anti periodic solutions for bam neural networks with time delays in the paper bidirectional associative memory neural networks with time delays are studied by using the fundamental solution matrix of coefficients and lyapunow function sufficient conditions are obtained for the existence and global exponential stability of the anti periodic solution of the model an example and numerical simulations are also given to illustrate the theoretical results

weighted pseudo almost periodic mild solutions of semilinear evolution equations with nonlocal conditions in this paper applying the theory of semigroups of operators to evolution families and banach fixed point theorem we prove the existence and uniqueness of the weighted pseudo almost periodic mild solution of the semilinear evolution equation x t a t x t f t x t with nonlocal conditions x 0 x 0 g x in banach space x under some suitable hypotheses

on a class of second order anti periodic boundary value problems of concern is the existence and uniqueness of anti periodic solutions to a class of abstract nonlinear second order differential equations the investigation relies on the theory of m accretive operators in banach or hilbert spaces examples of boundary value problems for ordinary and partial differential equations are also discussed

weighted pseudo almost periodic solutions of a class of abstract differential equations abstract for abstract linear functional differential equations with a weighted pseudo almost periodic forcing term we prove that the existence of a bounded solution on r implies the existence of a weighted pseudo almost periodic solution our results extend the classical theorem due to massera on the existence of periodic solutions for linear periodic ordinary differential equations to illustrate the results we consider the lotka volterra model with diffusion

weighted pseudo antiperiodic solutions for fractional integro differential equations in banach spaces in this paper we prove the existence of weighted pseudo antiperiodic mild solutions for fractional integro differential equations in the form d u t au t t a t s au s ds f t u t t r where f u is stepanov like weighted pseudo antiperiodic and a generates a resolvent family of bounded and linear operators on a banach space x a l loc 1 r and 0 here the fractional derivative is considered in the sense of weyl also we give a short proof to show that the vector valued space of stepanov like weighted pseudo antiperiodic functions is a banach space

magnetic hierarchical deposition abstract we consider random deposition of debris or blocks on a line with block sizes following a rigorous hierarchy the linear size equals 1 n in generation n in terms of a rescaling factor without interactions between the blocks this model is described by a logarithmic fractal studied previously which is characterized by a constant increment of the length area or volume upon proliferation we study to what extent the logarithmic fractality survives if each block is equipped with an ising pseudo spin s 1 and the interactions between those spins are switched on ranging from antiferromagnetic to ferromagnetic it turns out that the dependence of the surface topology on the interaction sign and strength is not trivial for instance deep in the ferromagnetic regime our numerical experiments and analytical results reveal a sharp crossover from a euclidean transient consisting of aggregated domains of aligned spins to an asymptotic logarithmic fractal growth in contrast deep into the antiferromagnetic regime the surface roughness is important and is shown analytically to be controlled by vacancies induced by frustrated spins finally in the weak interaction regime we demonstrate that the non interacting model is extremal in the sense that the effect of the introduction of interactions is only quadratic in the magnetic coupling strength in all regimes we demonstrate the adequacy of a mean field approximation whenever vacancies are rare in sum the logarithmic fractal character is robust with respect to the introduction of spatial correlations in the hierarchical deposition process

forward backward and symmetric stochastic integration we define three types of non causal stochastic integrals forward backward and symmetric our approach consists in approximating the integrator two optics are considered the first one is based on traditional usual stochastic calculus and the second one on wiener distributions

weighted pseudo almost periodic solutions to some differential equations abstract the paper considers some new classes of functions called weighted pseudo almost periodic functions which implement in a natural fashion the classical pseudo almost periodic functions due to zhang properties of these weighted pseudo almost periodic functions are discussed including a composition result for weighted pseudo almost periodic functions the results obtained are subsequently utilized to study the existence and uniqueness of a weighted pseudo almost periodic solution to the heat equation with dirichlet conditions

numerical approximations of algebraic riccati equations for abstract systems modelled by analytic semigroups and applications this paper provides a numerical approximation theory of algebraic riccati operator equations with unbounded coefficient operators a and b such as arise in the study of optimal quadratic cost problems over the time interval 0 oo for the abstract dynamics j ay bu here a is the generator of a strongly continuous analytic semigroup and b is an unbounded operator with any degree of unboundedness less than that of a convergence results are provided for the riccati operators as well as for all the other relevant quantities which enter into the dynamic optimization problem the present numerical theory is the counterpart of a known continuous theory several examples of partial differential equations with boundary point control where all the required assumptions are verified illustrate the theory they include parabolic equations with l2 dirichlet control as well as plate equations with a strong degree of damping and point control

growth of cayley and diluted cayley trees with two kinds of entities a kinetic growth model derived from the magnetic eden model is introduced in order to simulate the growth of hierarchical structures such as cayley trees we only consider the case where two kinds of entities are competing with each other and can be further subjected to an external field the very relevant case in which both kinds of entities have different coordination numbers is introduced here for the first time and is called the diluted cayley tree physical and geometrical properties of the finite and infinite trees are exactly found and simulated finite size effects are emphasized and illustrated on the global or local magnetization and on the chemical activity asymptotic limits are given in each case the generated patterns can be related to a correlated percolation problem briefly discussed in the appendix

h1 parametrizations of complex planar physical domains in isogeometric analysis abstract isogeometric analysis is a method for solving geometric partial differential equations pdes generating parametrizations of a pde s physical domain is a basic and important issue within isogeometric analysis framework in this paper we present a global h 1 parametrization method for a complex planar physical domain

weighted pseudo almost automorphic functions and applications to abstract differential equations abstract this paper is concerned with weighted pseudo almost automorphic functions which are more general and complicated than weighted pseudo almost periodic functions using these properties we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a banach space which extends known results

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type abstract this paper studies suitable sufficient conditions to ensure the existence and uniqueness of weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type introduced by t a burton in the literature the abstract results are then utilized to characterize weighted pseudo almost periodic solutions to the well known logistic equation

stochastic evolution equations in umd banach spaces we discuss existence uniqueness and space time holder regular ity for solutions of the parabolic stochastic evolution equation du t au t f t u t dt b t u t dwh t t 2 0 t0 u 0 u0 where a generates an analytic c0 semigroup on a umd banach space e and wh is a cylindrical brownian motion with values in a hilbert space h we prove that if the mappings f 0 t e e and b 0 t e l h e satisfy suitable lipschitz conditions and u0 is f0 measurable and bounded then this problem has a unique mild solution which has trajectories in c 0 t d a provided 0 and 0 satisfy 1 2 vari ous extensions of this result are given and the results are applied to parabolic stochastic partial dierential equations

pseudodifferential operators on bochner spaces and an application we consider pseudodifferential operators with operator valued symbols a x acting on a umd banach space x assuming some regularity of holder type in x and mihlin type in we prove l p n x boundedness of such operators this result is then applied to the study of l p maximal regularity for nonautonomous parabolic evolution equations

decomposition of weighted pseudo almost periodic functions abstract first we show by constructing two counterexamples that the decomposition of weighted pseudo almost periodic functions is not unique in general then we prove that the decomposition of such functions is unique if p a p 0 x is translation invariant but not necessarily unique without the assumption moreover we give an example to show that the mean value under a certain weight may not exist for all almost periodic functions with these results we answer some fundamental questions on weighted pseudo almost periodic functions

a new approach to stochastic evolution equations with adapted drift abstract in this paper we develop a new approach to stochastic evolution equations with an unbounded drift a which is dependent on time and the underlying probability space in an adapted way it is well known that the semigroup approach to equations with random drift leads to adaptedness problems for the stochastic convolution term in this paper we give a new representation formula for the stochastic convolution which avoids integration of non adapted processes here we mainly consider the parabolic setting we establish connections with other solution concepts such as weak solutions the usual parabolic regularity properties are derived and we show that the new approach can be applied in the study of semilinear problems with random drift at the end of the paper the results are illustrated with two examples of stochastic heat equations with random drift

isogeometric analysis with trimming technique for problems of arbitrary complex topology trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to cad files created by using nurbs in the present work it is shown that any complex multiply connected nurbs domain can be described by using trimming curves only isogeometric analysis for linear elasticity problems of complex topology described in this way is presented for fully communicative interaction between cad and cae a specific searching algorithm and an integration scheme of trimmed elements are introduced to utilize the iges files exported from cad system for isogeometric analysis schemes for imposing essential and traction boundary conditions on trimming curves are presented it has been demonstrated that with the presented schemes trimmed cases in any complicated situations can be successfully treated with the examples of complex topology that could be described by employing trimming curves only effectiveness and robustness of present method are demonstrated

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

weighted pseudo almost periodic functions and applications to evolution equations with delay in this paper we introduce a new class of vector valued weighted pseudo almost periodic functions and present some basic properties about these new functions moreover we obtain an new existence theorem of vector valued weighted pseudo almost periodic solution to the evolution equations x t ax t f t x t with delay in a banach space x

massera problem for non autonomous retarded differential equations abstract in this paper under acquistapace terreni conditions we study the existence of periodic solutions for some non autonomous semilinear partial functional differential equation with delay we assume that the linear part is non densely defined the delayed part is assumed to be periodic with respect to the first argument using a fixed point theorem for multivalued mapping some sufficient conditions are given to prove the existence of periodic solutions an example is shown to illustrate our results

chandrasekhar equations for infinite dimensional systems ii unbounded input and output case abstract a set of equations known as chandrasekhar equations arising in the linear quadratic optimal control problem is considered in this paper we consider the linear time invariant systems defined in hilbert spaces involving unbounded input and output operators for a general class of such systems we derive the chandrasekhar equations and establish the existence uniqueness and regularity results of their solutions

stochastic heat equation with random coefficients we prove the existence of a unique solution for a one dimensional stochastic parabolic partial differential equation with random and adapted coefficients perturbed by a two parameter white noise the proof is based on a maximal inequality for the skorohod integral deduced from ito s formula for this anticipating stochastic integral

the fredholm alternative for parabolic evolution equations with inhomogeneous boundary conditions abstract we study the fredholm properties of parabolic evolution equations on r with inhomogeneous boundary values these problems are transformed into evolution equations with inhomogeneities taking values in certain extrapolation spaces assuming that the underlying homogeneous problem is asymptotically hyperbolic we show the fredholm alternative for these equations the results are applied to parabolic partial differential equations

optimal regularity and fredholm properties of abstract parabolic operators in l p spaces on the real line we study the operator mathcal l u t u t a t u t on l p mathbb r x for sectorial operators a t with t in mathbb r on a banach space x that are asymptotically hyperbolic satisfy the acquistapace terreni conditions and have the property of maximal l p regularity we establish optimal regularity on the time interval mathbb r showing that mathcal l is closed on its minimal domain we further give conditions for ensuring that mathcal l is a semi fredholm operator the fredholm property is shown to persist under a t bounded perturbations provided they are compact or have small a t bounds we apply our results to parabolic systems and to generalized ornstein uhlenbeck operators

isogeometric analysis on implicit domains using weighted extended pht splines abstract the urging quest for diminishing the gap between finite element methods and computer aided design is growing every day isogeometric analysis is driving that search a step forward in contrast with traditional finite element methods one of the areas that need more investigation is using isogeometric analysis on domains that contain singularities in this case the parameterization process is occasionally non trivial and some of the inherited basis functions are not well defined producing rough solutions moreover nurbs basis functions are not the best choice to perform local refinement since adaptivity is indispensable in this study a new approach that serves as a generalization for some of the ideas in both the isogeometric analysis and the web method is introduced isogeometric analysis on implicit domains replaces mesh generation with implicit spline weight function generation and construct weighted extended pht splines for analysis the geometry and the analysis both are built starting from the same function space avoiding parameterization the pht splines are adaptive and allow local refinement naturally leading to a higher accuracy while dealing with singularities an illustration with numerical examples demonstrates the efficiency and performance of the proposed method

riccati equation arising in a boundary control problem with distributed parameters global existence is proved for the solution of a riccati differential equation connected with the synthesis of a boundary control problem governed by parabolic partial differential equations

existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations this paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations upon making some suitable assumptions the existence and uniqueness of a weighted pseudo almost periodic solution is obtained to illustrate our main result we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional differential equations with feedback control

the linear quadratic control problem for infinite dimensional systems with unbounded input and output operators this paper establishes a general semigroup framework for solving quadratic control problems with infinite dimensional state space and unbounded input and output operators

composition of pseudo almost periodic functions and semilinear differential equations under the assumption of uniformly continuity we establish a composition theorem of pseudo almost periodic functions in general banach spaces as an application we give some existence theorems of pseudo almost periodic solutions and mild pseudo almost periodic solutions for some differential equations

bounding the influence of domain parameterization and knot spacing on numerical stability in isogeometric analysis abstract isogeometric analysis iga was introduced by hughes et al 2005 1 as a new method to bridge the gap between the geometry description and numerical analysis similar to the finite element approach the iga concept to solve a partial differential equation leads to a linear system of equations the condition number of the coefficient matrix is a crucial factor for the stability of the system it depends strongly on the domain parameterization which provides the isogeometric discretization in this paper we derive a bound for the condition number of the stiffness matrix of the poisson equation in particular we investigate the influence of the domain parameterization and the knot spacing on the stability of the numerical system the factors appearing in our bound reflect the stability properties of a given domain parameterization

bounds for eigenvalues and condition numbers in the p version of the finite element method in this paper we present a theory for bounding the minimum eigenvalues maximum eigenvalues and condition numbers of stiffness matrices arising from the p version of finite element analysis bounds are derived for the eigenvalues and the condition numbers which are valid for stiffness matrices based on a set of general basis functions that can be used in the p version for a set of hierarchical basis functions satisfying the usual local support condition that has been popularly used in the p version explicit bounds are derived for the minimum eigenvalues maximum eigenvalues and condition numbers of stiffness matrices we prove that the condition numbers of the stiffness matrices grow like p 4 d 1 where d is the number of dimensions our results disprove a conjecture of olsen and douglas in which the authors assert that regardless of the choice of basis the condition numbers grow like p 4d or faster numerical results are also presented which verify that our theoretical bounds are correct

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

existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis abstract isogeometric analysis is a numerical simulation method which uses the nurbs based representation of cad models nurbs stands for non uniform rational b splines and is a generalization of the concept of b splines the isogeometric method uses the tensor product structure of 2 or 3 dimensional nurbs functions to parameterize domains which are structurally equivalent to a rectangle or a hexahedron the special case of singularly parameterized nurbs surfaces and nurbs volumes is used to represent non quadrangular or non hexahedral domains without splitting which leads to a very compact and convenient representation if the parameterization of the physical domain is available the test functions for the isogeometric analysis are obtained by composing the inverse of the domain parameterization with the nurbs basis functions in the case of singular parameterizations however some of the resulting test functions are not well defined at the singular points and they do not necessarily satisfy the required integrability assumptions consequently the stiffness matrix integrals which occur in the numerical discretizations may not exist after summarizing the basics of the isogeometric method we discuss the existence of the stiffness matrix integrals for 1 2 and 3 dimensional second order elliptic partial differential equations we consider several types of singularities of nurbs parameterizations and derive conditions which guarantee the existence of the required integrals in addition we present cases with diverging integrals and show how to modify the test functions in these situations

existence of weighted pseudo almost periodic solutions to some classes of differential equations with sp weighted pseudo almost periodic coefficients abstract in this paper we introduce the concept of weighted pseudo almost periodicity in the sense of stepanov also called s p weighted pseudo almost periodicity and study its properties next we present a result on the existence of weighted pseudo almost periodic solutions to the n dimensional heat equation with s p weighted pseudo almost periodic coefficients

anti periodic solutions to a class of nonlinear differential equations in hilbert space abstract a broad class of nonlinear non monotone anti periodic boundary value problems in a hilbert space is considered as a preliminary step the existence uniqueness and continuous dependence upon data of anti periodic solutions to some first and second order evolution equations associated to odd noncoercive monotone operators is established applications of the theory to nonlinear partial differential equations are also discussed

initial boundary value problems and optimal control for nonautonomous parabolic systems a large class of linear nonautonomous parabolic systems in bounded domains is considered with control acting on the boundary through dirichlet or neumann conditions from the point of view of semigroup theory the results from rend sem mat univ padova 78 1987 pp 47 107 on fundamental solutions for abstract parabolic equations lecture notes in math vol 1223 springer verlag berlin heidelberg 1986 pp 1 11 on abstract homogeneous parabolic cauchy problems allow operators with varying domains and holder continuous coefficients to be handled a representation formula for solutions corresponding to square integrable control functions is derived and used to solve a linear quadratic regulator problem over finite time horizon by a direct study of the associated integral riccati equation

riccati theory and singular estimates for a bolza control problem arising in linearized fluid structure interaction abstract we consider a bolza boundary control problem involving a fluid structure interaction model the aim of this paper is to develop an optimal feedback control synthesis based on riccati theory the model considered consists of a linearized navier stokes equation coupled on the interface with a dynamic wave equation the model incorporates convective terms resulting from the linearization of the navier stokes equation around equilibrium the existence of the optimal control and its feedback characterization via a solution to a riccati equation is established the main mathematical difficulty of the problem is caused by unbounded action of control forces which in turn result in riccati equations with unbounded coefficients and in singular behavior of the gain operator this class of problems has been recently studied via the so called singular estimate control systems secs theory which is based on the validity of the singular estimate se g avalos differential riccati equations for the active control of a problem in structural acoustic j optim theory appl 91 1996 695 728 i lasiecka mathematical control theory of coupled pde s in nsf cmbs lecture notes siam 2002 with unbounded controls i lasiecka a tuffaha riccati equations for the bolza problem arising in boundary point control problems governed by c0 semigroups satisfying a singular estimate j optim theory appl 136 2008 229 246 it is shown that the fluid structure interaction does satisfy the singular estimate se condition this is accomplished by showing that the maximal abstract parabolic regularity is transported via hidden hyperbolic regularity of the boundary traces on the interface thus the established singular estimate allows for the application of recently developed general theory which in turn implies well posedness of the feedback synthesis and of the associated riccati equation moreover the singularities in the optimal control and in the feedback operator at the terminal time are quantitatively described

pseudo almost automorphic mild solutions to nonautonomous differential equations and applications abstract in this paper we introduce a new concept of bi almost automorphic functions and obtain new existence and uniqueness theorems for pseudo almost automorphic mild solutions to several nonautonomous differential equations moreover two examples are given to illustrate the general theorems

control of parabolic pdes with time varying spatial domain czochralski crystal growth process this paper considers the optimal control problem for a class of convection diffusion reaction systems modelled by partial differential equations pdes defined on time varying spatial domains the class of pdes is characterised by the presence of a time dependent convective transport term which is associated with the time evolution of the spatial domain boundary the functional analytic description of the pde yields the representation of the initial and boundary value problem as a nonautonomous parabolic evolution equation on an appropriately defined infinite dimensional function space the properties of the time varying evolution operator to guarantee existence and well posedness of the initial and boundary value problem are demonstrated which serves as the basis for the optimal control problem synthesis an industrial application of the crystal temperature regulation problem for the czochralski crystal growth process is considered and numerical simulation results are provided

parameterization of computational domain in isogeometric analysis methods and comparison parameterization of computational domain plays an important role in isogeometric analysis as mesh generation in finite element analysis in this paper we investigate this problem in the 2d case i e how to parametrize the computational domains by planar b spline surface from the given cad objects four boundary planar b spline curves firstly two kinds of sufficient conditions for injective b spline parameterization are derived with respect to the control points then we show how to find good parameterization of computational domain by solving a constraint optimization problem in which the constraint condition is the injectivity sufficient conditions of planar b spline parametrization and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of planar b spline parameterization by using this method the resulted parameterization has no self intersections and the isoparametric net has good uniformity and orthogonality after introducing a posteriori error estimation for isogeometric analysis we propose r refinement method to optimize the parameterization by repositioning the inner control points such that the estimated error is minimized several examples are tested on isogeometric heat conduction problem to show the effectiveness of the proposed methods and the impact of the parameterization on the quality of the approximation solution comparison examples with known exact solutions are also presented

on mesh geometry and stiffness matrix conditioning for general finite element spaces the performance of finite element computation depends strongly on the quality of the geometric mesh and the efficiency of the numerical solution of the linear systems resulting from the discretization of partial differential equation pde models it is common knowledge that mesh geometry affects not only the approximation error of the finite element solution but also the spectral properties of the corresponding stiffness matrix in this paper for typical second order elliptic problems some refined relationships between the spectral condition number of the stiffness matrix and the mesh geometry are established for general finite element spaces defined on simplicial meshes the derivation of such relations for general high order elements is based on a new trace formula for the element stiffness matrix it is shown that a few universal geometric quantities have the same dominant effect on the stiffness matrix conditioning for different finite element spaces these results provide guidance to the studies of both linear algebraic solvers and the unstructured geometric meshing

existence of anti periodic mild solutions to semilinear nonautonomous evolution equations abstract in this paper applying the theory of evolution family and schauder s fixed point theorem we prove the anti periodic mild solutions for semilinear nonautonomous evolution equations in banach space under conditions furthermore an example is given to illustrate our results

weighted pseudo almost periodic solutions for some partial functional differential equations abstract in this work we give sufficient conditions for the existence and uniqueness of a weighted pseudo almost periodic solution for some partial functional differential equations to illustrate our main result we study the existence of a weighted pseudo almost periodic solution for some diffusion equation with delay

irreversible growth of binary mixtures on small world networks binary mixtures growing on small world networks under far from equilibrium conditions are studied by means of extensive monte carlo simulations for any positive value of the shortcut fraction of the network p 0 the system undergoes a continuous order disorder phase transition while it is noncritical in the regular lattice limit p 0 using finite size scaling relations the phase diagram is obtained in the thermodynamic limit and the critical exponents are evaluated the small world networks are thus shown to trigger criticality a phenomenon analogous to similar observations reported recently in the investigation of equilibrium systems

stochastic integration in umd banach spaces in this paper we construct a theory of stochastic integration of processes with values in l h e where h is a separable hilbert space and e is a umd banach space i e a space in which martingale differences are unconditional the integrator is an h cylindrical brownian motion our approach is based on a two sided l p decoupling inequality for umd spaces due to garling which is combined with the theory of stochastic integration of l h e valued functions introduced recently by two of the authors we obtain various characterizations of the stochastic integral and prove versions of the ito isometry the burkholder davis gundy inequalities and the representation theorem for brownian martingales

pseudo almost periodic solutions of some differential equations ii we first present some results about pseudo almost periodic functions then we use these results to show some theorems about existence and uniqueness of the pseudo almost periodic solutions of the linear and the quasi linear nonautonomous equations finally we set up some theorems of the existence of pseudo almost periodic solutions implying the existence of almost periodic solutions of general ordinary differential equation systems

stochastic evolution equations with random generators we prove the existence of a unique mild solution for a stochastic evolution equation on a hilbert space driven by a cylindrical wiener process the generator of the corresponding evolution system is supposed to be random and adapted to the filtration generated by the wiener process the proof is based on a maximal inequality for the skorohod integral deduced from the ito s formula for this anticipating stochastic integral

antiperiodic solutions of semilinear integrodifferential equations in banach spaces abstract we are concerned in this paper with the existence of antiperiodic mild solutions of some semilinear integrodifferential equations in a banach space we study further properties of antiperiodic functions including a new composition theorem and introduce the new concept of asymptotically antiperiodic functions

existence results for some damped second order volterra integro differential equations abstract in this paper we make a subtle use of operator theory techniques and the well known schauder fixed point principle to establish the existence of pseudo almost automorphic solutions to some second order damped integro differential equations with pseudo almost automorphic coefficients in order to illustrate our main results we will study the existence of pseudo almost automorphic solutions to a structurally damped plate like boundary value problem

linear skorohod stochastic differential equations let andb be bounded processes on the wiener space p c 0 1 which are possibly anticipating the brownian motionw t t and let be a bounded random variable we deduce the existence and uniqueness of a solutionx for the linear equation with skorohod integral x t eta int limits 0 t sigma s x s dw s int limits 0 t b s x s ds t in 0 1 1 under rather weak assumptions on and no additional requirement onb and the description of the solutionx requires to study the family t t t 0 1 of transformationt t of into itself associated to 1 by the equation t t omega int limits 0 t wedge sigma s t s omega ds omega in omega t in 0 1

invertibility of riccati operators and controllability of a related systems abstract injectivity and existence of a bounded inverse of riccati operators is investigated for various classes of systems a unified approach to this problem based on few general properties verified by several control systems is proposed the relation between the invertibility of riccati operators and the controllability of certain related systems is pointed out

on the existence of anti periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators the existence of anti periodic solutions hence also that of periodic solutions to the nonlinear parabolic type evolution equation ddt u t u t f t u t 0 t r is shown under the assumptions that the subdifferential operator is odd and that f t t r is a family of monotone operators satisfying the anti periodicity condition f t t v f t v v d f t hence f t t v f t v v d d f t t r for a fixed t r here coerciveness of is not assumed an application to a heat equation is given without assuming boundedness of the domain of rxn

anti periodic solutions for semilinear evolution equations in this paper we use the homotopy method to establish the existence and uniqueness of anti periodic solutions for the nonlinear anti periodic problem a t x bx f t a e t r x t t x t where a t x is a nonlinear map and b is a bounded linear operator from r n to r n sufficient conditions for the existence of the solution set are presented also we consider the nonlinear evolution problems with a perturbation term which is multivalued we show that for this problem the solution set is nonempty and weakly compact in w 1 2 i r n for the case of convex valued perturbation and prove the existence theorems of anti periodic solutions for the nonconvex case all illustrative examples are provided

second order hamilton jacobi equations in hilbert spaces and stochastic boundary control the paper is concerned with fully nonlinear second order hamilton jacobi bellman isaacs equations of elliptic type in separable hilbert spaces which have unbounded first and second order terms the viscosity solution approach is adapted to the equations under consideration and the existence and uniqueness of viscosity solutions are proved a stochastic optimal control problem driven by a parabolic stochastic pde with control of dirichlet type on the boundary is considered it is proved that the value function of this problem is the unique viscosity solution of the associated hamilton jacobi bellman equation

evolution equation of a stochastic semigroup with white noise drift we study the existence and uniqueness of the solution of a functionvalued stochastic evolution equation based on a stochastic semigroup whose kernel p s t y x is brownian in s and t the kernel p is supposed to be measurable with respect to the increments of an underlying wiener process in the interval s t the evolution equation is then anticipative and choosing the skorohod formulation we establish existence and uniqueness of a continuous solution with values in l r as an application we prove the existence of a mild solution of the stochastic parabolic equation dut xudt v dt x ru f t x u w dt x where v and w are brownian in time with respect to a common ltration in this case p is the formal backward heat kernel of x v dt x rx supported by the dgicyt grant no pb96 0087 ysupported by nsf international opportunities postdoctoral fellowship no int9600278 and nsf nato postdoctoral fellowship no dge 9633937 ams subject classi cation primary 60h15 secondary 60h07

almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations abstract in this paper applying the theory of semigroups of operators to evolution family and banach fixed point theorem we prove the existence and uniqueness of an a almost automorphic weighted pseudo almost automorphic mild solution of the semilinear evolution equation x t a t x t f t x t in banach space under conditions

a composition theorem for weighted pseudo almost automorphic functions and applications abstract in this paper we establish a composition theorem for weighted pseudo almost automorphic functions under a weaker lipschitz condition our composition theorem generalizes some known results moreover the existence and uniqueness of pseudo almost automorphic solutions for abstract semilinear evolution equations are studied

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

global existence for an abstract riccati initial value problem with possibly unbounded coefficients abstract we consider operator valued riccati initial value problems of the form r t tr t r t t ta t tb t r t r t tc t r t td t r t r 0 r 0 here a t through d t and r 0 have values as nonnegative bounded linear operators in l 1 where is a finite measure and t is a closed nonnegative operator in l 1 satisfying additional technical conditions for such problems the notion of strongly mild solutions is defined the main result is a set of conditions under which with sufficiently small initial value has a global solution

constructing analysis suitable parameterization of computational domain from cad boundary by variational harmonic method in isogeometric analysis parameterization of computational domain has great effects as mesh generation in finite element analysis in this paper based on the concept of harmonic mapping from the computational domain to parametric domain a variational harmonic approach is proposed to construct analysis suitable parameterization of computational domain from cad boundary for 2d and 3d isogeometric applications different from the previous elliptic mesh generation method in finite element analysis the proposed method focuses on isogeometric version and converts the elliptic pde into a nonlinear optimization problem in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso parametric structure near convex concave parts of the boundary several examples are presented to show the efficiency of the proposed method in 2d and 3d isogeometric analysis

existence results for some higher order evolution equations with operator coefficients abstract in this paper we study and obtain the existence of c r pseudo almost automorphic solutions to some higher order differential equations with operator coefficients whose forcing is c s pseudo almost automorphic we next use these abstract results to study the existence of c r pseudo almost automorphic solutions to some second order differential equations in hilbert space which among other things model the so called linear beam equation

existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations abstract in this paper under acquistapace terreni conditions we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations applications include the existence of weighted pseudo almost periodic solutions to a nonautonomous heat equation with gradient coefficients