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

approximate controllability for linearized compressible barotropic navier stokes system in one and two dimensions abstract in this paper we consider compressible barotropic navier stokes equations in one and two dimensions linearized around a constant steady state with dirichlet boundary conditions we explore the controllability of this linearized system using a control only for the velocity equation we prove that the system with homogeneous dirichlet boundary conditions is approximately controllable by a localized interior control when time is sufficiently large

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

some nonlinear dynamic integral inequalities on time scales in this paper we study some dynamic integral inequalities with mixed nonlinearities on time scales which provide explicit bounds on unknown functions our results include many existing ones in the literature as special cases and can be used as tools in the qualitative theory of certain classes of dynamic equations with mixed nonlinearities on time scales

some integral inequalities useful in the theory of certain partial dynamic equations on time scales our aim in this paper is to investigate some integral inequalities in two independent variables on time scales which unify and extend some integral inequalities and their corresponding discrete analogues the inequalities given here can be used as handy tools to study the properties of certain partial dynamic equations on time scales

oscillation for nonlinear second order dynamic equations on a time scale abstract we obtain some oscillation criteria for solutions to the nonlinear dynamic equation x q t x p t f x 0 on time scales in particular no explicit sign assumptions are made with respect to the coefficients p t q t we illustrate the results by several examples including a superlinear emden fowler dynamic equation

some controllability results for linear viscoelastic fluids we analyze the controllability properties of systems which provide a description at first approximation of a kind of viscoelastic fluid we consider linear maxwell fluids first we establish the large time approximate finite dimensional controllability of the system with distributed or boundary controls supported by arbitrary small sets then we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets the proofs of these results rely on classical arguments in particular the approximate controllability result is implied by appropriate unique continuation properties while exact controllability is a consequence of observability inverse inequalities we also discuss questions concerning the controllability of viscoelastic fluids and some related open problems

some new volterra fredholm type dynamic integral inequalities on time scales in this paper some new explicit bounds on solutions to a class of new volterra fredholm type dynamic integral inequalities on time scales are established which can be used as effective tools in the study of certain dynamic equations some applications for dynamic equations are also indicated

oscillation criteria for second order nonlinear neutral delay dynamic equations in this paper we will establish some oscillation criteria for the second order nonlinear neutral delay dynamic equation r t y t p t y t f t y t 0 on a time scale t here 0 is a quotient of odd positive integers with r t and p t real valued positive functions defined on t to the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales so this paper initiates the study

gronwall bellman type nonlinear delay integral inequalities on time scales abstract in this paper some gronwall bellman type nonlinear delay integral inequalities on time scales are established which provide a handy tool in deriving boundedness of solutions of certain delay dynamic equations on time scales our results generalize some of the main results in lipovan 2006 1 pachpatte 2000 2 ferreira and torres 2009 3 zhang and meng 2008 4 cheung and ren 2006 5 kim 2009 6 and some of our results unify continuous and discrete analysis in the literature

are viscoelastic flows under control or out of control we discuss the controllability of viscoelastic shear flows both linear and nonlinear results are reviewed an interesting aspect of the problem is that the nonlinear problem introduces new stress components which are automatically zero in the linear case it is therefore a challenging problem to determine to what extent these stresses are controllable

explicit observability estimate for the wave equation with potential and its application by means of the carleman type estimate we obtain an explicit observability estimate for the wave equation with a potential as its application we get the exact internal controllability of the semilinear wave equations in any space dimensions

approximate controllability results for viscoelastic flows with infinitely many relaxation modes abstract we prove results on approximate controllability for linear viscoelastic flows with a localized distributed control in the momentum balance equation the constitutive law is a multimode maxwell or jeffreys model with an infinite number of relaxation modes

on the control of viscoelastic jeffreys fluids abstract this paper is devoted to analyzing the control of vicoelastic fluids of the jeffreys kind also known as oldroyd models we will present the interesting problems with special emphasis in the difficulties that they involve then we will consider appropriate linear approximations and we will establish some partial approximate finite dimensional controllability results in an arbitrarily small time with distributed or boundary controls supported by arbitrarily small sets the proofs rely on some specific unique continuation properties which are implied by the structure of the solutions

some controllability results for the n dimensional navier stokes and boussinesq systems with n 1 scalar controls in this paper we deal with some controllability problems for systems of the navier stokes and boussinesq kind with distributed controls supported in small sets our main aim is to control n dimensional systems n 1 scalar unknowns in the case of the navier stokes equations with n 1 scalar control functions in a first step we present some global carleman estimates for suitable adjoint problems of linearized navier stokes and boussinesq systems in this way we obtain null controllability properties for these systems then we deduce results concerning the local exact controllability to the trajectories we also present global null controllability results for some truncated approximations of the navier stokes equations

initial value problem for first order integro differential equation of volterra type on time scales abstract in this paper we combine the monotone iterative technique with fixed point theory to investigate the extremal solutions of nonlinear integro differential equations on time scales several important lemmas and existence criteria are obtained

generalized gronwall bellman type delay dynamic inequalities on time scales and their applications abstract in this paper we establish some new gronwall bellman type delay dynamic inequalities on time scales which can be used as a handy tool in the investigation of qualitative as well as quantitative analysis of solutions of delay dynamic equations on time scales our results generalize the main results of ou iang l ou iang the boundedness of solutions of linear differential equations y a t y 0 shuxue jinzhan 3 1957 409 415 jiang f c jiang f w meng explicit bounds on some new nonlinear integral inequality with delay j comput appl math 205 2007 479 486 and yuan z l yuan x w yuan f w meng some new delay integral inequalities and their applications appl math comput 208 2009 231 237

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

a survey stability and boundedness of volterra difference equations abstract volterra difference equations arise in the modeling of many real phenomena in this survey stability and boundedness problems of some volterra nonlinear difference equations are investigated stability conditions and boundedness are formulated in terms of the characteristics of equations

some new nonlinear volterra fredholm type dynamic integral inequalities on time scales in this paper some new explicit bounds on solutions to a class of new nonlinear volterra fredholm type dynamic integral inequalities on time scales are established which can be used as effective tools in the study of certain dynamic equations some applications for dynamic equations are also indicated

generalized bosbach and riecan states based on relative negations in residuated lattices bosbach and riecan states on residuated lattices both are generalizations of probability measures on boolean algebras recently two types of generalized bosbach states on residuated lattices were introduced by georgescu and muresan through replacing the standard mv algebra in the original definition with arbitrary residuated lattices as codomains however several interesting problems there remain still open the first part of the present paper gives positive answers to these open problems it is proved that every generalized bosbach state of type ii is of type i and the similarity cauchy completion of a residuated lattice endowed with an order preserving generalized bosbach state of type i is unique up to homomorphisms preserving similarities where the codomain of the type i state is assumed to be cauchy complete consequently many existing results about generalized bosbach states can be further strengthened the second part of the paper introduces the notion of relative negation with respect to a given element called relative element in residuated lattices and then many issues with the canonical negation such as glivenko property semi divisibility generalized riecan state of residuated lattices can be extended to the context of such relative negations in particular several necessary and sufficient conditions for the set of all relatively regular elements of a residuated lattice to be special residuated lattices are given of which one extends the well known glivenko theorem and it is also proved that relatively generalized riecan states vanishing at the relative element are uniquely determined by their restrictions on the mv algebra consisting of all relatively regular elements when the domain of the states is relatively semi divisible and the codomain is involutive

some pachpatte type inequalities on time scales in this paper using the comparison theorem we investigate some pachpatte type integral inequalities on time scales which provide explicit bounds on unknown functions our results extend some known dynamic inequalities on time scales unify and extend some continuous inequalities and their corresponding discrete analogues some applications of the main results are given in the end of this paper

convergence in perfect mv algebras this paper investigates how the di nola lettieri functors d and can be applied to the study of convergence in perfect mv algebras after recalling the preliminaries on mv algras the concept of convergence in perfect mv algebras is presented and the connection between mv algebras and perfect mv algebras explicited

extremal solutions of nonlinear impulsive integrodifferential equations in banach spaces abstract in this paper we combine the monotone iterative technique with fixed point theory to investigate the extremal solutions of nonlinear impulsive integrodifferential equations in banach spaces existence criteria are obtained and several examples are worked out

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

nonlinear integro differential equations and optimal control problems on time scales this paper is mainly concerned with a class of optimal control problems of a system governed by the nonlinear integro differential equation on time scales using the contraction mapping principle the existence and uniqueness of a weak solution of the nonlinear integro differential equation on time scales are proved discussing l t 1 strong weak lower semicontinuity of integral functional on time scales we give sufficient conditions for the existence of optimal control by the virtue of the integration by parts formula on time scales the necessary conditions of optimality are derived

existence and multiplicity of positive solutions to nonlinear first order pbvps on time scales in this paper we consider the following nonlinear first order periodic boundary value problems on time scales x d t p t x s t f x t email protected 0 t t x 0 x s t some new existence and multiplicity criteria of positive solutions are established by using several well known fixed point theorems

limiting periodicity of the solutions for some volterra difference equations conditions of the limiting of periodicity of the solutions for some volterra difference equations are derived these conditions are formulated immediately in terms of the coefficients of equations and their resolvent using the second liapunov method and fixed point theorem

a unique solution of initial value problems for first order impulsive integro differential equations of mixed type in banach spaces in this paper we investigate initial value problem for first order impulsive integro differential equation of mixed type in a banach space without any compactness type assumption we obtain a unique solution of the equation an explicit iterative approximation of the solution and an error estimate of the approximation sequence our result improves and extends many recent results

stability by linear approximation for time scale dynamical systems abstract we study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods in this paper we consider linear systems and their small nonlinear perturbations in terms of time scales and of eigenvalues of matrices we formulate conditions sufficient for stability by linear approximation for non periodic time scales we use techniques of central upper lyapunov exponents a common tool of the theory of linear odes to study stability of solutions also time scale versions of the famous chetaev s theorem on conditional instability are proved in a nutshell we have developed a completely new technique in order to demonstrate that methods of non autonomous linear ode theory may work for time scale dynamics

some new dynamic inequalities on time scales in this paper based on some known dynamic inequalities we investigate certain new dynamic inequalities on time scales which provide explicit bounds on unknown functions our results unify and extend some continuous inequalities and their corresponding discrete analogues