stability of neuronal pulses composed of concatenated unstable kinks we demonstrate that a traveling pulse solution emerging from the concatenation of two unstable kinks can be stable by means of stability analysis and numerical simulations we show the stability of neuronal pulses action potentials with increasing refractory periods which decompose into two radiationally unstable kinks in the limit these action potentials are solutions of an ultrarefractory version of the fitzhugh nagumo system

pulse bifurcation and transition to spatiotemporal chaos in an excitable reaction diffusion model we address the stability of solitary pulses as well as some other traveling structures near the onset of spatiotemporal chaos in a two species reaction diffusion model describing the oxidation of c

fitting partial differential equations to space time dynamics the partial differential equations pdes governing the dynamics of reaction diffusion systems are reconstructed from data representing the spatially extended systems the fitted equations are validated by a comparison of their numerical solutions and the input data and by computation of the isoclines of the fitted pdes

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

t points a codimension two heteroclinic bifurcation the local bifurcation structure of a heteroclinic bifurcation which has been observed in the lorenz equations is analyzed the existence of a particular heteroclinic loop at one point in a two dimensional parameter space a t point implies the existence of a line of heteroclinic loops and a logarithmic spiral of homoclinic orbits as well as countably many other topologically more complicatedt points in a small neighborhood in parameter space

multiple solutions for strongly resonant periodic systems abstract we considered a semilinear second order periodic system we assumed that the differential operator x x a x has zero as an eigenvalue and has no negative eigenvalues also we imposed a strong resonance condition with respect to the zero eigenvalue on the potential function f t x using the second deformation theorem we established the existence of at least two nontrivial solutions to do this we needed to conduct a detailed analysis of the cerami compactness condition which is actually of independent interest

existence of infinitely many periodic solutions for ordinary p laplacian systems abstract in this paper we study the existence and multiplicity of non trivial periodic solutions of ordinary p laplacian systems by using the minimax technique in critical point theory we also give an example to illustrate that the obtained results are new even in the case p 2

modelling patterns of agreement for nominal scales the measurement of agreement of repeat rating is the usual method of assessing the reliability of categorical scales measurement of agreement is also important in genetic twin studies based on categorical scales one of the most commonly used methods of analysis for both types of study is the kappa coefficient for scales with more than two categories one approach is to use a single summary kappa coefficient while this may be sufficient for many studies in some instances investigation of heterogeneity in the pattern of agreement may give additional insights as there may be greater agreement for some pairs of categories than for others in this paper kappa type coefficients are used to model heterogeneity in the pattern of agreement constraints are added to the heterogeneous model to obtain simplified models procedures for estimation confidence intervals and inference for these coefficients are described for the case of two ratings per subject for a single sample and for the comparison of two independent samples formulae for sample size and power calculation are derived using the non central chi squared distribution two simulation studies are carried out to check the empirical test size and power methods are illustrated by two examples involving nominal scales with three categories

existence theorems of periodic solutions for a class of damped vibration problems abstract in the present paper we research the following damped vibration problem 1 1 u t g t u t f t u t a e t 0 t u 0 u t u 0 u t 0 where t 0 g l 0 t r g t 0 t g s ds g t 0 and f 0 t r n r the variational principle is given and three existence theorems for periodic solutions are obtained

a comparison of statistical methods for clustered data analysis with gaussian error we investigate by simulation the properties of four different estimation procedures under a linear model for correlated data with gaussian error maximum likelihood based on the normal mixed linear model generalized estimating equations a four stage method and a bootstrap method that resamples clusters rather than individuals we pay special attention to the group randomized trials where the number of independent clusters is small cluster sizes are big and the correlation within the cluster is weak we show that for balanced and near balanced data when the number of independent clusters is small 10 the bootstrap is superior if analysts do not want to impose strong distribution and covariance structure assumptions otherwise ml and four stage methods are slightly better all four methods perform well when the number of independent clusters reaches 50

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 accumulation of eigenvalues in a stability problem abstract when two waves propagating in a one dimensional medium are locked together as a composite wave a natural question arises as to whether the new wave is stable an interesting and novel instability mechanism is exposed here in which a cascade of eigenvalues accumulates at a distinguished point in the unstable half plane the underlying assumption is that the transition between the two waves occurs at an unstable homogeneous steady state of the partial differential equations this causes the individual waves to have an unstable continuous spectrum but the instability of the full wave cannot be predicted from the configuration of these spectra alone

nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups in this paper we consider a class of resonant cooperative elliptic systems based on some new results concerning the computations of the critical groups and the morse theory we establish some new results about the existence and multiplicity of solutions under new classes of conditions it turns out that our main results sharply improve some known results in the literature

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

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

a matrix of kappa type coefficients to assess the reliability of nominal scales to investigate the reliability of nominal scales kraemer proposed a measurement model from which kappa coefficients could be derived more recently she suggested a matrix of coefficients as a comprehensive summary of reliability contrasting this with use of a single summary kappa statistic the main diagonal of the matrix consists of binary kappa coefficients for each category which measure the reliability of each category relative to all others while the off diagonal elements are correlation coefficients for pairs of categories the off diagonal elements were suggested as measures of confusion between categories schouten also suggested coefficients to assess confusion between pairs of categories which might be used as alternative off diagonal elements in a summary matrix the two types of off diagonal element will be compared it will be shown that schouten s coefficients can be expressed in terms of the parameters of kraemer s measurement model and that they are more easily interpreted as measures of confusion first the maximum value for schouten s coefficient is one secondly for any pair of categories schouten s coefficient equals the proportionate reduction in the probability of classifying a subject in one category of the pair having previously classified them in the other thirdly where the coefficient for a pair of categories is less than the summary kappa statistic it will be shown that combining these two categories will increase the value of the summary kappa statistic the methods of analysis are applied to data from a study of the reliability of psychiatric diagnosis and used to identify pairs of classifications between which there is substantial confusion c 1998 john wiley sons ltd

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

transient spatiotemporal chaos is extensive in three reaction diffusion networks extensive asymptotic spatiotemporal chaos is comprised of statistically similar subsystems that interact only weakly a systematic study of transient spatiotemporal chaos reveals extensive system behavior in all three reaction diffusion networks for various boundary conditions the lyapunov dimension the sum of positive lyapunov exponents and the logarithm of the transient lifetime grow linearly with the system size the unstable manifold of the chaotic saddle has nearly the same dimension as the saddle itself and the stable manifold is nearly space filling

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

traveling waves of calcium in a pancreatic acinar cells model construction and bifurcation analysis abstract we construct and study a model for intracellular calcium wave propagation with particular attention to pancreatic acinar cells the model is based on a model of the inositol trisphosphate ip3 receptor which assumes that calcium modulates the binding affinity of ip3 to the receptor two versions of the model one simpler than the other are studied numerically in both versions solitary waves in the excitable regime arise via homoclinic bifurcations in the traveling wave equations as the background concentration of ip3 is increased the wave speed increases and for some values of the ip3 concentration the initial pulse gives rise to secondary pulses that travel in both directions this can give rise to irregular spatio temporal behavior or to trains of pulses in the simpler model these secondary waves are related to the presence of a t point a heteroclinic cycle and an associated spiral of homoclinic orbits which terminate the branch of homoclinic orbits

higher order kappa type statistics for a dichotomous attribute in multiple ratings we introduce a sequence of parameters called canonical moments to characterize the predictive value of the pattern of consensus among kappa 1 ratings to an additional rating the usual kappa coefficient of agreement among ratings two or more is just the second canonical moment by using the higher canonical moments we can evaluate the consensus of multiple binary ratings

numerical bifurcation and stability analysis of solitary pulses in an excitable reaction diffusion medium abstract we present a systematic computer assisted study of the bifurcations and instabilities of solitary pulses in an excitable medium capable of displaying both stable pulse propagation and spatiotemporally chaotic dynamics over intervals of parameter space the reaction diffusion model used is of the activator inhibitor type only the activator diffuses in this medium the control parameters are the ratio of time scales of the activator and inhibitor dynamics and the excitation threshold this study focuses on travelling pulses their domain of existence and the bifurcations that render them unstable these pulses are approximated as a homoclinic orbits in a travelling wave ode frame and b as solutions of the full partial differential equation pde with periodic boundary conditions in large domains a variety of bifurcations in the travelling wave ode frame are observed including heteroclinic loops so called t points a r champneys and y a kuznetsov numerical detection and continuation of codimension 2 homoclinic bifurcations int j bif chaos 4 1994 785 h kokobu homoclinic and heteroclinic bifurcations of vectorfields japan j appl math 5 1988 455 instabilities in the full pde frame include both hopf bifurcations to modulated travelling waves involving the discrete pulse spectrum as well as transitions involving the continuous spectrum such as the so called backfiring transition m bar m hildebrand m eiswirth m falcke h engel and m neufeld chemical turbulence and standing waves in a surface reaction model the influence of global coupling and wave instabilities chaos 4 1994 499 the stability of modulated pulses is computed through numerical floquet analysis and a cascade of period doubling bifurcations is observed as well as certain global bifurcations these results corroborated by observations from direct numerical integration provide a skeleton around which many features of the overall complex spatiotemporal dynamics of the pde are organized

computations of critical groups and periodic solutions for asymptotically linear hamiltonian systems the purpose of this paper is two fold firstly we will give some parabolic like conditions which improve the well known angle conditions and allow further computations of the critical groups both at degenerate critical points and at infinity as an application we then consider the second order hamiltonian systems u t h t u t 0 t r where h r rn r is t periodic in its first variable and h is asymptotically linear both at origin and at infinity based on the computations of the critical groups and the morse theory we obtain the existence and multiplicity results for periodic solutions under new classes of conditions it turns out that our main results improve sharply some known results in the literature

a skeleton structure of self replicating dynamics abstract self replicating patterns srp have been observed in several chemical reaction models such as the gray scott gs model as well as in physical experiments watching these experiments computational and physical is like watching the more familiar coarsening processes but in reverse the number of unit localized patterns increases until they fill the domain completely self replicating dynamics then can be regarded as a transient process from a localized trigger to a stable stationery or oscillating turing pattern since it is a transient process it is very difficult to give a suitable definition to characterize srp it cannot be described in terms of well studied structures such as the attractor or a singular saddle orbit for a dynamical system in this paper we present a new point of view to describe the transient dynamics of srp over a finite interval of time we focus our attention on the basic mechanism causing srp from a global bifurcational point of view and take our clues from two model systems including the gs model a careful analysis of the anatomy of the global bifurcation diagram suggests that the dynamics of srp is related to a hierarchical structure of limit points of folding bifurcation branches in parameter regions where the branches have ceased to exist thus the skeleton structure mentioned in the title refers to the remains of bifurcation branches the aftereffects of which are manifest in the dynamics of srp one of the natural and important problems is about the existence of an organizing center from which the whole hierarchical structure of limit points emerges in our setting the numerics suggests a strong candidate for that i e bogdanov takens turing btt singularity together with the presence of a stable critical point and so this indicates a universality of the above structure in the class of equations sharing this characteristic

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

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

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 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 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

local stability theory of solitary pulses in an active medium abstract if the spatio temporal chaos of an extended active medium is driven by repulsive or attractive interaction among localized coherent structures such as kinks and pulses its dynamics can often be described by a low dimensional dynamical system this welcomed reduction in the degrees of freedom only occurs when the localized structures remain stable during their mutual interaction it is shown that the structures can be destroyed by two types of local disturbance an expanding radiation packet and a localized disturbance which travels with the structure these two instabilities and the bifurcations they induce select the proper coherent structure and specify the dynamics of the generalized kuramoto sivashinsky gks equation in an extended domain the possibility of describing pulse radiation interaction by resonance poles also suggests that a more general coherent structure theory can be developed

subharmonic solutions of second order subquadratic hamiltonian systems with potential changing sign abstract with the aid of some symplectic transformations the existence of subharmonic solutions of the second order hamiltonian system v x t x is considered where the potential v is subquadratic in x as x goes to infinity and can change sign with respect to t

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

nominal scale agreement among observers experiments are considered where each of a sample of subjects is assigned to one of c categories separately by each of a fixed or varying group of observers building on earlier publications general procedures are proposed to analyze agreements and disagreements among observers in the case of a varying group of observers it is shown that it is not necessary to demand a constant number of observers per subject in the case of a fixed group of observers the problem of missing data is considered the procedures are illustrated within the context of two clinical diagnosis examples in the first example it is investigated which categories are relatively hard to distinguish from one another a new theorem is applied that shows a useful property of the statistic kappa in the second example it is investigated if a subgroup of observers can be found with a significantly higher degree of interobserver agreement

on the new variational principles and duality for periodic solutions of lagrange equations with superlinear nonlinearities periodic problem 1 1 was studied in the 1980s by many authors forthe sublinear as well as for the superlinear case see e g 6 however we believe that our paper may contribute some new look at this problem this is because we propose to study 1 1 by duality methods in a waythat is to some extent analogous to the methods developed for 1 1 insublinear cases 2 3 6 8 some cases of 1 1 for superlinear v

multiple periodic solutions for second order discrete hamiltonian systems some existence and multiplicity results are obtained for periodic solutions of nonautonomous second order discrete hamiltonian systems with partially periodic potentials by using critical point theory

periodic solutions of higher dimensional discrete systems consider the second order discrete system where f c r r m r m f t m z f t z for any t z r r m and m is a positive integer by making use of critical point theory the existence of m periodic solutions of is obtained

absolute and convective instabilities of waves on unbounded and large bounded domains abstract instabilities of nonlinear waves on unbounded domains manifest themselves in different ways an absolute instability occurs if the amplitude of localized wave packets grows in time at each fixed point in the domain in contrast convective instabilities are characterized by the fact that even though the overall norm of wave packets grows in time perturbations decay locally at each given point in the unbounded domain wave packets are convected towards infinity in experiments as well as in numerical simulations bounded domains are often more relevant we are interested in the effects that the truncation of the unbounded to a large but bounded domain has on the aforementioned in stability properties of a wave these effects depend upon the boundary conditions that are imposed on the bounded domain we compare the spectra of the linearized evolution operators on unbounded and bounded domains for two classes of boundary conditions it is proved that periodic boundary conditions reproduce the point and essential spectrum on the unbounded domain accurately spectra for separated boundary conditions behave in quite a different way firstly separated boundary conditions may generate additional isolated eigenvalues secondly the essential spectrum on the unbounded domain is in general not approximated by the spectrum on the bounded domain instead the so called absolute spectrum is approximated that corresponds to the essential spectrum on the unbounded domain calculated with certain optimally chosen exponential weights we interpret the difference between the absolute and the essential spectrum in terms of the convective behavior of the wave on the unbounded domain in particular it is demonstrated that the stability of the absolute spectrum implies convective instability of the wave but that convectively unstable waves can destabilize under domain truncation the theoretical predictions are compared with numerical computations

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

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

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

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

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

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

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 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

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 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

periodic solutions of second order superquadratic hamiltonian systems with potential changing sign ii abstract we consider the periodic solutions of the second order hamiltonian system x x h t v x with v being positive and superquadratic at infinity h being c 1 2 periodic sign changing and all zeros being simple some existence and multiplicity results of periodic solutions are given

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 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 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

on variational methods for a class of damped vibration problems abstract in the present paper the following damped vibration problems 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 and 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 are studied where t 0 0 q l 1 0 t r q t 0 t q s d s a t a i j t is a symmetric n n matrix valued function defined in 0 t with a i j l 0 t for all i j 1 2 n and there exists a positive constant such that a t 2 for all r n and a e t 0 t the variational principles are given and an existence theorem and three multiplicity theorems of periodic solutions are obtained

existence of forced oscillations for some nonlinear differential equations abstract this article studies the existence of t periodic solutions for systems of nonlinear second order ordinary differential equations assuming function v to be superquadratic it is shown that this system possesses infinitely many t periodic solutions the proof of this result rests on showing that certain homotopy groups of level sets of the functional associated with the system are not trivial some more general results concerning systems of another type are also presented

existence of critical point for abstract resonant problems with unbounded nonlinearities and applications to differential equations abstract in this paper using well known variational methods we prove a general abstract theorem on the existence of a critical point for resonant problems with unbounded nonlinearities and then apply it to ordinary and partial differential equations with generalized ahmad lazer paul conditions the abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations

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

periodic solutions to differential systems with unbounded or periodic nonlinearities we investigate the existence of multiple solutions of differential systems of josephson type with unbounded or periodic nonlinearities some new results are obtained and some results in the literature are improved

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

pulse bifurcations and instabilities in an excitable medium computations in finite ring domains we investigate the instabilities and bifurcations of traveling pulses in a model excitable medium in particular we discuss three different scenarios involving either the loss of stability or disappearance of stable pulses in numerical simulations beyond the instabilities we observe replication of pulses backfiring resulting in complex periodic or spatiotemporally chaotic dynamics as well as modulated traveling pulses we approximate the linear stability of traveling pulses through computations in a finite albeit large domain with periodic boundary conditions the critical eigenmodes at the onset of the instabilities are related to the resulting spatiotemporal dynamics and act upon the back of the pulses the first scenario has been analyzed earlier m g zimmermann et al physica d 110 92 1997 for high excitability low excitation threshold it involves the collision of a stable pulse branch with an unstable pulse branch in a so called t point in the framework of traveling wave ordinary differential equations pulses correspond to homoclinic orbits and the t point to a double heteroclinic loop we investigate this transition for a pulse in a domain with finite length and periodic boundary conditions numerical evidence of the proximity of the infinite domain t point in this setup appears in the form of two saddle node bifurcations alternatively for intermediate excitation threshold an entire cascade of saddle nodes causing a spiraling of the pulse branch appears near the parameter values corresponding to the infinite domain t point backfiring appears at the first saddle node bifurcation which limits the existence region of stable pulses the third case found in the model for large excitation threshold is an oscillatory instability giving rise to breathing traveling pulses that periodically vary in width and speed

periodic and subharmonic solutions of a class of subquadratic second order hamiltonian systems some solvability conditions of periodic and subharmonic solutions are obtained for a class of subquadratic nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

periodic solutions to hamiltonian inclusions abstract we prove the existence of periodic trajectories of hamiltonian inclusions which reduce to the usual hamiltonian equations in the presence of smoothness this is accomplished via a direct variational principle involving a new action integral in an extended sense

multiplicity of periodic solutions for a class of second order perturbed hamiltonian systems abstract consider the following second order perturbed hamiltonian systems u t f u u g t u t r u 0 u t u 0 u t 0 t 0 where f u k u w u k w c 2 r n r g c 2 r r n r with g t t u g t u k and w is even but g t u maybe has no parity in u assume that w is superquadratic and g is subquadratic at the infinity and k satisfies pinched condition the existence of infinitely many periodic solutions of the above perturbed systems is proved via the bolle s perturbation method which is a generalization of 21 theorem 1 2 and 3 theorem 2 in some sense

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

an abstract theorem on the existence of periodic motions of non autonomous lagrange systems abstract in this paper we established an abstract theorem on the existence of periodic solutions for lagrange systems under tonelli framework strictly convex and superlinear completeness of phase flow which is based on the principle of least action in geometry and dynamics an example of the application of the abstract theorem is given and the existence of periodic solutions for a class of time periodic lagrange systems will be proved

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

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