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

forced vibrations of superquadratic hamiltonian systems on etudie l existence des solutions t periodiques ter t 0 du systeme hamiltonien suivant z gh z f t ou g est la matrice asymetrique standard

infinitely many nontrivial periodic solutions for damped vibration problems with asymptotically linear terms in this paper we study a class of damped vibration problem with asymptotically quadratic terms at infinity we obtain infinitely many nontrivial periodic solutions by variational method to the best of our knowledge there is no published result focusing on this class of damped vibration problem with asymptotically quadratic terms at infinity

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 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

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

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

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

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

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

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

new results for perturbed hamiltonian systems with impulses abstract in this paper we study the existence of three solutions for second order impulsive hamiltonian systems by using a variational method and some critical points theorems of b ricceri we obtain some new criteria for guaranteeing that the impulsive hamiltonian systems have three solutions some recent results are extended and improved some examples are presented to demonstrate the application of our main results

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

memory induced anomalous dynamics emergence of diffusion subdiffusion and superdiffusion from a single random walk model we present a random walk model that exhibits asymptotic subdiffusive diffusive or superdiffusive behavior in different parameter regimes this appears to be an instance of a single random walk model leading to all three forms of behavior by simply changing parameter values furthermore the model offers the great advantage of analytical tractability our model is non markovian in that the next jump of the walker is probabilistically determined by the history of past jumps it also has elements of intermittency in that one possibility at each step is that the walker does not move at all this rich encompassing scenario arising from a single model provides useful insights into the source of different types of asymptotic behavior

exact solution of an anisotropic 2d random walk model with strong memory correlations over the last decade there has been progress in understanding one dimensional non markovian processes via analytic sometimes exact solutions the extension of these ideas and methods to two and higher dimensions is challenging we report the first exactly solvable two dimensional 2d non markovian random walk model belonging to the family of the elephant random walk model in contrast to levy walks or fractional brownian motion such models incorporate memory effects by keeping an explicit history of the random walk trajectory we study a memory driven 2d random walk with correlated memory and stops i e pauses in motion the model has an inherent anisotropy with consequences for its diffusive properties thereby mixing the dominant regime along one dimension with a subdiffusive walk along a perpendicular dimension the anomalous diffusion regimes are fully characterized by an exact determination of the hurst exponent we discuss the remarkably rich phase diagram as well as several possible combinations of the independent walks in both directions the relationship between the exponents of the first and second moments is also unveiled

on the multi dimensional elephant random walk the purpose of this paper is to investigate the asymptotic behavior of the multi dimensional elephant random walk merw it is a non markovian random walk which has a complete memory of its entire history a wide range of literature is available on the one dimensional erw surprisingly no references are available on the merw the goal of this paper is to fill the gap by extending the results on the one dimensional erw to the merw in the diffusive and critical regimes we establish the almost sure convergence the law of iterated logarithm and the quadratic strong law for the merw the asymptotic normality of the merw properly normalized is also provided in the superdiffusive regime we prove the almost sure convergence as well as the mean square convergence of the merw all our analysis relies on asymptotic results for multi dimensional martingales

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

existence and multiplicity of periodic solutions for a class of second order hamiltonian systems we study the existence and multiplicity of periodic solutions of the following second order hamiltonian system email protected t email protected k t u t w t u t 0 the existence of a nontrivial periodic solution is obtained when w is asymptotically linear at infinity and the existence of infinitely many periodic solutions is also obtained when w is superlinear

infinitely many solutions for cooperative elliptic systems with odd nonlinearity abstract by using the minimax technique in critical point theory we establish the existence of infinitely many solutions for a class of cooperative elliptic systems with odd nonlinearities our results improve several known results in the literature in contrast with the existing ones our results only demand restrictions on the behavior of the nonlinearities at infinity

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

solutions for resonant elliptic systems with nonodd or odd nonlinearities we consider by minimax techniques a class of cooperative elliptic systems at resonance if the nonlinear term is nonodd we establish some new existence theorems about nontrivial solutions if the nonlinearity is odd we obtain existence of infinitely many solutions a topic about which very little is known

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

elephants can always remember exact long range memory effects in a non markovian random walk we consider a discrete time random walk where the random increment at time step t depends on the full history of the process we calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter p at a critical value p 1 c 1 2 where memory effects vanish there is a transition from a weakly localized regime where the walker elephant returns to its starting point to an escape regime inside the escape regime there is a second critical value where the random walk becomes superdiffusive the probability distribution is shown to be governed by a non markovian fokker planck equation with hopping rates that depend both on time and on the starting position of the walk on large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time dependent spring constant k 2p 1 t the solution of this problem is a gaussian distribution with time dependent mean and variance which both depend on the initiation of the process

syzygies of canonical curves and special linear series 0 introduction 105 1 line bundles on scrolls 109 2 scrolls and pencils 113 3 syzygies of a subvariety of a scroll 115 4 canonical curves 118 5 on the equation of rational surfaces 121 6 d gonal curves for d 5 126 7 proof of the main result 131 references 136

a periodic solution for a second order asymptotically linear hamiltonian system abstract we study the existence of a periodic solution of the following second order hamiltonian system u t f t u t 0 t 0 t where f t x k t x w t x assuming that k satisfies the pinching condition and w is asymptotically linear at infinity the existence of a nontrivial periodic solution is obtained via the mountain pass theorem

existence and multiplicity of rotating periodic solutions for resonant hamiltonian systems abstract in the present paper we consider a class of resonant hamiltonian systems x j h x t x in r 2 n we will use saddle point reduction morse theory combining the technique of penalized functionals to obtain the existence of nontrivial rotating periodic solutions i e x t t q x t for any t r with t 0 and q an symplectic orthogonal matrix in the case q k i 2 n for any positive integer k such a rotating periodic solution is just a quasi periodic solution moreover if h is even in x we will give the multiplicity of nontrivial rotating periodic solutions by using two abstract critical theorems and previous techniques

periodic solutions for a class of nonautonomous second order hamiltonian systems abstract in this paper some existence theorems of periodic solutions of a class of the nonautonomous second order hamiltonian systems x t b t x t h t x t 0 t 0 t are obtained by a mountain pass theorem and a local link theorem