periodic solutions of integro differential equations in vector valued function spaces abstract operator valued fourier multipliers are used to study well posedness of integro differential equations in banach spaces both strong and mild periodic solutions are considered strong well posedness corresponds to maximal regularity which has proved very efficient in the handling of nonlinear problems we are concerned with a large array of vector valued function spaces lebesgue bochner spaces l p the besov spaces b p q s and related spaces such as the holder zygmund spaces c s and the triebel lizorkin spaces f p q s we note that the multiplier results in these last two scales of spaces involve only boundedness conditions on the resolvents and are therefore applicable to arbitrary banach spaces the results are applied to various classes of nonlinear integral and integro differential equations

homoclinic solutions for a class of the second order hamiltonian systems abstract we study the existence of homoclinic orbits for the second order hamiltonian system q v q t q f t where q r n and v c 1 r r n r v t q k t q w t q is t periodic in t a map k satisfies the pinching condition b 1 q 2 k t q b 2 q 2 w is superlinear at the infinity and f is sufficiently small in l 2 r r n a homoclinic orbit is obtained as a limit of 2 kt periodic solutions of a certain sequence of the second order differential equations

periodic solutions of abstract functional differential equations with infinite delay abstract we characterize the existence of periodic solutions for a class of abstract retarded functional differential equations with infinite delay we apply our results to the nonlinear equation x t a x t l x t n x t f t t r where a d a x x is a closed operator defined on a banach space x l is a bounded linear map n b x is a continuous function defined on an appropriate phase space b and f l p t x

existence of periodic solutions in shifts δ for neutral nonlinear dynamic systems abstract this paper focuses on the existence of a periodic solution of the delay neutral nonlinear dynamic systems x t a t x t q t x s t g t x t x s t in our analysis we utilize a new periodicity concept in terms of shifts operators which allows us to extend the concept of periodicity to time scales where the additivity requirement t t t for all t t and for a fixed t 0 may not hold more importantly the new concept will easily handle time scales that are not periodic in the conventional way such as q z and k 1 3 k 2 3 k 0 hence we will develop the tool that enables us to investigate the existence of periodic solutions of q difference systems since we are dealing with systems in order to convert our equation to an integral systems we resort to the transition matrix of the homogeneous floquet system y t a t y t and then make use of krasnoselskii s fixed point theorem to obtain a fixed point

fourier multipliers and periodic solutions of delay equations in banach spaces abstract in this paper we characterize the existence and uniqueness of periodic solutions of inhomogeneous abstract delay equations and establish maximal regularity results for strong solutions the conditions are obtained in terms of r boundedness of linear operators determined by the equations and l p fourier multipliers periodic mild solutions are also studied and characterized

bifurcation analysis in a neutral differential equation the dynamics of a neural network model in neutral form is investigated we prove that a sequence of hopf bifurcations occurs at the origin as the delay increases the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions are determined by using normal form method and center manifold theory global existence of periodic solutions is established using a global hopf bifurcation result of krawcewicz et al and a bendixson s criterion for higher dimensional ordinary differential equations due to li and muldowney

maximal regularity of second order equations with delay abstract we characterize existence and uniqueness of solutions of an inhomogeneous abstract delay equation in holder spaces the method is based on the theory of operator valued fourier multipliers

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

existence and stability for some partial neutral functional differential equations with infinite delay abstract in this paper we study a class of partial neutral functional differential equations with infinite delay we suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the hille yosida theorem we give some sufficient conditions ensuring the existence uniqueness and regularity of solutions a principle of linearized stability is also established in the autonomous case to illustrate our abstract results we conclude this work by an example

riemann hurwitz formula for finite morphisms of p adic curves given a finite morphism varphi y rightarrow x of quasi smooth berkovich curves over a complete non archimedean nontrivially valued algebraically closed field k of characteristic 0 we prove a riemann hurwitz formula relating their euler poincare characteristics calculated using de rham cohomology of their overconvergent structure sheaf the main tools are p adic runge s theorem together with valuation polygons of analytic functions using the results obtained we provide another point of view on riemann hurwitz formula for finite morphisms of curves over algebraically closed fields of positive characteristic

periodic solutions of a class of singular hamiltonian systems soit r n 0 n n n 3 et soit v c 1 rx r on etudie l existence des solutions periodiques t u t avec une periode prescrite du systeme suivant de n equations differentielles d ordre 2 u v t u

existence of periodic solutions of partial neutral functional differential equations with unbounded delay abstract in this article we establish a result of existence of periodic solutions for the class of quasi linear partial neutral functional differential equations with unbounded delay that can be described as the abstract functional differential equation d dt x t f t x t ax t g t x t where a is the infinitesimal generator of a strongly continuous semigroup of linear operators on a banach space and f and g are appropriate functions defined on a phase space

existence of homoclinic solutions for a class of time dependent hamiltonian systems n 1 n n 2 where q s q q g r w g c r r r and l t g c r r 1 n is a positive definite symmetric matrix for all t g r the case where l t and w t q are either periodic in t or independent of t were studied by several authors see for instance ambrosetti and w x w x bertotti 1 coti zelati ekeland and sere 4 coti zelati and rabinowitz w x w x w x 5 rabinowitz 15 17 sere 19 and their references in this kind of problem the function l t plays an important role for example if l t s ai where a 0 and i denotes the identity matrix n n w x felmer and silva 8 have showed the existence of homoclinic orbits as the limit of subharmonic solutions provided that hs is autonomous see also w x w x rabinowitz and tanaka 18 serra tarallo and terracini 20 using an w x w x approach introduced by 4 see also 19 treated the hs problem

homoclinic orbits for second order hamiltonian systems possessing superquadratic potentials received by the editors november 27 1990 1991 mathematics subject classification primary 34c99 58e99 58f99 the first author was supported by ministero p i gruppo 40 calcolo delle variazioni the second author s research was sponsored in part by the u s army research office under contract daal03 87 k 0043 the national science foundation under grant mcs 8110556 and the office of naval research under grant n00014 88 ko134 any reproduction for the purpose of the united states govemment is permitted

deformation spaces of one dimensional formal modules and their cohomology abstract let m m be the formal scheme which represents the functor of deformations of a one dimensional formal module over f p equipped with a level m structure by work of boyer in equal characteristic and harris and taylor the l adic etale cohomology of the generic fibre m m of m m realizes simultaneously the local langlands and jacquet langlands correspondences the proofs given so far use drinfeld modular varieties or shimura varieties to derive this local result in this paper we show without the use of global moduli spaces that the jacquet langlands correspondence is realized by the euler poincare characteristic of the cohomology under a certain finiteness assumption on the cohomology groups it is shown that the correspondence is realized in only one degree one main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the spaces m m

artin characters hurwitz trees and the lifting problem we study finite groups of automorphisms of the p adic open disk in particular we generalize results of green matignon and henrio from cyclic groups of order p to arbitrary finite groups as an application we produce a counterexample to a question of chinburg guralnick and harbater concerning the local lifting problem for generalized quaternion groups

the modulus semigroup for linear delay equations iii abstract in this paper we describe the modulus semigroup of the c 0 semigroup associated with the linear differential equation with delay u t au t lu t t 0 u 0 x x u 0 f l p h 0 x in the banach lattice x l p h 0 x where x is a banach lattice with order continuous norm the progress with respect to previous papers is that a may be an unbounded generator of a c 0 semigroup possessing a modulus semigroup

maximal regularity for perturbed integral equations on periodic lebesgue spaces we characterize the maximal regularity of periodic solutions for an additive perturbed integral equation with infinite delay in the vector valued lebesgue spaces our method is based on operator valued fourier multipliers we also study resonances characterizing the existence of solutions in terms of a compatibility condition on the forcing term

periodic solutions of abstract neutral functional differential equations abstract we characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a umd space

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations abstract we investigate spectral criteria for the existence of almost periodic solutions to linear 1 periodic evolution equations of the formdx dt a t x f t with in general unbounded a t and almost periodicf using the evolution semigroup associated with the evolutionary process generated by the equation under consideration we show that if the spectrum of the monodromy operator does not intersect the set e isp f then the above equation has an almost periodic mild solutionxfwhich is unique if one requiressp xf 2 k k z sp f we emphasize that our method allows us to treat the equations without assumption on the existence of floquet representation this improves recent results on the subject in addition we discuss some particular cases in which the spectrum of monodromy operator does not intersect the unit circle and apply the obtained results to study the asymptotic behavior of solutions finally an application to parabolic equations is considered

multiplicity results for periodic solutions to delay differential equations via critical point theory abstract by the critical point theory we study the existence and multiplicity of periodic solutions to the following system of delay differential equations x t f x t r where x r n f c r n r n and r 0 is a given constant a sufficient condition on the existence and multiplicity of periodic solutions for eq is obtained to the authors knowledge this is the first time the existence of periodic solutions to systems of delay differential equations is dealt with by using variational approaches directly

applications of a zp index theory to periodic solutions for a class of functional differential equations abstract by means of a new geometrical index with z p group actions multiplicity results for a certain class of nonautonomous time periodic functional differential systems are obtained

infinite periodic solutions to a class of second order sturm liouville neutral differential equations abstract by means of variational structure and z 2 group index theory we obtain infinite periodic solutions to a class second order sturm liouville neutral delay equations p t x t s q t x t s f t x t x t x t 2 x t 2 s 0

razumikhin type exponential stability criteria of neutral stochastic functional differential equations the paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations by using the razumikhin type technique the main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with lyapunov functionals the analysis is based on paper x mao razumikhin type theorems on exponential stability of neutral stochastic functional differential equations siam j math anal 28 2 1997 389 401 referring to mean square and almost sure exponential stability

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

self sustained oscillations in a ring array of coupled lossless transmission lines abstract in this paper we derive a neutral difference differential system with diffusion which arises from a ring array of coupled lossless transmission lines we investigate the problem of self sustained oscillations of the considered transmission lines and apply a global hopf bifurcation theorem to establish the existence of multiple large amplitude phase locked periodic solutions in the corresponding neutral system

properties of clebsch gordan coefficients and 3 j symbols for the quantum superalgebra uq osp 1 mod 2 this paper is a continuation of the study begun in an earlier paper of the structure of grade star representations of the quantum superalgebra uq osp 1 mod 2 the general case of the tensor product of two grade star representations acting in representation spaces with arbitrary not necessarily positive definite hermitian forms is considered an explicit analytical formula for clebsch gordan coefficients for this general case is derived using the projection operator method pseudo orthogonality relations are given and symmetry properties including regge symmetry are discussed the quantum analogues of super 3 j symbols are defined and their symmetry properties are analysed

homoclinic orbits for a nonperiodic hamiltonian system abstract in this paper we prove the existence and multiplicity of homoclinic orbits for first order hamiltonian systems of the form z j h z t z where h z is asymptotically linear at and is not assumed to be periodic

homoclinic orbits for asymptotically linear hamiltonian systems we study the existence of homoclinic orbits for first order time dependent hamiltonian systems z jhz z t where h z t depends periodically on t and hz z t is asymptotically linear in z as z we also consider an asymptotically linear schrodinger equation in rn

invariants and reduced matrix elements associated with the lie superalgebra gl m n we construct explicit formulae for the eigenvalues of certain invariants of the lie superalgebra gl m n using characteristic identities we discuss how such eigenvalues are related to reduced wigner coefficients and the reduced matrix elements of generators and thus provide a first step to a new algebraic derivation of matrix element formulae for all generators of the algebra

first order elliptic systems and the existence of homoclinic orbits in hamiltonian systems and h r x r 2 r is smooth by a homoclinic or a doubly asymptotic orbit to y where y is a periodic solution of 1 we mean a solution x y of 1 such that i x 0 y t l 0 as i tl oo finding homoclinic orbits in systems like 1 can be quite difficult in the case when y is a hyperbolic orbit this is equivalent to showing that the stable and unstable manifold of y intersect in some situation this can be done by melnikov s method recently some progress has been made by applying variational methods coti zelati and ekeland showed in 3 using dual variational methods that 1 has at least one homoclinic orbit if h satisfies some convexity and growth assumptions in their proof the convexity assumption enters in a crucial way already in the set up of the variational problem variational methods have been used by benci and giannoni 2 who studied homoclinic orbits on compact riemannian manifolds and by p rabinowitz in 9 who proved existence of heteroclinic orbits on the n dimensional torus as well as their multiplicity in 2 and 9 only special hamiltonian of lagrangian type are studied the associated variational problem is then at least semi definite the

tensor operators and wigner eckart theorem for the quantum superalgebra uq osp 1 2 tensor operators in graded representations of z2 graded hopf algebras are defined and their elementary properties are derived the wigner eckart theorem for irreducible tensor operators for uq osp 1 2 is proven examples of tensor operators in the irreducible representation space of hopf algebra uq osp 1 2 are considered the reduced matrix elements for the irreducible tensor operators are calculated a construction of some elements of the centre of uq osp 1 2 is given

the operator valued marcinkiewicz multiplier theorem and maximal regularity given a closed linear operator on a umd space we characterize maximal regularity of the non homogeneous problem

homoclinic orbits for a singular second order neutral differential equation using critical point theory and an approximation method we study the existence of homoclinic orbits for a singular second order neutral differential difference equations

racah coefficients and 6 j symbols for the quantum superalgebra uq osp 1 2 the tensor product of three irreducible representations of the quantum superalgebra uq osp 1 2 is studied and the super q analogs of racah coefficients and 6 j symbols for the quantum superalgebra uq osp 1 2 are defined racah coefficients and 6 j symbols depend on the superspin l and the parity which characterize the irreducible representations of uq osp 1 2 but the dependence on parities can be factored out so that one can define parity independent 6 j symbols it is shown that the 6 j symbols for the quantum superalgebra uq osp 1 2 satisfy symmetry properties and orthogonality relations similar to those of the 6 j symbols for quantum algebra uq su 2

homoclinic orbits for first order hamiltonian systems abstract we establish the existence of homoclinic orbits for a class of first order time dependent hamiltonian systems z jh z t z without any periodicity assumption on h

semigroups and linear partial differential equations with delay abstract we prove the equivalence of the well posedness of a partial differential equation with delay and an associated abstract cauchy problem this is used to derive sufficient conditions for well posedness exponential stability and norm continuity of the solutions applications to a reaction diffusion equation with delay are given

tensor operators for quantum groups and applications tensor operators are defined for hopf algebras if the hopf algebra is quasitriangular the properly defined tensor product of tensor operators is a tensor operator in one application the problem of defining invariant correlation functions for the uq sl 2 symmetric spin 1 2 heisenberg chain is considered in another application it is shown that suitably modified bosonic and fermionic q creation and annihilation operators are tensor operators of uq sl n

analytical formulas for racah coefficients and 6 j symbols of the quantum superalgebra uq osp 1 2 using the method of projection operators analytical formulas for racah coefficients and 6 j symbols of the quantum superalgebra uq osp 1 2 are derived the formulas obtained by this method are transformed by means of algebraic identities into symmetrical analytical formulas the form of which are very similar to the classical formulas obtained by racah and regge for su 2 racah coefficients and 6 j symbols symmetry properties of uq osp 1 2 racah coefficients and 6 j symbols following from these analytical formulas are studied in particular it is shown that similarly to the su 2 classical case in addition to the usual tetrahedral symmetry 6 j symbols of the quantum superalgebra uq osp 1 2 satisfy a regge type symmetry

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