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 a class of asymptotically p linear aperiodic p laplacian systems abstract by applying a variant version of mountain pass theorem in critical point theory the existence of homoclinic solutions is obtained for the following asymptotically p linear aperiodic p laplacian system d dt u t p 2 u t k t u t w t u t 0 where p 1 t r u r n k w c 1 r r n r are not periodic in t and w is asymptotically p linear at infinity

existence of infinitely many homoclinic orbits in discrete hamiltonian systems abstract by using the symmetric mountain pass theorem we establish some existence criteria to guarantee the second order self adjoint discrete hamiltonian system p n u n 1 l n u n w n u n 0 has infinitely many homoclinic orbits where n z u r n p l z r n n and w z r n r are no periodic in n our conditions on the potential w n x are rather relaxed

homoclinic solutions for a class of subquadratic second order hamiltonian systems in this paper we study the existence of infinitely many homoclinic solutions for a class of subquadratic second order hamiltonian systems by using the variant fountain theorem we obtain a new criterion for guaranteeing that second order hamiltonian systems has infinitely many homoclinic solutions recent results from the literature are generalized and significantly improved an example is also given in this paper to illustrate our main results

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

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

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 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

homoclinic solutions for a class of second order hamiltonian systems abstract some new results for the existence of homoclinic orbits are obtained for the second order hamiltonian systems u t v t u t f t where 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 our assumptions on k and f are rather loose

homoclinic solutions for nonautonomous second order hamiltonian systems with a coercive potential we shall be concerned with the existence of homoclinic solutions for the second order hamiltonian system q vq t q f t where t r and q rn a potential v c1 r rn r is t periodic in t coercive in q and the integral of v 0 over 0 t is equal to 0 a function f r rn is continuous bounded square integrable and f 0 we will show that there exists a solution q0 such that q0 t 0 and q 0 t 0 as t although q 0 is not a solution of our system we are to call q0 a homoclinic solution it is obtained as a limit of 2kt periodic orbits of a sequence of the second order differential equations

new existence of homoclinic orbits for a second order hamiltonian system abstract by using the mountain pass theorem and the symmetric mountain pass theorem we establish some existence criteria to guarantee that the second order hamiltonian system u t a t u t p 2 u t w t u t 0 has at least one or infinitely many homoclinic orbits where t r u r n a c r r and w c 1 r r n r are not periodic in t our conditions on the potential w t x are rather relaxed

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

non periodic damped vibration systems with sublinear terms at infinity infinitely many homoclinic orbits abstract in this paper we study a class of non periodic damped vibration systems with subquadratic terms we obtain infinitely many nontrivial homoclinic orbits by a variant fountain theorem developed recently by zou to the best of our knowledge there is no result published concerning the existence of infinitely many homoclinic orbits for this class of non periodic damped vibration systems with subquadratic terms at infinity

torsion subgroups of rational elliptic curves over the compositum of all d4 extensions of the rational numbers abstract let e q be an elliptic curve and let q d 4 be the compositum of all extensions of q whose galois closure has galois group isomorphic to a quotient of a subdirect product of a finite number of transitive subgroups of d 4 in this article we first show that q d 4 is in fact the compositum of all d 4 extensions of q and then we prove that the torsion subgroup of e q d 4 is finite and determine the 24 possibilities for its structure we also give a complete classification of the elliptic curves that have each possible torsion structure in terms of their j invariants

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

periodic and homoclinic solutions generated by impulses for asymptotically linear and sublinear hamiltonian system in this paper we get the existence of periodic and homoclinic solutions for a class of asymptotically linear or sublinear hamiltonian systems with impulsive conditions via variational methods however without impulses there is no homoclinic or periodic solution for the system considered in this paper moreover our results can be used to study the existence of periodic and homoclinic solutions of difference equations

homoclinic solutions for nonautonomous second order hamiltonian systems with a coercive potential abstract a new existence result of homoclinic orbits is obtained for the second order hamiltonian systems u t f t u t f t where f t x is periodic with respect to t this result generalizes some known results in the literature

poisson intensity estimation for tomographic data using a wavelet shrinkage approach we consider a two dimensional 2 d problem of positron emission tomography pet where the random mechanism of the generation of the tomographic data is modeled by poisson processes the goal is to estimate the intensity function which corresponds to emission density using the wavelet vaguelette decomposition wvd we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on besov function classes furthermore we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term

homoclinic orbits for asymptotically linear hamiltonian systems we study the existence of homoclinic orbits for first order time dependent hamiltonian systems z jhz z t where h z t depends periodically on t and hz z t is asymptotically linear in z as z we also consider an asymptotically linear schrodinger equation in rn

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

homoclinic orbits for first order hamiltonian systems abstract we establish the existence of homoclinic orbits for a class of first order time dependent hamiltonian systems z jh z t z without any periodicity assumption on h

homoclinic solutions for a class of second order hamiltonian systems with locally defined potentials abstract in this paper we study the existence of infinitely many homoclinic solutions for a class of second order hamiltonian systems u l t u w u t u 0 t r where l t is unnecessarily positive definite for all t r and w t u is only locally defined near the origin with respect to u and not assumed to be periodic with respect to t

homoclinic solutions for some second order non autonomous hamiltonian systems without the globally superquadratic condition abstract this paper deals with the existence of homoclinic solutions for the following second order non autonomous hamiltonian system hs q v q t q f t where v c 1 r r n r v t q k t q w t q is t periodic in t f is aperiodic and belongs to l 2 r r n under the assumptions that k satisfies the pinching condition b 1 q 2 k t q b 2 q 2 w t q is not globally superquadratic on q and some additionally reasonable assumptions we give a new existence result to guarantee that hs has a homoclinic solution q t emanating from 0 the homoclinic solution q t is obtained as a limit of 2 k t periodic solutions of a sequence of the second order differential equations and these periodic solutions are obtained by the use of a standard version of the mountain pass theorem recent results in the literature are generalized and significantly improved