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

existence of homoclinic orbits for second order hamiltonian systems without ar condition abstract the existence of homoclinic orbits is obtained for a class of the second order hamiltonian systems u t l t u t w t u t 0 t r by the local linking lemma where w t x is superquadratic and need not be nonnegative globally

on the partial realization problem abstract in this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra most of which were originally developed in other contexts we approach the partial realization problem from several different angles and explore the connections to such topics as factoriza tion of hankel matrices block tridiagonalization generalizations of the lanczos process for biorthogonalization the euclidean algorithm and the principal part con tinued fractions of arne magnus the pade table and the berlekamp masseyalgo rithm in this way we are able to clarify some previous results by rissanen kalman and others and place them in a broader context this leads to several results and concepts which we think are new our analysis is restricted to the scalar case but some definitions and formulations have been rigged to facilitate an extension to the matrix case

fast homoclinic solutions for some second order non autonomous systems abstract this paper is concerned with the existence of homoclinic solutions for the following second order non autonomous system fhs q c q u q t q 0 where q r n c 0 is a constant and u t q c 1 r r n r under some reasonable assumptions for the first time we introduce the concept of fast homoclinic solutions of fhs and establish some criteria to guarantee the existence of fast homoclinic solutions of fhs besides that in some particular case the uniqueness of homoclinic solutions of fhs is also obtained recent results in the literature are generalized and significantly improved

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

infinitely many homoclinic orbits for hamiltonian systems with indefinite sign subquadratic potentials abstract in this paper we deal with the existence and multiplicity of homoclinic solutions of the second order hamiltonian system u t l t u t w t u t 0 where l t and w t x are neither autonomous nor periodic in t under the assumption that w t x is indefinite sign and subquadratic as x and l t is a n n real symmetric positive definite matrices for all t r we establish some existence criteria to guarantee that the above system has at least one or infinitely many homoclinic solutions by using the genus properties in critical theory

homoclinic solutions for ordinary p laplacian systems abstract a new result for the existence of homoclinic orbits is obtained for ordinary p laplacian system d dt u t p 2 u t v t u t f t where p 1 t r u r n and v c 1 r r n r v t x k t x w t x is t periodic with respect to t t 0 and f r r n is a continuous and bounded function this result generalizes and improves some known results in the previous literature

existence of homoclinic solutions for a class of second order hamiltonian systems abstract a new result for existence of homoclinic orbits is obtained for the second order hamiltonian systems under a class of new superquadratic conditions a homoclinic orbit is obtained as a limit of solutions of a certain sequence of boundary value problems which are obtained by the minimax methods

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

infinitely many homoclinic orbits for the second order hamiltonian systems with general potentials abstract in this paper we study the following nonperiodic second order hamiltonian systems u t l t u t r t u t r where l t may not be uniformly positive definite for all t r under more general conditions on r u t u we prove that the above system has infinitely many homoclinic orbits provided r is even in u

homoclinic orbits for a class of hamiltonian systems consider the second order hamiltonian system where q n and v c 1 n is t periodic in t suppose v q t 0 0 0 is a local maximum for v t and v t x x under these and some additional technical assumptions we prove that hs has a homoclinic orbit q emanating from 0 the orbit q is obtained as the limit as k of 2 kt periodic solutions i e subharmonics q k of hs the subharmonics q k are obtained in turn via the mountain pass theorem

on the use of product structure in secant methods for nonlinear least squares problems the problem of adjusting the second order term in secant methods for nonlinear least squares problems with zero residual is addressed the author uses the framework of structured secant methods to derive and investigate a new way to resize the approximation of the second order term using some exact information the resulting method is a self adjusting structured secant method for nonlinear least squares problems yielding a q quadratic convergence rate for zero residual and a q superlinear convergence rate for nonzero residual problems

existence of even homoclinic orbits for second order hamiltonian systems some existence theorems for even homoclinic orbits are obtained for a class of second order nonautonomous hamiltonian systems with symmetric potentials under a class of new superquadratic conditions a homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil boundary value problems which are obtained by the minimax methods

existence of homoclinic solution for the second order hamiltonian systems abstract an existence theorem of homoclinic solution is obtained for a class of the nonautonomous second order hamiltonian systems u t l t u t w t u t 0 t r by the minimax methods in the critical point theory specially the generalized mountain pass theorem where l t is unnecessary uniformly positively definite for all t r and w t x satisfies the superquadratic condition w t x x 2 as x uniformly in t and need not satisfy the global ambrosetti rabinowitz condition

a unified proof on existence of homoclinic orbits for some semilinear ordinary differential equations with periodic potentials abstract this paper gives a direct short and unified proof of rabinowitz s theorem grossinho minhos tersian s theorem and tersian chaparova s theorems on existence of homoclinic orbits for second order periodic hamiltonian systems fourth and sixth order periodic ordinary differential equations respectively by brezis nirenberg type mountain pass lemma

symmetrically homoclinic orbits for symmetric hamiltonian systems in this paper we study the existence of symmetric homoclinic orbits for first order and second order hamiltonian systems with some symmetric hamiltonian functions

homoclinic solutions of some second order non autonomous systems abstract in this paper we investigate the existence of homoclinic solutions for the following second order non autonomous system q a q l t q w q t q 0 ds where a is an antisymmetric constant matrix l c r r n 2 is a symmetric and positive definite matrix for all t r w t q a t v q such that a r r is a continuous function and v c 1 r n r assuming that v q is subquadratic as q and some technical assumptions on a and l we establish two existence criteria to guarantee that ds has at least one nontrivial homoclinic solution by using a standard minimizing argument besides that in some particular case for the first time the uniqueness of homoclinic solutions of ds is also obtained recent results in the literature are generalized and significantly improved

the first order necessary conditions for nonsmooth variational and control problems the first order necessary conditions for nonsmooth problems of lagrange bolza multiple integral and optimal control are given the necessary conditions are expressed in terms of differential inclusions we deal with some new differentials that generalize the differential of frechet in particular the pontryagin maximum principle is proved without the assumption of continuous differentiability

fast homoclinic solutions for a class of damped vibration problems in this paper we deal with the existence and multiplicity of homoclinic solutions of the following damped vibration problemsu t q t u t l t u t w t u t 0 where l t and w t x are neither autonomous nor periodic in t our approach is variational and it is based on the critical point theory we prove existence and multiplicity results of fast homoclinic solutions under general growth conditions on the potential function moreover some open problems proposed by zhang and ruan are resolved our theorems appear to be the first such result

homoclinic solutions for a class of nonperiodic and noneven second order hamiltonian systems abstract the existence of homoclinic solutions is obtained for second order hamiltonian systems u t l t u t w t u t f t as the limit of the solutions of a sequence of nil boundary value problems which are obtained by the mountain pass theorem when l t and w t x are neither periodic nor even with respect to t

homoclinic solutions for a class of non autonomous subquadratic second order hamiltonian systems abstract in this paper we consider the existence of homoclinic solutions for the following second order non autonomous hamiltonian system hs q l t q w q t q 0 where l t c r r n 2 is a symmetric and positive definite matrix for all t r w t q a t q with a t r r is a positive continuous function and 1 2 is a constant adopting some other reasonable assumptions for l and w we obtain a new criterion for guaranteeing that hs has one nontrivial homoclinic solution by use of a standard minimizing argument in critical point theory recent results from the literature are generalized and significantly improved

extrapolation on lp μ we solve the extrapolation problem concerning bounded operators on lp that is we give end point estimates for sublinear operators t such that t lp lp is bounded with constant less than or equal to 1 p 1 m applications to the hardy littlewood maximal operator the hilbert transform and composition of operators are also given

a review of the parameter estimation problem of fitting positive exponential sums to empirical data exponential sum models are used frequently in heat diffusion diffusion of chemical compounds time series in medicine economics physical sciences and technology thus it is important to find good methods for the estimation of parameters in exponential sums in this paper we review and discuss results from the last forty years of research there are many different ways of estimating parameters in exponential sums and model a fit criterion which gives a valid result from the fit we find that a good choice is a weighted two norm objective function with weights based on the maximum likelihood ml criterion if the number of exponential terms is unknown statistical methods based on an information criterion or cross validation can be used to determine the optimal number it is suitable to use hybrid gauss newton gn and quasi newton algorithms to find the unknown parameters in the constrained weighted nonlinear least squares nlls problem formulated using an maximal likelihood ml objective function the problem is highly ill conditioned and it is crucial to find good starting values for the parameters to find the initial parameter values a modified prony method or a method based upon rewriting partial sums as geometrical sums is proposed

some results on connecting orbits for a class of hamiltonian systems abstract the existence of various kinds of connecting orbits is established for a certain hamiltonian system as well as its time dependent analogue for the autonomous case our main assumption is that v has a global maximum e g at x o and we find a various kinds of orbits terminating at o for the time dependent case v has a local but not global maximum at x o and we find a homoclinic orbit emanating from and terminating at o keywords periodic solution

existence and multiplicity of homoclinic orbits for the second order hamiltonian systems in this paper we study the following nonperiodic second order hamiltonian system u t l t u t ur t u t r where l t may not be uniformly positive definite for all t r and r t u is asymptotically quadratic in u as u by applying a generalized linking theorem in bartsch and ding 2006 8 we obtain the existence and multiplicity of homoclinic orbits for the above system

exponential interpolation theory and numerical algorithms we consider the problem of exponential interpolation and show that in some cases it can be solved with effective numerical procedures we show that the problem is closely related to gaussian quadrature and to the problem of partial realization in linear control theory

homoclinic orbits for superquadratic hamiltonian systems without a periodicity assumption abstract in this paper we consider the second order hamiltonian system q t v t q t f t where v t q k t q w t q under suitable conditions on the growth of w and k we establish the existence of a nontrivial homoclinic orbit without any assumption of periodicity on v this homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil boundary value problems which are obtained by the minimax methods

on the recovery and resolution of exponential relaxation rates from experimental data ii the optimum choice of experimental sampling points for laplace transform inversion in a previous paper bertero boccacci pike proc r soc lond a 383 15 1982 we investigated the benefits of a priori knowledge of finite support of the solution in the inversion of the laplace transform and determined the number of exponential components that could be recovered from given data in the presence of quantified amounts of noise the support of the data was assumed to be unrestricted in the present paper these calculations are extended to cover the case of a necessarily finite number of experimental data points we consider two cases uniform distribution and geometric distribution of data points in both cases the condition number of singular value inversions is minimized with respect to the placing of the data points for fixed numbers of data samples the results allow optimum placing of the experimental data points as a function of the ratio of given upper and lower bounds of the support of the solution the number of exponentials recoverable is less than in the unrestricted case but for 8 we find that with 32 linearly spaced data points optimally placed this reduction is rather small geometrical sampling of experimental data reduces further the number of sample points required for inversion for 8 we show that with 5 geometrically spaced data points points optimally placed the ill conditioning in the restoration of 2 to 4 exponential components is smaller than with 32 linearly spaced data samples this has important implications for the design of a number of scientific experiments and instruments