remarks on the periodic boundary value problems for first order differential equations this paper is concerned with the existence of solutions and the monotone method of first order periodic boundary value problems when the lower and upper solutions and violate the boundary conditions 0 2 and 0 2 using the topological degree theory two existence theorems are established under weaker conditions than the one side lipschitz conditions an example is given which illustrates that pbvp may not have solutions between and without further restrictions to f t u the monotone method is also discussed with some new results

periodic boundary value problems for a class of functional differential equations in this paper we show that the method of upper and lower solutions coupled with the monotone iterative technique is valid to obtain constructive proofs of existence of solutions for nonlinear periodic boundary value problems of functional differential equations without assuming properties of monotonicity in the nonlinear part

monotone method for second order delayed differential equations with boundary value conditions in this paper we investigate the existence of extremal solutions of boundary value problems for second order differential equations with delayed arguments we show that a lower and upper solution method has been applied successfully to such problems an one sided lipschitz condition with corresponding constants is important assumption in our research

multiple positive solutions of periodic boundary value problems for second order impulsive differential equations abstract this paper is devoted to study the existence of multiple positive solutions for the second order periodic boundary value problem with impulse effects the main results here are the generalization of jiang daqing jiang on the existence of positive solutions to second order periodic bvps acta math sci 18 1998 31 35 for ordinary differential equations existence is established via the theory of fixed point index in cones

first order functional difference equations with nonlinear boundary value problems the monotone iterative method is used to show that corresponding difference problems with boundary conditions have extremal solutions in the region bounded by lower and upper solutions it is important to indicate that the right hand sides of problems depend on r delayed arguments difference inequalities of such types are also discussed two examples satisfying the assumptions are presented

on boundary value problems for singular second order functional differential equations abstract positive solutions to the boundary value problem y f x y w x 0 y x y x x a x 0 y x y x x 1 x b are obtained by applying the schauder fixed point theorem where w x is a continuous function defined on 0 1 and f x y is a function defined on 0 1 0 which satisfies certain restrictions and may have singularity at y 0 the result corrects and improves an existence theorem due to erbe and kong j comput appl math 53 1994 377 388

the schwinger su 3 construction i multiplicity problem and relation to induced representations the schwinger oscillator operator representation of su 3 is analyzed with particular reference to the problem of multiplicity of irreducible representations it is shown that with the use of an sp 2 r unitary representation commuting with the su 3 representation the infinity of occurrences of each su 3 irreducible representation can be handled in complete detail a natural generating representation for su 3 containing each irreducible representation exactly once is identified within a subspace of the schwinger construction and this is shown to be equivalent to an induced representation of su 3

second order functional differential equations with past present and future dependence abstract in this paper we obtain a result on existence of extremal quasisolutions and solutions for second order functional differential equations with functional boundary conditions and past present and future dependence in order to do that we develop a generalized monotone method in presence of lower and upper solutions some examples of application are provided too

monotone method for first order functional differential equations we study periodic boundary value problems relative to a general class of first order functional differential equations for this class of problems we develop the monotone iterative technique our formulation is very general including delay differential equations functional differential equations with maxima and integro differential equations but the case where the operator defining the functional dependence is not necessarily lipschitzian is also considered

generalized coherent states for su n systems generalized coherent states are developed for su n systems for arbitrary n this is done by first iteratively determining explicit representations for the su n coherent states and then determining parametric representations useful for applications for su n the set of coherent states is isomorphic to a coset space su n su n 1 and thus shows the geometrical structure of the coset space these results provide a convenient 2n 1 dimensional space for the description of arbitrary su n systems we further obtain the metric and measure on the coset space and show some properties of the su n coherent states

su n coherent states and irreducible schwinger bosons we exploit the su n irreducible schwinger boson to construct su n coherent states this construction of an su n coherent state is analogous to the construction of the simplest heisenberg weyl coherent states the coherent states belonging to irreducible representations of su n are labeled by the eigenvalues of n 1 su n casimir operators and characterized by n 1 complex orthonormal vectors describing the su n group manifold

solvability of three point boundary value problems for second order differential equations with deviating arguments the monotone iterative technique is used to boundary problems for second order ordinary differential equations with deviating arguments corresponding results are formulated when the problem has extremal solutions or weakly coupled extremal quasi solutions

quasi solutions for generalized second order differential equations with deviating arguments this paper deal with boundary value problems for generalized second order differential equations with deviating arguments existence of quasi solutions and solutions are proved by monotone iterative method examples with numerical results are added

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problem for second order functional differential equations by using the method of lower and upper solutions coupled with monotone iterative technique

existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions abstract this paper is concerned with the existence and approximation of solutions for a class of first order functional differential equations with periodic boundary conditions we present a new comparison result and extend previous results

multi point boundary value problems for second order functional differential equations this paper is concerned with the existence of extreme solutions of multi point boundary value problem for a class of second order functional differential equations we introduce a new concept of lower and upper solutions by using the method of upper and lower solutions and monotone iterative technique we obtain the existence of extreme solutions

remarks on periodic boundary value problems for functional differential equations we extend some results on existence and approximation of solution for a class of first order functional differential equations with periodic boundary conditions we show the validity of the monotone iterative technique under weaker hypotheses and present some examples

periodic boundary value problems for delay differential equations with impulses existence and approximation of solutions for an impulsive delay differential equation with periodic boundary value conditions are presented we use comparison principles and monotone iterative techniques

existence results to delay fractional differential equations with nonlinear boundary conditions this paper concerns boundary value problems for delay fractional differential equations we formulate sufficient conditions under which such problems have extremal solutions in the corresponding region delay differential inequalities are also discussed examples are given to illustrate the effectiveness of the results

periodic boundary value problems for the second order functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problems for second order functional differential equations a new concept of lower and upper solutions is introduced and we present a new comparison principle meanwhile we extend previous results

existence theorems for a class of nonlocal differential equations abstract a class of nonlocal second order ordinary differential equations of the form y x f x y x y x y x for continuous f and is studied the equation is supplemented with none one or two robin boundary conditions depending on whether the interval of interest i is finite semi infinite or infinite the only other restriction on the function is that it maps i into itself sufficient conditions for the existence of a solution are found which include the assumption of the existence of upper and lower solutions the upper and lower solutions provide bounds for the solution on i

coherent states and the classical limit on irreducible representations we give an explicit construction of the coherent states for an arbitrary irreducible representation we also construct the symplectic structure on the manifold of coherent states find canonical variables and discuss various classical limits of quantum mechanical systems with relevant observables that obey commutation relations

boundary value problems for singular second order functional differential equations abstract we consider general linear boundary value problems for equations of the form y f x y x 0 0 x x is continuous and f x y has a singularity at y 0 the results improve and extend earlier results for the case x x due to taliaferro 1979 and gatica 1989

su n irreducible schwinger bosons we construct su n irreducible schwinger bosons satisfying certain u n 1 constraints which implement the symmetries of su n young tableaues as a result all su n irreducible representations are simple monomials of n 1 types of su n irreducible schwinger bosons further we show that these representations are free of multiplicity problems thus all su n representations are made as simple as su 2

existence of solutions of boundary value problems for differential equations with delayed arguments we study the existence and approximation of solution of boundary value problems for differential equations with delayed arguments sufficient conditions are established for the existence of a unique solution or extremal ones of the given problem a monotone iterative technique is applied

nonlinear boundary value problems for second order differential equations with causal operators in this paper we deal with second order differential equations with causal operators to obtain sufficient conditions for existence of solutions we use a monotone iterative method we investigate both differential equations and differential inequalities an example illustrates the results obtained

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

generalized euler angle parametrization for su n in a previous paper 1 an euler angle parametrization for su 4 was given here we present the derivation of a generalized euler angle parametrization for su n the formula for the calculation of the haar measure for su n as well as its relation to marinov s volume formula for su n 2 3 will also be derived as an example of this parametrization s usefulness the density matrix parametrization and invariant volume element for a qubit qutrit three qubit and two three state systems also known as two qutrit systems 4 will also be given

monotone iterative method for first order functional difference equations with nonlinear boundary value conditions in this paper we show that the method of monotone iterative coupled with the upper and lower solutions is valid to obtain constructive proofs to the existence of solutions for first order functional difference equations with nonlinear boundary value conditions an example is given to illustrate the results obtained

the schwinger su 3 construction ii relations between heisenberg weyl and su 3 coherent states the schwinger oscillator operator representation of su 3 studied in a previous paper from the representation theory point of view is analyzed to discuss the intimate relationships between standard oscillator coherent state systems and systems of su 3 coherent states both su 3 standard coherent states based on choice of highest weight vector as fiducial vector and certain other specific systems of generalized coherent states are found to be relevant a complete analysis is presented covering all the oscillator coherent states without exception and amounting to su 3 harmonic analysis of these states

boundary value problems for first order impulsive delay differential equations with a parameter in this paper by means of the method of upper and lower solutions and monotone iterative technique the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established

coherent states for su 3 we define coherent states for su 3 using six bosonic creation and annihilation operators these coherent states are explicitly characterized by six complex numbers with constraints for the completely symmetric representations n 0 and 0 m only three of the bosonic operators are required for mixed representations n m all six operators are required the coherent states provide a resolution of identity satisfy the continuity property and possess a variety of group theoretic properties we introduce an explicit parametrization of the group su 3 and the corresponding integration measure finally we discuss the path integral formalism for a problem in which the hamiltonian is a function of su 3 operators at each site

periodic boundary value problems of second order impulsive differential equations abstract this paper discusses periodic boundary value problems of second order impulsive differential equations by using schaeffer s fixed point theorem and monotone iterative technique some existence results are obtained

discontinuous functional differential equations with delayed or advanced arguments we provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced the boundary condition is allowed to be discontinuous and to depend functionally on the unknown solution

boundary value problems for first order differential equations of mixed type abstract we apply the monotone iterative method to formulate existence results for integro differential equations with nonlinear boundary conditions some results for integro differential inequalities are also given examples illustrate obtained results

existence of solutions of boundary value problems for differential equations in which deviated arguments depend on the unknown solution this paper concerns differential equations with boundary conditions given are sufficient conditions under which such problems with deviated arguments have a unique solution in a corresponding sector to obtain existence results we apply a monotone iterative method

advanced differential equations with nonlinear boundary conditions we investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions sufficient conditions when the problem has extremal solutions or a unique solution are formulated linear advanced differential inequalities are also discussed

the causal structure of microlocalized rough einstein metrics this is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the einstein vacuum equations expressed relative to wave coordinates by very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and sobolev inequalities in this paper we develop the geometric analysis of the eikonal equation for microlocalized rough einstein metrics this is a crucial step in the derivation of the decay estimates needed in the first paper

existence of positive solutions for boundary value problem of second order fde abstract we use a fixed point theorem in cones to investigate the existence of positive solutions for boundary value problem of a second order functional differential equation fde with the form y t r t y t 0 0 y t y t t r t 0 y t y t n t 1 t 1 a where y t y t for a we allow that r t has the singularity at the endpoints t 0 and t 1 of 0 1 our results include the situations that f is either superlinear or sublinear

su n coherent states we generalize schwinger boson representation of su 2 algebra to su n and define coherent states of su n using 2 2n 1 1 bosonic harmonic oscillator creation and annihilation operators we give an explicit construction of all n 1 casimirs of su n in terms of these creation and annihilation operators the su n coherent states belonging to any irreducible representations of su n are labeled by the eigenvalues of the casimir operators and are characterized by n 1 complex orthonormal vectors describing the su n manifold the coherent states provide a resolution of identity satisfy the continuity property and possess a variety of group theoretic properties

monotone iterative technique for second order delayed periodic problem in banach spaces in this paper we deal with the existence of periodic solutions for second order functional differential equation with delay in e u t f t u t u t t r where e is an ordered banach space f r e e e is a continuous function which is periodic in t and 0 is a constant we first build a new maximum principle for the periodic solutions of the corresponding linear equation with delay with the aid of this maximum principle under the assumption that the nonlinear function is quasi monotonicity we study the existence of the minimal and maximal periodic solutions for abstract delayed equation by combining perturbation method and monotone iterative technique of the lower and upper solutions