on the existence of periodic solutions to p laplacian rayleigh differential equation with a delay abstract in this paper the authors study the existence of periodic solutions to a p laplacian rayleigh differential equation with a delay as follows p y t f y t g y t t e t where p 1 is a constant p r r p u u p 2 u f g e c r r t t t with t 0 t 0 t and e t t e t t 0 is a constant by using mawhin s continuation theorem some new results are obtained

positive periodic solutions for a neutral delay lotka volterra system abstract applying a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions for a class of neutral delay lotka volterra systems x i t x i t r i t j 1 n a i j t x j t j 1 n b i j t x j t i j t j 1 n c i j t x j t i j t i 1 2 n compared to known results our main generalization is that delays of the derivatives are not assumed to be constants and our results are more easily verifiable

periodic solutions of a second order ordinary differential equation a necessary and sufficient condition for nonresonance the nonlinearity g in 1 1 is a continuous function from r to r and the forcing term h is taken in l o 27r nonresonance means that 1 1 admits at least one solution x for any given h integrating eq 1 1 over a period one immediately sees that a necessary condition for nonresonance is that the function g be unbounded from above and from below on r it will appear later cf 1 6 that this unboundedness can be looked at as a condition relating the behaviour at infinity of the nonlinearity g with respect to the first eigenvalue 1 0 of the associated linear problem xf ax in 0 27r x 0 x 27r x 0 x1 271 1 2

global stability in a periodic delayed predator prey system abstract in this paper we establish a periodic delayed predator prey system according to two types of single species growth population models with delay by using some analysis methods easily verifiable sufficient conditions for the existence and global asymptotic stability of positive periodic solution of the above system are derived some previous results are generalized and improved biological interpretations on the main results are also given

some expansions related to the hubbell rectangular source integral abstract four series expansions are presented and examined for the hubbell rectangular source integral f a b b0 arctan a 1 x 2 1 x 2 1 dx for the extremal situations when one or both of the parameters a b tend to zero or infinity

w gordon s integral 1929 and its representations by means of appell s functions f2 f1 and f3 exact analytical representations for w gordon s integral by means of appell s functions are given it is shown that they correlate between each other but representation of this integral by means of appell s function f2 is more attractive

tau method approximation of some integrals related to radiation field problems abstract a more general and unified form of the hubbell rectangular source integral is defined as h a b p v b d 2 p 1 2 b 2 f beta a 2 2 p d subject to 0 a b p 0 1 special cases of this integral occur in some radiation field problems under certain restrictions h may be expressed in terms of appell s double hypergeometric functions f2 and f4 tau method approximations of the gauss hypergeometric function 2f1 are employed in the evaluation of this integral and upper bound estimates on the tau error are given

on the existence of positive periodic solutions to a lotka volterra cooperative population model with multiple delays abstract in this paper the author studies the existence of positive periodic solutions to a lotka volterra cooperative population model with multiple delays as follows x i t x i t r i t p i i t x i t k i n p i k t x k t j 1 n q i j t x i t i j t k i n j 1 n c i k j t x k t i k j t i 1 2 n by using mawhin s continuation theorem of coincidence degree principle a new result is obtained the interesting thing is that the result is related to the delays which is different from the corresponding ones of the known literature

existence of positive periodic solutions for neutral functional differential equations abstract applying a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions of the following neutral functional differential equation x t x t a t f t x t x t 1 t x t n t x t 1 t x t m t

on the existence of periodic solutions of a neutral delay model of single species population growth abstract in this paper we employ some new techniques to study the existence of positive periodic solutions of the neutral delay model n t n t a t t n t b t n t t c t n t t our result gives a correct answer to the open problem 9 2 due to y kuang 1993 delay differential equations with applications in population dynamics academic press new york

periodic solutions for p laplacian neutral rayleigh equation with a deviating argument abstract by using topological degree theory and some analytical skill some criteria to guarantee the existence of periodic solutions are derived for p laplacian neutral rayleigh equation with a deviating argument of the following form p x t c x t f x t g x t t e t

on the construction of perfect morse functions on compact manifolds of coherent states perfect morse functions on the manifold of coherent states are effectively constructed the case of a compact connected simply connected lie group of symmetry having the same rank as the stationary group of the manifold of coherent states such that the manifold of coherent states is a kahlerian c space is considered it is proved that the set of perfect morse functions is dense in the set of energy functions for linear hamiltonians in the elements of the cartan algebra of the lie algebra of the representation of the group considered it is proved that the maximum number of orthogonal vectors on a coherent vector manifold is equal to the euler poincare characteristic of the manifold

evaluation of a ln tan integral arising in quantum field theory we analytically evaluate a dilogarithmic integral that is prototypical of volumes of ideal tetrahedra in hyperbolic geometry we additionally obtain new representations of the clausen function cl2 and the catalan constant g cl2 2 as well as new relations between sine and clausen function values

continuation theorems for periodic perturbations of autonomous systems it is first shown in this paper that whenever it exists the coincidence degree of the left hand member of an autonomous differential equation x g x 0 in the space of periodic functions with fixed period omega can be computed in terms of the brouwer degree of g this result provides efficient continuation theorems specially for omega periodic perturbations of autonomous systems extensions to differential equations in flow invariant enr s are also given

existence of positive periodic solutions for neutral population model with multiple delays in this paper the authors employ an abstract continuous theorem of k set contractive operator and some analysis techniques to study the existence of positive periodic solutions for a neutral delay population model with multiple delays as followsdndt n t a t b t n t j 1 nb j t n t s i t i 1 mc i t n t t i t a new result on the existence of positive periodic solutions is obtained

two periodic solutions of neutral difference systems depending on two parameters in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order neutral difference systems our approach is based on a fixed point theorem in cones as well as some analysis techniques

generalized bivariate beta distributions involving appell s hypergeometric function of the second kind let x 1 x 2 and x 3 be independent random variables x 1 and x 2 having a confluent hypergeometric function kind 1 distribution with probability density function proportional to x i n i 1 1f 1 a i b i x i i 1 2 and x 3 having a standard gamma distribution with shape parameter n 3 define y 1 y 2 x 1 x 3 x 2 x 3 and z 1 z 2 x 1 x 2 x 1 x 2 x 3 in this article we derive probability density functions of y 1 y 2 and z 1 z 2 and study their properties we use the second hypergeometric function of appell to express these density functions

periodic solutions for a kind of second order neutral differential systems with deviating arguments by means of the generalized continuation theorem of coincidence degree theory a kind of second order neutral differential systems with deviating arguments as followsd 2dt 2 x t cx t r ddtgradf x t gradg x email protected t p t is studied a new result on the existence of periodic solutions is obtained which relates to the deviating arguments t t and r

a note on the epstein hubbell generalized elliptic type integral abstract the main object of this note is to present a remarkably simple derivation of the explicit representation of the epstein hubbell generalized elliptic type integral as a gauss hypergeometric function of argument k4 the method applied here is based upon rather elementary formulas and unlike the earlier derivations it does not make use of complex integration with or without residues it is also pointed out how this method can be applied mutatis mutandis in substantially more general cases

periodic solution of neutral lotka volterra system with periodic delays abstract a nonautonomous n species lotka volterra system with neutral delays is investigated a set of verifiable sufficient conditions is derived for the existence of at least one strictly positive periodic solution of this lotka volterra system by applying an existence theorem and some analysis techniques where the assumptions of the existence theorem are different from that of gaines and mawhin s continuation theorem r e gaines j l mawhin coincidence degree and nonlinear differential equations springer verlag berlin 1977 and that of abstract continuation theory for k set contraction w petryshyn z yu existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems nonlinear anal 6 1982 943 969 moreover a problem proposed by freedman and wu h i freedman j wu periodic solution of single species models with periodic delay siam j math anal 23 1992 689 701 is answered

periodic solutions of linear and quasilinear neutral functional differential equations abstract in this paper we will use the fourier expansions to generalize hale s alternative results for the existence of periodic solutions of linear retarded functional differential equations to neutral equations using some a priori estimation and the leray schauder degree theory we will obtain some existence theorems of periodic solutions for a class of quasilinear neutral equations the results also generalize the works of hatvani and krisztin on retarded equations

an abstract existence theorem at resonance and its applications abstract by using brouwer degree theory and a continuation theorem based on mawhin s coincidence degree an abstract existence theorem at resonance for operator equations is developed as applications of this result some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimension n n 2 the results due to nagle and sinkala are generalized improved and unified

on a three dimensional symmetric ising tetrahedron and contributions to the theory of the dilogarithm and clausen functions perturbative quantum field theory for the ising model at the three loop level yields a tetrahedral feynman diagram c a b with masses a and b and four other lines with unit mass the completely symmetric tetrahedron ctet c 1 1 has been of interest from many points of view with several representations and conjectures having been given in the literature we prove a conjectured exponentially fast convergent sum for c 1 1 as well as a previously empirical relation for c 1 1 as a remarkable difference of clausen function values our presentation includes propositions extending the theory of the dilogarithm li2 and clausen cl2 functions as well as their relation to other special functions of mathematical physics the results strengthen connections between feynman diagram integrals volumes in hyperbolic space number theory and special functions and numbers specifically including dilogarithms clausen function values and harmonic numbers

the existence of solutions for impulsive neutral functional differential equations this work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed not necessarily bounded operators a t email protected i

periodic solutions for generalized lienard neutral equation with variable parameter abstract by means of mawhin s continuation theorem existence criteria is established for the periodic solutions to a neutral equation with variable parameter it is worth stating that the coefficient c is not a constant which is different from the corresponding ones of past work

on positive periodic solutions of a nonautonomous neutral delay n species competitive system abstract the purpose of this paper is to investigate a general neutral delay n species competitive nonautonomous system different from gaines and mawhin s continuation theorem r e gaines j l mawhin coincidence degree and nonlinear differential equations springer verlag berlin 1977 and abstract continuation theory for k set contraction w petryshyn z yu existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems nonlinear anal 6 1982 943 969 r e gaines j l mawhin lecture notes in mathematics vol 586 springer verlag berlin 1977 a new existence theorem is introduced with the help of the theorem and some techniques a set of sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution as an application we also examine some special cases which have been studied extensively in the literature some known results are improved and generalized

periodic solutions for a higher order p laplacian neutral functional differential equation with a deviating argument abstract in this paper a higher order p laplacian neutral functional differential equation with a deviating argument p x t c t x t n m f x t x t g t x t t e t has been studied by applying mawhin s continuation degree theorem some new criteria to guarantee the existence of periodic solutions are obtained it is interesting that the power of the variable x in function g is allowed to be greater than p 1

morse theory for lagrangian intersections soit p une variete symplectique compacte et soit l p une sous variete lagrangienne avec 2 p l 0 pour un diffeomorphisme exact de p avec la propriete que l coupe l transversalement on demontre une inegalite de morse reliant l ensemble l l a la cohomologie de l

some generalised radiation field integrals in this paper two families of integrals that are generalisations of the radiation field integrals are considered i a b 0b 0ao 2 2 1 2 2 1 d d and y a b 0b 0ao 1 lambda 1 d d where and are arbitrary constants except that 0 1 2 and o x is the confluent hypergeometric function of the first kind they are expressed in the form of an infinite series and the corresponding coefficients are evaluated some particular cases are mentioned algorithms for the tabulation of these integrals are developed and tables with better precision than those available in the literature for numerical values have been obtained for some parameter values

on a modified beta function and some applications abstract in this work we study the modified beta function b 1 2 x a b 1 2 x 1 v a 1 v b 1 dv x 0 1 that appeared in marus ic and bajzer s solution m marus ic z bajzer generalized two parameter equation of growth j math anal appl 179 1993 446 462 of the generalized two parameter equation of tumor growth y ay by in particular we provide methods for computing this function for special values of the function s parameters some analytic solutions of the generalized two parameter growth equation are obtained

periodic solutions for n dimensional generalized lienard type p laplacian functional differential system abstract we consider the n dimensional generalized lienard system d d t p x t c x t d d t f x t g x t t e t driven by the scalar p laplacian c is an n n symmetric matrix of constants using the degree theory we establish some criteria to guarantee the existence of periodic solutions for the above system which generalize and improve on the corresponding results in the related literature

formulae concerning the computation of the clausen integral cl2 θ the main problem under study concerns the expression of the clausen integral cl2 in closed form in terms of known constants and special functions when is equal to a rational multiple of belonging to 0 2 a general formula giving cl2 p q in terms of the derivative of the di gamma function and the sine function is deduced from an appropriate fourier series expansion some variants of this formula are obtained in further sections the formulae expressing cl2 2 and more generally cl2 m m 2 3 4 as linear combinations of terms of the form cl2 const are established the various results are illustrated by means of typical examples of practical application the last section contains two simple approximations enabling the computation of cl for any in 0 with a relative error smaller than 0 63 and 0 003 resp the paper ends with an appendix in which among other things a peculiar trigonometric identity is established as a by product

on the existence of harmonic solutions of lie nard systems we discuss the existence of harmonic solutions of lienard systems of the form x d dtgradf x gradg x p t where f c 2 r n r g c 1 r n r p c 0 r r n and p t t p t for a constant t 0

boundedness of solutions of a nonlinear nonautonomous neutral delay equation abstract sufficient conditions are obtained for the boundedness of solutions of the non linear nonautonomous neutral equation x t r t x t a t x t 1 c t x t 1 which arise in a food limited population model this partially answers a recent open question proposed by k gopalsamy and b g zhang

contiguous relations for the fox wright function abstract contiguous relations are a powerful tool for dealing with hypergeometric functions in this paper four different types of contiguous relations for the fox wright function are given we demonstrate the usefulness of our formulas by showing how they can be used to recover the famous hagen rothe convolution

generalizations of the borsuk theorem for any subgroup h of g we will denote by v the fixed point subspace of h action i e i xeir t x x dh h for xrz wn let o x t x 1 g e g be the g orbit of 3 if g is finite we let l x denote the order of o x suppose that 2 is an open bounded g invariant set in iwn andf s wn is a continuous g equivariant map if 0 f x the brouwer degree deg f 52 o is well defined it is known that we can obtain important informations on deg f q 0 if the g action on abn is of some special types for example in the case that g z 0 1 t i and t z where i is the identity transformation on iwn the borsuk theorem asserts that deg f 52 0 is an odd number provided 0 e q recently efforts have been made to generalize the borsuk theorem for the study of differential equations with various symmetries under the assumption that vg 0 marzantowicz 4 obtains the following results in the sequel we always assume that c2 is an open bounded g invariant subset of rn

on one dimensional digamma and polygamma series related to the evaluation of feynman diagrams we consider summations over digamma and polygamma functions often with summands of the form 1 n j n p q n r and 1 n j m n p q n r where m p q and r are positive integers we develop novel general integral representations and present explicit examples special cases of the sums reduce to known linear euler sums the sums of interest find application in quantum field theory including evaluation of feynman amplitudes

periodic solution of a periodic neutral delay equation abstract sufficient conditions are obtained for the existence of a positive periodic solution of the periodic neutral delay equation t n t a t n j 1 b j t n t j j 1 n c j t t j which arise in a food limited population model

some reduction and transformation formulas for the appell hypergeometric function f2 abstract an integral representation of the appell series f 2 1 2 1 2 x y is used here to obtain several finite sum expansions in terms of the less cumbersome hypergeometric functions 2f1 and 3f2 in the case when the parameters 1 2 1 and 2 are all positive integers some of our results may be seen as a generalization of the finite sum expansions of the appell series f 1 obtained by cuyt et al j comput appl math 5 1999 213 219 other important consequences as well as potential applications of our results are discussed and a listing of some useful reduction and transformation formulas is provided

periodic solutions to a second order p laplacian neutral functional differential system abstract by analyzing some properties of the linear difference operator a a x t x t c x t first and then using an extension of mawhin s continuation theorem a second order p laplacian neutral functional differential system as follows d d t p x t c x t f t x t x t t x t is studied some new results on the existence of periodic solutions is obtained the result is related to the deviating arguments and meanwhile the approaches to estimate a priori bounds of periodic solutions are different from the corresponding ones of the known literature

two periodic solutions of second order neutral functional differential equations in this paper we consider a type of second order neutral functional differential equations we obtain some existence results of multiplicity and nonexistence of positive periodic solutions our approach is based on a fixed point theorem in cones

on the existence of periodic solutions to rayleigh differential equation of neutral type in the critical case abstract in this paper the authors study the existence of periodic solutions for a second order neutral functional differential equation x t c x t f x t g t x t t e t in the critical case c 1 by analyzing some properties of the linear difference operator a a x t x t c x t and using mawhin s continuation theorem some new results are obtained

derivatives of horn hypergeometric functions with respect to their parameters the derivatives of eight horn hypergeometric functions four appell f1 f2 f3 and f4 and four degenerate confluent 1 2 1 and 1 with respect to their parameters are studied the first derivatives are expressed systematically as triple infinite summations or alternatively as single summations of two variable kampe de feriet functions taking advantage of previously established expressions for the derivative of the confluent or gaussian hypergeometric functions the generalization to the nth derivative of horn s functions with respect to their parameters is rather straightforward in most cases the results are expressed in terms of n 2 infinite summations following a similar procedure mixed derivatives are also treated an illustration of the usefulness of the derivatives of f1 with respect to the first and third parameters is given with the study of autoionization of atoms occurring as part of a post collisional process their evaluation setting the coulomb charge to zero provides the

an instanton invariant for 3 manifolds to an oriented closed 3 dimensional manifoldm withh1 m 0 we assign a 8 graded homology groupi m whose euler characteristic is twice casson s invariant the definition uses a construction on the space of instantons onm

existence of periodic solutions for a p laplacian neutral functional differential equation abstract in this paper the author study the existence of periodic solutions for a p laplacian neutral functional differential equation as follows p u t j 1 n c j u t r j f u t u t t g u t j 1 n j t g u t j t p t by analyzing some properties of operator a c t c t a x t x t i 1 n c i x t r i and then using continuation theorem of coincidence degree theory developed by mawhin some new results on the existence of periodic solutions are obtained the example shows that the results of this paper are more general and easily applicable and improve and generalize some corresponding ones of the known literature

the existence uniqueness and global attractivity of periodic solution for a type of neutral functional differential system with delays in this article by applying the coincidence degree theory and constructing a suitable lyapunov functional the authors study a kind of neutral functional differential system with delays some sufficient conditions which guarantee the existence uniqueness and global attractivity of periodic solution for this system are obtained

gauss legendre approximations for the hubbell rectangular source integral gauss legendre quadrature is used to develop a family of approximation formulas for the accurate numerical computation of the hubbell rectangular source integral

existence of periodic solutions for a p laplacian neutral functional differential equation with multiple variable parameters abstract by means of mawhin s continuation theorem a kind of p laplacian neutral functional differential equation with multiple variable parameters as follows p u t i 1 n c i t u t r i f u t u t t g u t j 1 n j t g u t j t e t is studied the interesting thing is that the coefficient c is not a constant by analyzing some properties of operator a c t c t a x t x t i 1 n c i t x t r i and then using mawhin s continuation theorem some new results on the existence of periodic solutions are obtained

periodic solutions for a kind of second order differential equation with multiple deviating arguments by means of continuation theorem of coincidence degree theory some new results on the existence and nonexistence of periodic solutions for a kind of second order functional differential equation with multiple deviating arguments are obtained

on the existence of periodic solutions for a kind of high order neutral functional differential equation abstract by using the coincidence degree theory of mawhin we study a kind of high order neutral functional differential equation with distributed delay as follows x t c x t n f x t x t g r 0 x t s d s p t some new results on the existence of periodic solutions are obtained

periodic solutions of neutral differential equation with multiple deviating arguments in this paper by means of an abstract continuous theorem of k set contractive operator and some analysis techniques the authors study the existence of periodic solution of the nonlinear neutral differential equation with multiple deviating argumentsddt x t cx email protected email protected i 1 email protected i t f x email protected i t email protected j 1 email protected j t g x email protected j t p t a new result is obtained

periodic solutions for some nonlinear differential equations of neutral type where f ir x ir ir is a caratheodory function f x is 2n periodic for every x ci e r and r e io 2n this problem has been studied by sadovskii in 151 by hale and mawhin in 6 in the case ial 1 to the previous one our interest is particularly motivated by the fact that represents a simple and meaningful model for a general phenomenon which often arises in the study of functional differential equations in fact as is well known in some cases a delayed differential equation can be seen as a perturbation of an ordinary differential equation in particular this occurs when the delayed term in the equation can be considered smaller than the ordinary one or dominated by it when such domination is available many good properties can be proved and several results such as those of 6 and 16 take advantage of this fact on the contrary when no domination is present the situation is much more complicated and in general very little is known in problem the delayed term can be considered dominated by the ordinary one whenever ial 1 as a matter of fact in this case one can prove the invertibility of the differential operator l x x a r ux the compactness of its inverse and even some a priori estimates for the solutions consequently one can reduce to a fixed point problem and solve it by means of some topological degree argument however when 11 1 so that the weight of the two terms x t and x t t is the same the above properties fail and moreover for some delays the kernel of the differential operator lx x a r is infinite dimensional therefore one must look for different methods problem is thus a simple but nevertheless significant example of the considerations illustrated by hale in 5 about the difficulty of undertaking a unified approach in the study of functional differential equations at the same time it provides an analogy between neutral equations and the wave equation in the line suggested by hale in 5

closed form summation of some trigonometric series the problem of numerical evaluation of the classical trigonometric series formule where 1 in the case of s 2n and c 2n 1 with n 1 2 3 has been recently addressed by dempsey liu and dempsey boersma and dempsey and by gautschi we show that when is equal to a rational multiple of 2 these series can in the general case be summed in closed form in terms of known constants and special functions general formulae giving c and s in terms of the generalized riemann zeta function and the cosine and sine functions respectively are derived some simpler variants of these formulae are obtained and various special results are established

calculation of the generalized hubbell rectangular source integrals using binomial coefficients the series expansion formulas in terms of binomial coefficients are derived for the family of generalized source integrals hrsis appearing in the evaluation of radiation field from a plane isotropic rectangular source the formulas given in this study for the evaluation of radiation integrals hrsis show good rate of convergence and great numerical stability the results obtained by the present approach are found to be in excellent agreement with other theoretical studies

periodic solutions to a second order nonlinear neutral functional differential equation in the critical case abstract in this paper the authors study the existence of periodic solutions for a second order neutral functional differential equation x t cx t f x t x t g t x t t e t in the critical case c 1 by employing mawhin s continuation theorem and some analysis techniques sufficient conditions are given for the existence of periodic solutions

positive periodic solutions of a periodic neutral delay logistic equation with impulses by using a fixed point theorem of strict set contraction some criteria are established for the existence of positive periodic solutions for a periodic neutral functional differential equation with impulses of the form dx t dt x t a t email protected i 1mb i t x email protected i t email protected j 1nc j t x email protected j t x t k x t k i k x t k k 1 2

periodic solutions to neutral differential equation with deviating arguments by employing the continuation theorem of coincidence degree theory and some analysis techniques we study a kind of neutral differential equation with deviating arguments as follows x t cx t r f x t g x t t p t some new results on the existence of periodic solutions are obtained our result generalizes main work of wang app math lett 12 1999 41 44

recursion formulas for appell s hypergeometric function f2 with some applications to radiation field problems abstract using some contiguous function relations for the classical gauss hypergeometric series 2 f 1 we establish a number of new recursion formulas for the appell functions f 2 1 2 n 1 2 x y and f 2 1 2 1 2 n x y where n n 0 0 1 2 n 0 some important applications of our results to the evaluation of radiation field integrals are discussed and a listing of some useful reduction and transformation formulas is provided

on the existence of periodic solutions for neutral functional differential equation abstract by means of mawhin s continuation theorem existence criteria are established for the periodic solutions of neutral functional differential equation

periodic solutions to a kind of neutral functional differential equation in the critical case in this paper we consider a kind of neutral functional differential equation as follows x t cx t gt xt t e t in the critical case c 1 by employing the topological degree theory and some analysis techniques we obtain some new results on the existence of periodic solutions

chebyshev coefficients for the clausen function cl 2 x abstract twenty digit chebyshev coefficients are given for the clausen function cl 2 x allowing a fast computation of this function for real values of the argument x

the floer homotopy type of height functions on complex grassmann manifolds a family of floer functions on the infinite dimensional complex grassmann manifold is defined by taking direct limits of height functions on adjoint orbits of unitary groups the floer cohomology of a generic function in the family is computed using the schubert calculus the floer homotopy type of this function is computed and the floer cohomology which was computed al gebraically is recovered from the floer homotopy type certain non generic elements of this family of floer functions were shown to be related to the symplectic action functional on the universal cover of the loop space of a finite dimensional complex grassmann manifold in the author s preprint the floer homotopy type of com plex grassmann manifolds

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

two periodic solutions of n dimensional neutral functional difference systems in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order n dimensional neutral functional difference systems our approach requires the krasnoselskii fixed point theorem in cones

new properties of the d operator and its applications on the problem of periodic solutions to neutral functional differential system abstract in this paper the authors first investigate some new properties of the d operator which is associated with neutral functional differential equations then by using these new properties the problem of existence of periodic solutions of the d operator neutral functional differential system is studied the interesting thing is that the d operator is allowed to be unstable which is generalized by the corresponding studies in the past under the crucial assumption that the d operator is stable

existence theorem for periodic solutions of higher order nonlinear differential equations abstract we study the existence of periodic solutions to differential equations of the form l x g t x x x m f t with l x x m a m 1 x m 1 a 1 x

the problem of existence of periodic solutions for neutral functional differential system with nonlinear difference operator abstract in this paper the authors investigate some new properties of nonlinear difference operator in the first which is associated with neutral functional differential equations then by using these new properties the problem of existence of periodic solutions for neutral functional differential system with nonlinear operator d 1 0 b h is studied the interesting thing is that the periodic solution to the system is allowed to be not differentiable

on the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments by means of the abstract continuation theory for k contractions some criteria are established for the existence and nonexistence of positive periodic solutions of the following neutral functional differential equation dndt n t a t t n t j 1nbj t nt j t i 1mci t n t i t

existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations abstract in this paper we use the coincidence degree theory to establish new results on the existence and uniqueness of t periodic solutions for the first order neutral functional differential equation of the form x t b x t g 1 t x t g 2 t x t p t

existence of periodic solutions for a pp laplacian neutral functional differential equation in this paper the author study the existence of periodic solutions for a pp laplacian neutral functional differential equation as follows p u t j 1ncju t rj f u t u t t g u t j 1n j t g u t j t p t by analyzing some properties of operator a ct ct ax t x t i 1ncix t ri and then using continuation theorem of coincidence degree theory developed by mawhin some new results on the existence of periodic solutions are obtained the example shows that the results of this paper are more general and easily applicable and improve and generalize some corresponding ones of the known literature

on the clausen integral cl2 θ and a related integral abstract in this article the clausen integral cl 2 0 ln 2 sin t 2 d t whereby is equal to a rational multiple of belonging to 0 2 is developed into a finite series of derivatives of the di gamma function for the same values of a method is presented to calculate the related integral 1 0 ln 2 2 cos 1 d

multiple gamma and related functions the authors give several new and potentially useful relationships between the multiple gamma functions and other mathematical functions and constants as by products of some of these relationships a classical definite integral due to euler and other definite integrals are also considered together with closed form evaluations of some series involving the riemann and hurwitz zeta functions

existence and multiplicity results for periodic solutions of semilinear duffing equations we obtain existence an multiplicity of harmonic and subharmonic solutions to the periodically forced nonlinear duffing s equation x g x p t in the semi linear case 0 a g x x b for x large we introduce new conditions of nonresonance with respect to the spectrum of the associated linear differential operator x x and show by some nonlinear counterexamples that the results are sharp

existence of periodic solutions for a kind of second order neutral functional differential equation by means of the continuation theorem of coincidence degree theory we study a kind of second order neutral functional differential equation as followsd 2dt 2u t j 1 nc ju t r j f u t u t a t g u t j 1 n b j t g u t c j t p t some new results on the existence of periodic solutions are obtained