the minimal period problem for nonconvex even second order hamiltonian systems abstract in this paper we study the minimal period problem for even autonomous second order hamiltonian systems defined on r nwithout any convexity assumption by using the variational methods we obtain estimates on the minimal period of the corresponding nonconstant periodic solution of the superquadratic and asymptotically linear hamiltonian systems

analysis parameter estimation and optimal control of non linear systems via general orthogonal polynomials general orthogonal polynomials are introduced to approximate the solution of a class of non linear systems using the integration operational matrix the product operational matrix and the derived non linear operational matrix the dynamical equation of a non linear system can be reduced to a set of simultaneous non linear algebraic equations thus greatly simplifying the solution the parameter identification problem for non linear systems is also dealt with an approximate solution for a non linear optimal control problem with quadratic performance measure is also considered three examples are given to demonstrate the validity and applicability of the orthogonal polynomial approximations

multiple solutions for nonlinear systems with gyroscopic terms abstract in this paper we investigate the existence of multiple solutions to some nonlinear systems with gyroscopic terms via variational methods some new results are obtained and some results from the literature are improved

application of general orthogonal polynomials to the optimal control of time varying linear systems the operational matrices for forward or backward integration of general orthogonal polynomials are derived the tensor expression for the generalized orthogonal polynomial approximation of any two arbitrary functions is also introduced it is shown that the approximation solution obtained using the chebyshev polynomial is readily obtainable as a special case of the results derived thus the present results include results presented by shih in 1983 and chou and horng in 1984 a linear time varying optimal control system with a quadratic performance measure is solved by using the generalized orthogonal polynomials comparison of the results with those obtained using several different classical orthogonal polynomial approximations is also included

non autonomous second order hamiltonian systems abstract we study the existence of periodic solutions for a second order non autonomous dynamical system containing variable kinetic energy terms our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other we study sublinear problems and the existence of non constant solutions

existence of periodic solutions to second order hamiltonian systems with potential indefinite in sign we have presented some new results for periodic solutions to a class of hamiltonian systems with potential indefinite in sign these results improve and correct some known results in the literature

the minimal period problem of periodic solutions for autonomous superquadratic second order hamiltonian systems abstract in this paper we study the existence of periodic solutions with prescribed minimal period for superquadratic autonomous second order hamiltonian systems defined on r n with no convexity assumptions we use the direct variational approach for this problem on a w 1 2 space of even functions and prove new iteration inequalities on morse indices using these tools and the saddle point theorem we obtain results under precisely rabinowitz superquadratic condition on potential functions we show that for every t 0 the above mentioned system possesses a t periodic even solution with minimal period not smaller than t n 2

periodic and subharmonic solutions for a class of superquadratic hamiltonian systems abstract some existence theorems are obtained for periodic and subharmonic solutions of a class of superquadratic hamiltonian systems by the minimax methods in critical point theory specially a local link theorem due to li and willem and the generalized mountain pass theorem respectively

analysis and optimal control of time varying linear systems via block pulse functions succinct and clear sighted operational properties of block pulse functions are fully applied to the analysis and optimal control of time varying linear systems with quadratic performance index piecewise constant solutions equally distributed which are simple in form and convenient for use or implementation are consequently obtained another advantage of this method is that any positive integer can be chosen as the number of sub intervals whereas in the case of walsh function approximation the choice can only be made from 2 4 8 16 32 and so on the algorithms developed in the paper are illustrated by appropriate examples

infinitely many solutions for hamiltonian systems abstract we consider two classes of the second order hamiltonian systems with symmetry if the systems are asymptotically linear with resonance we obtain infinitely many small energy solutions by minimax technique if the systems possess sign changing potential we also establish an existence theorem of infinitely many solutions by morse theory

non linear systems identification and optimal control we consider analytical control affine non linear continuous systems by the introduction of a notation based on the tensor product we can use the matrix calculus to solve the problems of model identification by orthogonal functions and the construction of a non linear state feedback for the optimal control problem

on the existence of periodic solutions for a class of symetric hamiltonian systems abstract hamiltonian systems are used to model the motion of discrete mechanical systems this paper establishes the existence of periodic solutions for a class of such systems the method developed to prove existence should be useful for other such problems keywords minimax technique ordinary differential equations and variational problem

periodic second order superlinear hamiltonian systems abstract we consider periodic solutions for superlinear second order non autonomous dynamical systems including both kinetic and potential terms we study the existence of nontrivial and ground state solutions

identification of a class of nonlinear continuous time systems using hartley modulating functions most of the existing approaches to identification of nonlinear dynamic systems involve matching a given input output behaviour with empirical discrete time approximations such as artificial neural networks kolmogorov gabor polynomials radial basis function networks etc techniques for dealing with physically based continuous time models are either applicable to only a restricted class of systems or are computationally very demanding in this paper a new methodology is presented that is applicable to a large class of nonlinear continuous time systems by defining a set of hartley modulating functions for characterizing the continuous process signals the advantages of this new class of modulating functions are that a set of algebraic equations with real coefficients results the formulations are free from boundary conditions and the computations can be made using fast algorithms for the discrete hartley transformation the resulting estimation scheme is applied to different categories of nonlinear syst

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

infinitely many periodic solutions for second order hamiltonian systems in this paper we study the existence of infinitely many periodic solutions for second order hamiltonian systems u uv t u 0 where v t u is either asymptotically quadratic or superquadratic as u

periodic and subharmonic solutions for a class of superquadratic second order hamiltonian systems abstract some existence theorems are obtained for periodic and subharmonic solutions of a class of superquadratic second order hamiltonian systems by the minimax methods in critical point theory especially a local linking theorem due to luan and mao and the generalized mountain pass theorem due to rabinowitz

periodic solutions of second order non autonomous hamiltonian systems with local superquadratic potential abstract some existence theorems are obtained for periodic solutions of a class of non autonomous second order hamiltonian systems with local superquadratic potential by making use of the generalized mountain pass theorem

periodic solutions for some second order systems abstract in this paper we use the minimax theorem to investigate periodic solutions of some second order systems and give some sufficient conditions for the existence for periodic solutions the results generalize and improve some known results

applications of local linking to critical point theory we prove the existence of nontrivial critical points of functionals with a local linking at 0 applications to elliptic boundary value problems and to hamiltonian systems are given c 1995 academic press inc

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

periodic solutions for some nonautonomous second order hamiltonian systems the existence and multiplicity of periodic solutions are obtained for nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

simple unified form for the major no hidden variables theorems two examples are given that substantially simplify the no hidden variables theorem of kochen and specker greatly reducing the number of observables considered and requiring no intricate geometric argument while one of the examples also obeys a more powerful version of bell s theorem the other does not the examples provide a new perspective on both of these fundamental theorems and on the relation between them

periodic and subharmonic solutions of second order hamiltonian systems abstract some solvability conditions of periodic solutions and subharmonic solutions are obtained for a class of new superquadratic non autonomous second order hamiltonian systems by the minimax methods in critical point theory

walsh stretch matrices and functional differential equations this correspondence presents a new operational matrix for stretch via walsh functions and discusses some interesting properties of this matrix and its role in the solution of certain functional differential equations the solutions of differential equations are obtained in a series of walsh functions the results are piecewise constant with minimal mean square error the single term approximation combined with the technique of extension 8 reduces the computational effort to a minimum

periodic non autonomous second order dynamical systems we study the existence of periodic solutions for a second order non autonomous dynamical system we give three sets of hypotheses which guarantee the existence of non constant solutions we were able to weaken the hypotheses considerably from those used previously for such systems we employ a saddle point theorem using linking methods

infinitely many solutions for a floquet type bvp with superlinearity indefinite in sign abstract by the application of a technique developed by g j butler we find infinitely many solutions of the bvp formula where q 0 r is allowed to change sign g r r is superlinear and g x x 0 for all x 0 and r 2 r 2 is a continuous positively homogeneous and nondegenerate map at first we apply the main result to obtain solutions with a prescribed large number of zeros when is the rotation of a fixed angle second we find infinitely many subharmonic solutions of any order and again solutions with a prescribed large number of zeros for the periodic problem associated to the equation c q t g x 0 with q and g as above and c r

multiplicity and concentration of homoclinic solutions for some second order hamiltonian systems abstract in this paper we present some new results of homoclinic solutions for second order hamiltonian systems u l t u w u t u 0 here 0 is a parameter l c r r n n and w c 1 r r n r unlike most other papers on this problem we require that l t is a positive semi definite symmetric matrix for all t r that is l t 0 is allowed to occur in some finite interval t of r under some suitable assumptions on w we prove the existence of two different homoclinic solutions u 1 u 2 which both vanish on r t as and converge to u 0 1 u 0 2 in h 1 r respectively here u 0 1 u 0 2 h 0 1 t are two nontrivial solutions of the dirichlet bvp for hamiltonian systems on the finite interval t

the computation of ck spline functions abstract we present in this paper an algorithm for computing ck spline functions i e spline functions which generate k time continuous and derivable approximations these functions seem to be very efficient in several applied nonlinear differential problems like nonlinear control or nonlinear simulation

hudson s theorem for finite dimensional quantum systems we show that on a hilbert space of odd dimension the only pure states to possess a non negative wigner function are stabilizer states the clifford group is identified as the set of unitary operations which preserve positivity the result can be seen as a discrete version of hudson s theorem hudson established that for continuous variable systems the wigner function of a pure state has no negative values if and only if the state is gaussian turning to mixed states it might be surmised that only convex combinations of stabilizer states give rise to non negative wigner distributions we refute this conjecture by means of a counterexample further we give an axiomatic characterization which completely fixes the definition of the wigner function and compare two approaches to stabilizer states for hilbert spaces of prime power dimensions in the course of the discussion we derive explicit formulas for the number of stabilizer codes defined on such systems

notes on periodic solutions of subquadratic second order systems some existence theorems are obtained for periodic solutions of the subquadratic second order systems by the minimax methods in critical point theory

subharmonics near an equilibrium for some second order hamiltonian systems this work is devoted to the study of subharmonic solutions of a second order hamiltonian system near an equilibrium point say q 0 the problem of existence of periodic solutions from the global point of view is also considered this problem has been studied for the case where the potential is positive and superquadratic in this work a potential v that has change in sign is considered the potential is decomposed as where p is homogeneous superquadratic and nondegenerate and is of higher order near 0 in this paper the existence is shown of a sequence of subharmonic solutions of the equation above that converges to the equilibrium such that their minimal periods converge to infinity this problem is approached from a variational point of view existence of subharmonic and periodic solutions is obtained via minimax techniques

new existence of periodic solutions for second order non autonomous hamiltonian systems abstract by using mountain pass theorem and local link theorem some existence theorems are obtained for periodic solutions of second order non autonomous hamiltonian systems under local superquadratic condition and other suitable conditions

periodic solutions for some nonautonomous second order systems some existence theorems are obtained for periodic solutions of nonautonomous second order systems by using the least action principle and the minimax methods

identification of time varying nonlinear systems using chebyshev polynomials abstract this paper is devoted to an identification of time varying nonlinear systems using chebyshev polynomials of the first kind for systems being linear relatively unknown functional parameters a method of approximate determination of these parameters has been worked out as the identification problems are ill posed to solve the obtained redefinite system of linear algebraic equations a regularization method is used

periodic solutions of second order discrete hamiltonian systems with potential indefinite in sign abstract in this paper an existence theorem is obtained for the periodic solutions of second order discrete hamiltonian systems with potential indefinite in sign by linking theorem in the critical point theory

existence result for periodic solutions of a class of hamiltonian systems with super quadratic potential abstract we have presented a variant existence result for periodic solutions to a class of hamiltonian systems with a potential which is both super quadratic and sign indefinite

periodic solutions of a discrete hamiltonian system with a change of sign in the potential in this paper an existence theorem is obtained for periodic solutions of a second order discrete hamiltonian system with a change of sign in the potential by the minimax methods in the critical point theory

periodic solutions for second order hamiltonian systems with a change sign potential an existence theorem is obtained for periodic solutions of nonautonomous second order hamiltonian systems with a change sign potential by the minimax methods in critical point theory

periodic solutions for a class of nonautonomous subquadratic second order hamiltonian systems some existence theorems are obtained for periodic solutions of a class of unbounded nonautonomous nonconvex subquadratic second order hamiltonian systems by using the minimax methods in critical point theory

periodic solutions of a class of non autonomous second order systems some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second order systems with a potential which is the sum of a subconvex function and a subquadratic function

periodic and subharmonic solutions of a class of superquadratic hamiltonian systems abstract periodic solutions and infinitely distinct subharmonic solutions are obtained for a class of nonconvex and nonautonomous superquadratic hamiltonian systems z j h z z t by using the minimax methods in critical point theory

periodic solutions of non autonomous second order systems with γ quasisubadditive potential abstract the existence of periodic solutions to non autonomous second order systems with quasisubadditive potential is proved with classical theorems of variational calculus

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

periodic solutions for hamiltonian systems without ambrosetti rabinowitz condition and spectrum 0 abstract in this paper we consider the superquadratic second order hamiltonian system u t a t u t h t u t 0 t r our main results here allow the classical ambrosetti rabinowitz superlinear condition to be replaced by a general superquadratic condition and 0 lies in a gap of b where b d 2 d t 2 a t we will study the ground state periodic solutions for this problem the main idea here lies in an application of a variant generalized weak linking theorem for strongly indefinite problem developed by schechter and zou

non collision periodic solutions of second order singular dynamical systems we study the existence of non collision periodic solutions for second order singular dynamical systems the repulsive case and the attractive case are dealt with using a unified topological approach the proof is based on a well known fixed point theorem for completely continuous operators involving a new type of cone we do not need to consider so called strong force conditions moreover for the repulsive case the critical case can be covered recent results in the literature even in the scalar case are complemented generalized and improved

shifted chebyshev series analysis of linear optimal control systems incorporating observers the analysis of optimal control systems incorporating observers has been approached by the shifted chebyshev series in this study the method simplifies the system of equations into the successive solution of a set of linear algebraic equations one example is illustrated and only a small number of the chebyshev polynomials is needed to obtain a very attractive and excellent result

periodic solutions for second order discrete hamiltonian system with a change of sign in potential some existence results of periodic solutions are obtained for nonautonomous second order discrete hamiltonian system with a change of sign in potential by the minimax methods in critical point theory

periodic solutions of second order non autonomous singular dynamical systems abstract in this paper we establish two different existence results of positive periodic solutions for second order non autonomous singular dynamical systems the first one is based on a nonlinear alternative principle of leray schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity the second one is based on schauder s fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions recent results in the literature are generalized and significantly improved

nonlinear oscillations and boundary value problems for hamiltonian systems we prove the existence of solutions of various boundary value problems for nonautonomous hamiltonian systems with forcing terms begin gathered dot x t h p t x t p t g t hfill dot p t h x t x t p t f t hfill end gathered