability i e the probability of global existence can be made arbitrarily close to one if the initial date are small accordingly

vector lyapunov functions and the technique in perturbation theory in l a new comparison theorem is developed that connects the solution of perturbed and unperturbed differential systems in a manner useful in the theory of perturbations this comparison result blends in a sense the two approaches namely the method of lyapunov functions and the method of variation of parameters and consequently provides a flexible mechanism to preserve the nature of perturbations the results that are given in l show that the usual comparison theorem in terms of a lyapunov function is included as a special case and that perturbation theory could be studied in a more fruitful way in the study of large scale dynamic systems s by the method of decomposition and aggregation several lyapunov functions result in a natural way this is because one assumes that the given large scale system is decomposed into isolated subsystems and interconnections between them if the solution of these subsystems possesses good behavior like uniform asymptotic stability then one can construct a lyapunov function relative to each subsystem which can then be utilized to investigate the stability properties of the given large scale dynamic system as a perturbed system by employing the method of vector lyapunov functions in this

iterative method for coupled quasi solutions of mixed monotone operator equations in this paper we obtain some new existence theorems of the coupled quasi fixed points for mixed monotone operators under more general conditions our results improve and extend many well known results finally we apply our results to hammerstein integral equations

iterative method for solutions and coupled quasi solutions of nonlinear integro differential equations of mixed type in banach spaces we consider in this paper the existence of solutions coupled minimal and maximal quasi solutions and iterative approximation of the unique solution for the following initial value problems ivp of the nonlinear integro di erential equations of mixed type in ordered banach spaces e u f t u u tu su t i u t0 x0 1 where i t0 t0 a a 0 x0 e f c i e e e e e and

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

monotone iterative methods for a general class of discrete boundary value problems abstract in this paper we shall offer comparison results as well as monotone iterative schemes for the construction of solutions to a very general class of discrete boundary value problems the discrete system we consider includes in particular the n th order prototype systems finite as well as infinite discrete delay equations and discrete integral equations further the boundary conditions we consider include the initial terminal periodic and transport type problems numerical examples illustrating the usefulness of the proposed schemes to a variety of boundary value problems are also included

existence of solutions of boundary value problems for differential equations with delayed arguments we study the existence and approximation of solution of boundary value problems for differential equations with delayed arguments sufficient conditions are established for the existence of a unique solution or extremal ones of the given problem a monotone iterative technique is applied

picard and weakly picard operators technique for nonlinear differential equations in banach spaces abstract in this paper we study nonlocal cauchy problems for differential equations in banach spaces using picard and weakly picard operators technique and suitable bielecki norms some existence uniqueness and data dependence results are obtained under some mild conditions as an application we also discuss a class of impulsive cauchy problems by adapting the same methods

strong solutions for differential equations in abstract spaces abstract let e f be a locally convex space we denote the bounded elements of e by e b x e x f sup f x in this paper we prove that if b e b is relatively compact with respect to the f topology and f i e b e b is a measurable family of f continuous maps then for each x 0 e b there exists a norm differentiable i e differentiable with respect to the f norm local solution to the initial valued problem u t t f t u t u t 0 x 0 all of this machinery is developed to study the lipschitz stability of a nonlinear differential equation involving the hardy littlewood maximal operator

positive fixed points for nonlinear operators this paper is concerned with the existence and uniqueness of positive fixed points for nonlinear decreasing operators with sublinear perturbation operators in ordered banach spaces a new fixed point theorem without the assumption of compactness and continuity of operators is established and an iterative sequence yielding the fixed point is also given in addition an application to nonlinear integral equations is shown

boundary value problems for first order differential equations of mixed type abstract we apply the monotone iterative method to formulate existence results for integro differential equations with nonlinear boundary conditions some results for integro differential inequalities are also given examples illustrate obtained results

a note on the theorem of lakshmikantham and leela we study the initial value problem u f t u u 0 u 0 in a real banach space using the fixed point principle of daher and the theorem of monch and von harten we obtain a theorem which is an extension of that established by lakshmikantham and leela in 1

monotone iterative technique for delay differential equations in abstract cones a monotone iterative technique is developed for delay differential equations in a banach space by utilizing the method of upper and lower solutions

existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions this paper is concerned with the existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions the proof of our main results is based upon a new fixed point theorem of generalized concave operators

φ h e concave operators and applications abstract in this article by introducing a new set and a new concept of h e concave operators and by using the cone theory and monotone iterative method we present some new existence and uniqueness theorems of fixed points for increasing h e concave operators without requiring the existence of upper and lower solutions as an application we establish the existence and uniqueness of a nontrivial solution for a new form of fractional differential equation with integral boundary conditions the main results of this paper improve and extend some known results and present a new method to study nonlinear equation problems

advanced differential equations with nonlinear boundary conditions we investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions sufficient conditions when the problem has extremal solutions or a unique solution are formulated linear advanced differential inequalities are also discussed

monotone iterative technique for differential equations in a banach space iffis continuous steps i and iii are standard and straightforward it is step ii that deserves attention this in turn leads to three possibilities namely to show that the sequence of approximate solutions is a a cauchy sequence b relatively compact so that one can appeal to ascoli s theorem and c a monotone sequence in a cone the first two possibilities are well known and are discussed in 2 31 this paper is devoted to the investigation of c which leads to the development of a monotone iterative technique in an arbitrary cone

extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order this paper studies the existence of solutions of first order impulsive functional differential equations with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence of solutions by establishing a new comparison principle and using the monotone iterative technique a concrete example is presented and solved to illustrate the obtained results

mixed monotone iterative technique for a class of semilinear impulsive evolution equations in banach spaces abstract this paper deals with the existence of mild l quasi solutions to the initial value problem for a class of semilinear impulsive evolution equations in an ordered banach space e under a new concept of upper and lower solutions a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established the results improve and extend some relevant results in ordinary differential equations and partial differential equations an example is also given

monotone iterative technique for addressing impulsive integro differential equations in banach spaces abstract in this paper we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence of solutions for the initial value problem of the impulsive integro differential equation of volterra type in a banach space e u t f t u t t u t t j t t k u t t k i k u t k k 1 2 m u 0 x 0 where f c j e e e j 0 a 0 t 1 t 2 t m a and i k c e e k 1 2 m under wide monotone conditions and the noncompactness measure condition of nonlinearity f we obtain the existence of extremal solutions and a unique solution between lower and upper solutions our result improves and extends some relevant results in abstract differential equations

boundary value problems for systems of nonlinear integro differential equations with deviating arguments by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique we investigate the systems of nonlinear mixed integro differential equations with deviating arguments and mixed boundary value conditions sufficient conditions are established for the existence of extremal system of solutions of the given problem

an algorithm for approximate solving of differential equations with maxima an algorithm for constructing two sequences of successive approximations of the solution of the initial value problem for nonlinear differential equations with maxima is given this algorithm is based on the monotone iterative technique it is proved that both sequences are monotonically convergent each term of the constructed sequences is a solution of an initial value problem for linear differential equations with maxima and it is a lower upper solution of the given problem both the scalar case and the multidimensional case are studied an example solved by computer realization of the suggested algorithm illustrates the practical application of the method

on α convex operators in this paper the existence and uniqueness of positive fixed points for a class of convex operators is obtained by means of the properties of cone concave operators and the monotonicity of set valued maps in the end we give a simple application to certain integral equations

differential equations with integral boundary conditions the method of lower and upper solutions combined with monotone iterative technique is used for ordinary differential equations with integral boundary conditions problems of existence of extremal and unique solutions are discussed some comparison results are formulated too