a note on the second order non autonomous neutral stochastic evolution equations with infinite delay under caratheodory conditions abstract in this note we aim to study a class of second order non autonomous neutral stochastic evolution equations with infinite delay driven by a standard cylindrical wiener process and an independent cylindrical fractional brownian motion with hurst parameter h 1 2 1 in which the initial value belongs to the abstract space b we establish the existence and uniqueness of mild solutions for this kind of equations under some caratheodory conditions by means of the successive approximation the obtained result extends some well known results an example is proposed to illustrate the theory

stochastic controllability and minimum energy control of systems with multiple delays in control in recent years various controllability problems for different types of linear dynamical systems have been considered in many publications and monographs

primal dual interior point methods for semidefinite programming convergence rates stability and numerical results primal dual interior point path following methods for semidefinite programming are considered several variants are discussed based on newton s method applied to three equations primal feasibility dual feasibility and some form of centering condition the focus is on three such algorithms called the xz xz zx and q methods for the xz zx and q algorithms the newton system is well defined and its jacobian is nonsingular at the solution under nondegeneracy assumptions the associated schur complement matrix has an unbounded condition number on the central path under the nondegeneracy assumptions and an additional rank assumption practical aspects are discussed including mehrotra predictor corrector variants and issues of numerical stability compared to the other methods considered the xz zx method is more robust with respect to its ability to step close to the boundary converges more rapidly and achieves higher accuracy

feedback control for fractional impulsive evolution systems this paper is mainly concerned with feedback control systems governed by fractional impulsive evolution equations involving riemann liouville derivatives in reflexive banach spaces we firstly give an existence and uniqueness result of mild solutions for the equations by applying the banach s fixed point theorem next by using the filippove theorem and the cesari property a new set of sufficient assumptions are formulated to guarantee the existence result of feasible pairs we also present an existence result of optimal control pairs for the lagrange problem

approximate controllability of impulsive differential equations with state dependent delay in order to describe various real world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process impulsive differential equations have been used to describe the system model in this article the problem of approximate controllability for nonlinear impulsive differential equations with state dependent delay is investigated we study the approximate controllability for nonlinear impulsive differential system under the assumption that the corresponding linear control system is approximately controllable using methods of functional analysis and semigroup theory sufficient conditions are formulated and proved finally an example is provided to illustrate the proposed theory

superlinear convergence of a symmetric primal dual path following algorithm for semidefinite programming this paper establishes the superlinear convergence of a symmetric primal dual path following algorithm for semidefinite programming sdp under the assumptions that the semidefinite program has a strictly complementary primal dual optimal solution and that the size of the central path neighborhood tends to zero the interior point algorithm considered here closely resembles the mizuno todd ye predictor corrector method for linear programming which is known to be quadratically convergent it is shown that when the iterates are well centered the duality gap is reduced superlinearly after each predictor step indeed if each predictor step is succeeded by r consecutive corrector steps then the predictor reduces the duality gap superlinearly with order 2 1 2 r the proof relies on a careful analysis of the central path for sdp it is shown that under the strict complementarity assumption the primal dual central path converges to the analytic center of the primal dual optimal solution set and the distance from any point on the central path to this analytic center is bounded by the duality gap

l2 l filtering for stochastic systems driven by poisson processes and wiener processes this paper investigates the l2 l filtering problem for stochastic systems driven by poisson processes and wiener processes firstly this paper presents an approach to transform the expectation of stochastic integral with respect to poisson process into the expectation of lebesgue integral by the martingale theory then based on this a filter is designed to guarantee that the filtering error system is mean square asymptotically stable and its l2 l performance satisfies a prescribed level finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme

existence results for impulsive multivalued semilinear neutral functional differential inclusions in banach spaces in this paper the existence of mild solutions for first and second order impulsive semilinear neutral functional differential inclusions in banach spaces is investigated the results are obtained by using a fixed point theorem for condensing multivalued maps due to martelli and semigroup theory

critical exponents for semilinear dissipative wave equations in rn abstract we shall present new critical exponents 1 2m n with m 1 2 to the cauchy problem utt u ut u p 1u with the initial data u 0 u 1 h 1 r n l m r n l 2 r n l m r n that is the small data global existence property can be derived to the cauchy problem above with power 1 2m n

approximate controllability of semi linear neutral integro differential systems with finite delay abstract this paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in hilbert space since the considered equation admits nonlinear terms involving spatial derivatives the fraction power theory and norm are used to discuss the problem so that the established results can be applied to them the results are obtained by using the sadovskii fixed point theorem and the theory of analytic resolvent operator an example is presented to illustrate the applications of the obtained results

avoiding numerical cancellation in the interior point method for solving semidefinite programs the matrix variables in a primal dual pair of semidefinite programs are getting increasingly ill conditioned as they approach a complementary solution multiplying the primal matrix variable with a vector from the eigenspace of the non basic part will therefore result in heavy numerical cancellation this effect is amplified by the scaling operation in interior point methods a complete example illustrates these numerical issues in order to avoid numerical problems in interior point methods we propose to maintain the matrix variables in a cholesky form we discuss how the factors of the v space cholesky form can be updated after a main iteration of the interior point method with nesterov todd scaling an analogue for second order cone programming is also developed numerical results demonstrate the success of this approach

critical regularity of nonlinearities in semilinear classical damped wave equations in this paper we consider the cauchy problem for the semilinear damped wave equation begin aligned u tt vardelta u u t h u quad u 0 x phi x quad u t 0 x psi x end aligned where h s s 1 frac 2 n mu s here n is the space dimension and mu is a modulus of continuity our goal is to obtain sharp conditions on mu to obtain a threshold between global in time existence of small data solutions stability of the zero solution and blow up behavior even of small data solutions

controllability of measure driven evolution systems with nonlocal conditions this paper investigates complete controllability of semilinear measure driven differential systems with nonlocal conditions without assuming the compactness of the evolution system related to the linear part of the measure system some sufficient conditions for controllability are established by using the measure of noncompactness and the monch fixed point theorem the results obtained here improve and generalize many known results

product form cholesky factorization in interior point methods for second order cone programming second order cone programming socp problems are typically solved by interior point methods as in linear programming lp interior point methods can in theory solve socps in polynomial time and can in practice exploit sparsity in the problem data specifically when cones of large dimension are present the density that results in the normal equations that are solved at each iteration can be remedied in a manner similar to the treatment of dense columns in an lp here we propose a product form cholesky factorization pfcf approach and show that it is more numerically stable than the alternative sherman morrison woodbury approach we derive several pfcf variants and compare their theoretical perfomance finally we prove that the elements of l in the cholesky factorizations ldlt that arise in interior point methods for socp are uniformly bounded as the duality gap tends to zero as long as the iterates remain is some conic neighborhood of the cental path

on the implementation of interior point decomposition algorithms for two stage stochastic conic programs in this paper we develop a practical primal interior decomposition algorithm for two stage stochastic programming problems the framework of this algorithm is similar to the framework in s mehrotra and m g ozevin decomposition based interior point methods for two stage stochastic convex quadratic programs with recourse to appear in oper res s mehrotra and m g ozevin siam j optim 18 2007 pp 206 222 and g zhao math program 90 2001 pp 507 536 however their algorithm is altered in a simple yet fundamental way to achieve practical performance in particular this new algorithm weighs the log barrier terms in the second stage problems differently from the theoretical algorithms analyzed in s mehrotra and m g ozevin oper res to appear s mehrotra and m g ozevin siam j optim 18 2007 pp 206 222 and g zhao math program 90 2001 pp 507 536 we give a method for generating a suitable starting point a method for selecting a good starting barrier parameter a heuristic for first stage step length calculation without performing line searches and a method for adaptive addition of new scenarios over the course of the algorithm the decomposition algorithm is implemented to solve two stage stochastic conic programs with recourse whose underlying cones are cartesian products of linear second order and semidefinite cones the performance of primal decomposition method is studied on a set of randomly generated test problems as well as a two stage stochastic programming extension of the markowitz portfolio selection model the computational results show that an efficient and stable implementation of the primal decomposition method is possible these results also show that in problems with a large number of scenarios the adaptive addition of scenarios can yield computational savings of up to 80

approximate controllability for semilinear second order stochastic evolution systems with infinite delay in this work we study the approximate controllability for a class of semilinear second order stochastic evolution systems with infinite delay the main technique is the fundamental solution theory

some comments on existence of solutions of abstract nonlinear second order neutral functional integrodifferential equations we establish the existence of mild solutions for a class of abstract second order partial neutral functional integro differential equations with finite delay in a banach space using the theory of cosine families of bounded linear operators and schaefer s fixed point theorem

approximate controllability of second order distributed implicit functional systems abstract in this paper we study the approximate controllability of control systems with states and controls in hilbert spaces and described by a second order semilinear abstract functional differential equation with infinite delay initially we establish a characterization for the approximate controllability of a second order abstract linear system and in the last section we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system

complementarity and nondegeneracy in semidefinite programming primal and dual nondegeneracy conditions are defined for semidefinite programming given the existence of primal and dual solutions it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution the converses hold if strict complementarity is assumed primal and dual nondegeneracy assumptions do not imply strict complementarity as they do in lp the primal and dual nondegeneracy assumptions imply a range of possible ranks for primal and dual solutions x and z this is in contrast with lp where nondegeneracy assumptions exactly determine the number of variables which are zero it is shown that primal and dual nondegeneracy and strict complementarity all hold generically numerical experiments suggest probability distributions for the ranks of x and z which are consistent with the nondegeneracy conditions

on a wide region of centers and primal dual interior point algorithms for linear programming in the adaptive step primal dual interior point method for linear programming polynomial algorithms are obtained by computing newton directions towards targets on the central path and restricting the iterates to a neighborhood of this central path in this paper the adaptive step methodology is extended by considering targets in a certain central region which contains the usual central path and subsequently generating iterates in a neighborhood of this region the size of the central region can vary from the central path to the whole feasible region by choosing a certain parameter an o nl iteration bound is obtained under mild conditions on the choice of the target points in particular we leave plenty of room for experimentation with search directions the practical performance of the new primal dual interior point method is measured on part of the netlib test set for various sizes of the central region

existence and controllability results for impulsive partial functional differential inclusions abstract in this paper we prove the existence and the controllability of mild and extremal mild solutions for first order semilinear densely defined impulsive functional differential inclusions in separable banach spaces with local and nonlocal conditions

partial approximate controllability of nonlocal fractional evolution equations via approximating method abstract in this paper we study partial approximate controllability of semilinear nonlocal fractional evolution equations in hilbert spaces by using fractional calculus variational approach and approximating technique we give the approximate problem of the control system and get the compactness of approximate solution set then new sufficient conditions for the partial approximate controllability of the control system are obtained when the compactness conditions or lipschitz conditions for the nonlocal function are not required finally we apply our abstract results to the partial approximate controllability of the semilinear heat equation and delay equation

controllability of second order semilinear neutral functional differential systems in banach spaces abstract sufficient conditions for controllability of semilinear second order neutral functional differential systems in banach spaces are established using the theory of strongly continuous cosine families the results are obtained by using the leray schauder alternative

interior point trajectories in semidefinite programming in this paper we study interior point trajectories in semidefinite programming sdp including the central path of an sdp this work was inspired by the seminal work of megiddo on linear programming trajectories progress in math programming interior point algorithms and related methods n megiddo ed springer verlag berlin 1989 pp 131 158 under an assumption of primal and dual strict feasibility we show that the primal and dual central paths exist and converge to the analytic centers of the optimal faces of respectively the primal and the dual problems we consider a class of trajectories that are similar to the central path but can be constructed to pass through any given interior feasible or infeasible point and study their convergence finally we study the derivatives of these trajectories and their convergence

existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions abstract in this paper we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable banach spaces we shall rely on a fixed point theorem for the sum of completely continuous and contraction operators the question of controllability of these equations and the topological structure of the solutions set are considered too

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

approximate controllability of second order damped mckean vlasov stochastic evolution equations in this paper sufficient conditions for the approximate controllability of a class of second order nonlinear stochastic functional differential equations of mckean vlasov type are derived the nonlinearities at a given time t considered depend not only on the state of the solution at time t but also on the corresponding probability distribution at time t an example is given to illustrate the theory

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

a note on exponential stability for impulsive neutral stochastic partial functional differential equations in this note the problem on the exponential stability in mean square moment of mild solution to impulsive neutral stochastic partial functional differential equations is considered by employing the inequality technique some sufficient conditions are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained result

interior point methods for the monotone semidefinite linear complementarity problem in symmetric matrices the sdlcp semidefinite linear complementarity problem in symmetric matrices introduced in this paper provides a unified mathematical model for various problems arising from systems and control theory and combinatorial optimization it is defined as the problem of finding a pair x y of n times n symmetric positive semidefinite matrices which lies in a given n n 1 2 dimensional affine subspace fc of sc 2 and satisfies the complementarity condition x bullet y 0 where sc denotes the n n 1 2 dimensional linear space of symmetric matrices and x bullet y the inner product of x and y the problem enjoys a close analogy with the lcp in the euclidean space in particular the central trajectory leading to a solution of the problem exists under the nonemptiness of the interior of the feasible region and a monotonicity assumption on the affine subspace fc the aim of this paper is to establish a theoretical basis of interior point methods with the use of newton directions toward the central trajectory for the monotone sdlcp

existence of solutions of non autonomous second order functional differential equations with infinite delay in this paper the existence of solutions of a non autonomous abstract retarded functional differential equation of second order with infinite delay is considered assuming the existence of an evolution operator corresponding to the associate abstract cauchy problem of second order we establish the existence of mild solutions of the functional equation furthermore we study the existence of classical solutions of the abstract cauchy problem of second order and we apply these results to establish the existence of classical solutions of the functional equation finally we apply our results to study the existence of solutions of the non autonomous wave equation with delay

on controllability of second order nonlinear impulsive differential systems abstract many dynamical systems in physics chemistry biology and engineering sciences have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes the mathematical models of such processes are called differential systems with impulse effect this paper studies the exact controllability issue of certain types of second order nonlinear impulsive control differential systems sufficient conditions are formulated and proved for the exact controllability of such systems without imposing a compactness condition on the cosine family of operators we establish controllability results by using a fixed point analysis approach finally an example is presented to illustrate the utility of the proposed result the results improve some recent results

approximate controllability for stochastic evolution inclusions of clarke s subdifferential type in this paper we deal with the approximate controllability of stochastic evolution inclusions of clarke s subdifferential type firstly by using stochastic analysis nonsmooth analysis theory of operator semigroups and fixed point theorems of multivalued maps we show the existence of mild solutions for the stochastic evolution inclusions then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution inclusions actually our results cover a broader class of inclusion problems involving time depending operators finally an example is included to illustrate the applicability of the main results

sharp upper bound for lifespan of solutions to some critical semilinear parabolic dispersive and hyperbolic equations via a test function method abstract this paper is concerned with the blowup phenomena for initial boundary value problem 0 1 t 2 u x t u x t a x t u x t u x t p x t c 0 t u x t 0 x t c 0 t u x 0 e f x x c t u x 0 e g x x c where c is a cone like domain in r n n 2 defined as c int r r n r 0 with a connected open set in s n 1 with smooth boundary if n 1 then we only consider two cases c 0 and c r here a x is a non zero coefficient of t u which could be complex valued and space dependent is a fixed constant and e 0 is a small parameter the constants 0 1 switch the parabolicity and hyperbolicity of the problem 0 1 the result proposes an argument for sharp upper lifespan estimates of solutions to 0 1 by a test function method based on mitidieri and pokhozhaev 2001 the crucial idea is to introduce an ordinary differential inequality with a parameter as a variable

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

approximate controllability of a multi valued fractional impulsive stochastic partial integro differential equation with infinite delay in this paper the approximate controllability of a new class of multi valued fractional impulsive stochastic partial integro differential equations with infinite delay in hilbert spaces is studied firstly by using stochastic analysis analytic resolvent operator fractional powers of closed operators and a fixed point theorem for multi valued maps we prove an existence result of mild solutions for the control systems under the mixed lipschitz and caratheodory conditions secondly we discuss a new set of sufficient conditions for the approximate controllability of the systems the results are obtained under the assumption that the associated linear system is approximately controllable finally an example is provided to illustrate the proposed theory

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

controllability of evolution differential inclusions in banach spaces abstract in this paper we consider the controllability of a certain class of evolution differential inclusions in banach spaces a sufficient condition is established by using a recent fixed point theorem for multi valued maps due to dhage combined with an evolution system an example is also given to illustrate our result

topological structure of solution sets for impulsive differential inclusions in frechet spaces abstract in this paper we consider the existence of solutions as well as the topological and geometric structure of solution sets for first order impulsive differential inclusions in some frechet spaces both the initial and terminal problems are considered using ingredients from topology and homology the topological structures of solution sets closedness and compactness as well as some geometric properties contractibility acyclicity a r and r are investigated some of our existence results are obtained via the method of taking the inverse system limit on noncompact intervals

periodic solutions for differential equations with state dependent delay and positive feedback existence of a nontrivial periodic orbit and a homoclinic orbit connecting 0 to the periodic orbit is shown for the differential equation x t x t f x t r r r x t with state dependent delay and positive feedback here 0 f and r are smooth real functions with r 0 1 and f 0

controllability of integrodifferential systems in banach spaces sufficient conditions for controllability of integrodifferential systems in a banach space are established the results are obtained by using the schaefer fixed point theorem an example is provided to illustrate the theory

the solution sets for second order semilinear impulsive multivalued boundary value problems a second order semilinear differential inclusion with some boundary continuous and impulse characteristics in a separable banach space is considered some existence theorems for mild solutions are given when the multivalued nonlinearity of the inclusion is only a locally integrably bounded upper caratheodory map with convex and weakly compact values then the compactness of the set of all mild solutions for the problem is proved the results are obtained by using the theory of continuous cosine families of bounded linear operators and a fixed point theorem for multivalued maps due to agarwal meehan and o regan a corresponding result for closed graph of composition is extended

controllability of sobolev type integrodifferential systems in banach spaces sufficient conditions for controllability of sobolev type integrodifferential systems in banach spaces are established the results are obtained using compact semigroups and the schauder fixed point theorem as an example is provided to illustrate the results

a note on exponential stability for second order neutral stochastic partial differential equations with infinite delays in the presence of impulses in this work the problem on the exponential stability for second order neutral stochastic partial differential equations with infinite delays is considered in the presence of impulses under some conditions by employing the new integral inequality technique some algebraic criteria of stability are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained results

controllability of impulsive neutral functional differential inclusions with infinite delay abstract the paper is concerned with the controllability of the first order impulsive neutral functional differential inclusions with infinite delay in a banach space sufficient conditions for controllability are obtained by using a fixed point theorem for condensing maps due to martelli as an application we also consider an impulsive neutral partial functional differential equation

similarity and other spectral relations for symmetric cones abstract the similarity relations that are derived in this paper reduce to well known results in the special case of symmetric matrices in particular for two positive definite matrices x and y the square of the spectral geometric mean is known to be similar to the matrix product xy it is shown in this paper that this property carries over to symmetric cones more elementary similarity relations such as xy 2 x yx 2 y are generalized as well we also extend the result that the eigenvalues of a matrix product xy are less dispersed than the eigenvalues of the jordan product xy yx 2 the paper further contains a number of inequalities on norms and spectral values this type of inequality is often used in the analysis of interior point methods in optimization we also derive an extension of stein s theorem to symmetric cones

existence and controllability results for second order impulsive stochastic evolution systems with state dependent delay in this paper we discuss a kind of impulsive second order stochastic evolution systems with state dependent delay in a real separable hilbert space the results concerning the existence and controllability of mild solutions have been addressed by means of the fixed point techniques some sufficient conditions are formulated as well as an application involving partial differential equation with impulses is presented

existence results for an impulsive abstract partial differential equation with state dependent delay in this paper we establish the existence of mild solutions for a class of impulsive abstract partial functional differential equation with state dependent delay

solving second order cone programming via a reduced augmented system approach the standard schur complement equation based implementation of interior point methods for second order cone programming may encounter stability problems in the computation of search directions and as a consequence accurate approximate optimal solutions are sometimes not attainable based on the eigenvalue decomposition of the 1 1 block of the augmented equation a reduced augmented equation approach is proposed to ameliorate the stability problems numerical experiments show that the new approach can achieve more accurate approximate optimal solutions than the schur complement equation based approach

lp lq estimates of solutions to the damped wave equation in 3 dimensional space and their application it has been asserted that the damped wave equation has the diffusive structure as t in this paper we consider the cauchy problem in 3 dimensional space for the linear damped wave equation and the corresponding parabolic equation and obtain the lp lq estimates of the difference of each solution which represent the assertion precisely explicit formulas of the solutions are analyzed for the proof the second aim is to apply the lp lq estimates to the semilinear damped wave equation with power nonlinearity if the power is larger than the fujita exponent then the time global existence of small weak solution is proved and its optimal decay order is obtained

computational experience with a primal dual interior point method for linear programming abstract a new comprehensive implementation of a primal dual algorithm for linear programming is described it allows for easy handling of simple bounds on the primal variables and incorporates free variables which have not previously been included in a primal dual implementation we discuss in detail a variety of computational issues concerning the primal dual implementation and barrier methods for linear programming in general we show that in a certain way lustig s method for obtaining feasibility is equivalent to newton s method this demonstrates that the method is in some sense the natural way to reduce infeasibility the role of the barrier parameter in computational practice is studied in detail numerical results are given for the entire expanded netlib test set for the basic algorithm and its variants as well as version 5 3 of minos

controllability of semilinear control systems dominated by the linear part while various equivalent conditions for controllability have been obtained in the case of linear control systems controllability problems of semilinear control systems usually require some complicated and limited assumptions in this paper we show the approximate controllability of an abstract semilinear control system under the assumption which has a simple form and can be easily checked in many examples

controllability of second order neutral functional differential inclusions in banach spaces in this paper we prove the controllability of second order neutral functional differential inclusions in banach spaces the result are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for condensing maps due to martelli

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative

controllability of second order integrodifferential evolution systems in banach spaces in this paper we study the controllability of second order nonlinear integrodifferential systems in banach spaces further we derive a set of sufficient conditions for the controllability of second order nonlinear integrodifferential evolution systems in banach spaces the results are established by using the theory of strongly continuous cosine families of bounded linear operators and the schaefer fixed point theorem