on homoclinic orbits for a class of noncoercive superquadratic hamiltonian systems abstract in this paper we prove the existence of homoclinic solutions for a class of noncoercive first order hamiltonian systems j x m t x u g t u x 0 by the minimax methods in critical point theory specially a generalized mountain pass theorem when u is a linear operator with adjoint u and g t y satisfies the superquadratic condition g t x y 2 as y uniformly in t and need not satisfy the global ambrosetti rabinowitz condition

existence of homoclinic solutions for a class of second order systems abstract in this paper we study the existence of nontrivial homoclinic solutions for a second order differential equation of the form q a q l t q w q t q 0 here we assume that a is a antisymmetric constant matrix l t is a continuous positive definite symmetric matrix valued function depending periodically on t and assume that potential w is asymptotically quadratic as q 0 and q

solutions of nonlinear dirac equations abstract we study the dirac equation i t i c k 1 3 k k m c 2 g x and obtain existence and multiplicity results of stationary solutions for several classes of nonlinearities g r 3 c 4 r modeling various types of interaction a typical result states that if g x u depends periodically on x and is even in u the problem has infinitely many geometrically different localized solutions the arguments are variational the associated lagrangian functional is strongly indefinite and the palais smale condition does not hold we apply some recently developed critical point theorems

determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

homoclinic orbits on compact hypersufaces in 293 1293 1293 1 of restricted contact type consider a smooth hamiltonian system in 2n dot x jh x the energy surface x h x h 0 being compact and 0 being a hyperbolic equilibrium we assume moreover that 0 is of restricted contact type these conditions are symplectically invariant by a variational method we prove the existence of an orbit homoclinic i e non constant and doubly asymptotic to 0

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

existence of infinitely many homoclinic orbits for fourth order difference systems containing both advance and retardation abstract by using the symmetric mountain pass theorem we establish some existence criteria to guarantee the fourth order difference system 4u n 2 q n u n f n u n 1 u n u n 1 have infinitely many homoclinic orbits where n z u r n q z r n n and f z r 3 n r are no periodic in n

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

existence and multiplicity results for heteroclinic orbits of second order hamiltonian systems abstract connecting orbits of nonlinear differential equations have long been studied in the dynamical systems literature generally in a setting involving perturbations and using a melnikov function in this article we consider a class of second order hamiltonian systems which possess infinitely many or finite number of equilibria using variational arguments and penalization methods we obtain the existence of multiple heteroclinic orbits joining pairs of equilibria

existence and multiplicity of homoclinic orbits for potentials on unbounded domains we study the system in r n where v is a potential with a strict local maximum at 0 and possibly with a singularity first using a minimising argument we can prove the existence of a homoclinic orbit when the component of x r n v x containing 0 is an arbitrary open set in the case unbounded we allow v x to go to 0 at infinity although at a slow enough rate then we show that the presence of a singularity in implies that a homoclinic solution can also be found via a minimax procedure and comparing the critical levels of the functional associated to the system we see that the two solutions are distinct whenever the singularity is not too far from 0

genericity of the multibump dynamics for almost periodic duffing like systems in this paper we consider slowly oscillating perturbations of almost periodic du ng like systems i e systems of the form u u a t t w0 u t r u rn where w c2n rn r is superquadratic and a and are positive and almost periodic by variational methods we prove that if 0 is small enough then the system admits a multibump dynamics as a corollary we get that the system u u a t w0 u t r u rn admits multibump solutions whenever a a where a is an open dense subset of a c r r a is almost periodic and a t 0 t r

homoclinic orbits for a class of first order nonperiodic asymptotically quadratic hamiltonian systems with spectrum point zero in this paper we study the existence and multiplicity of homoclinic orbits for a class of first order nonperiodic hamiltonian systems by applying two recent critical point theorems for strongly indefinite functionals we give some new criteria to guarantee that hamiltonian systems with asymptotically quadratic terms and spectrum point zero have at least one and a finite number of pairs of homoclinic orbits under some adequate conditions respectively

infinitely many homoclinic solutions for a class of subquadratic second order hamiltonian systems in this paper we mainly consider the existence of infinitely many homoclinic solutions for a class of subquadratic second order hamiltonian systems u l t u w u t u 0 where l t is not necessarily positive definite and the growth rate of potential function w can be in 1 3 2 using the variant fountain theorem we obtain the existence of infinitely many homoclinic solutions for the second order hamiltonian systems

homoclinic orbits and subharmonics for nonlinear second order difference equations abstract we show the existence of a nontrivial homoclinic orbit and subharmonic solutions for a class of second order difference equations by applying the mountain pass theorem relying on ekeland s variational principle and the diagonal method and the homoclinic orbit as the limit of the subharmonics a completely new way is provided for dealing with the existence of solutions for difference equations

infinitely many solutions for diffusion equations without symmetry abstract we consider the following diffusion system t u x u b t x x u v x u h v t x u v t v x v b t x x v v x v h u t x u v t x r r n which is an unbounded hamiltonian system in l 2 r r n r 2 m z u v r r n r m r m b c r r n r n v c r n r and h c 1 r r n r 2 m r suppose that h b and v depend periodically on t and x and that h t x z is superquadratic in z as z without a symmetry assumption on h we establish the existence of infinitely many geometrically distinct solutions via a variational approach

a global condition for periodic duffing like equations we study duffing like equations of the type q qa t w q with a e c r r periodic we prove that if the stable and unstable manifolds to the origin do not coincide then the system exhibits positive topological entropy

existence of infinitely many homoclinic orbits for nonperiodic superquadratic hamiltonian systems abstract in this paper we study the following nonperiodic hamiltonian system z j h z t z where h t z is superquadratic in z r 2 n as z by applying a generalized linking theorem for strongly indefinite functionals we obtain infinitely many homoclinic orbits for the above system

infinitely many solutions for a class of nonlinear dirac equations without symmetry abstract this paper is concerned with the multiplicity of solutions for the nonlinear dirac equations i k 1 3 k k u v x a u u f u x u without symmetry assumption on f we establish the existence of infinitely many geometrically distinct solutions for superquadratic as well as asymptotically quadratic nonlinearities via variational approach

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

on uniqueness of recovery of a discontinuous conductivity coefficient on considere le probleme de retrouver le coefficient a de l equation elliptique div a u 0 dans un domaine avec la condition aux limites u sur quand u n est donnee pour tout regulier on demontre l unicite pour a a 0 b discontinu ou est la fonction indicateur d un ensemble ouvert a o est une fonction c 2 donnee et b est une fonction c 2 inconnue

universal connections gauge anomalies and lie group cohomology the geometric interpretation due to thierry mieg 1980 of the ghost field as certain components of an ehresmann connection on the total space of a principal bundle and of the brs transformation as part of the exterior derivative on the total space is discussed and amended to incorporate the spacetime dependence of the ghost field using this interpretation it is shown that non trivial solutions to the wess zumino consistency condition for gauge anomalies are related to non trivial de rham cohomology of the lie group

uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects abstract this paper considers the inverse problem of scattering of time harmonic acoustic and electromagnetic plane waves by a bounded inhomogeneous penetrable obstacle with embedded objects inside a new method is proposed to prove that the inhomogeneous penetrable obstacle can be uniquely determined from the far field pattern at a fixed frequency disregarding its contents our method is based on constructing a well posed interior transmission problem in a small domain associated with the helmholtz or modified helmholtz equation and the maxwell or modified maxwell equations a key role is played by the smallness of the domain which ensures that the lowest transmission eigenvalue is large so that a given wave number k is not an eigenvalue of the interior transmission problem another ingredient in our proofs is a priori estimates of solutions to the transmission scattering problems with data in l p 1 p 2 which are established in this paper by using the integral equation method a main feature of the new method is that it can deal with the acoustic and electromagnetic cases in a unified way and can be easily applied to deal with inverse scattering by unbounded rough interfaces

homoclinic solutions of hamiltonian systems with symmetry abstract we prove the existence of infinitely many homoclinic solutions for a first order hamiltonian system symmetric with respect to an action of a compact lie group by means of variational methods we make no convexity assumption on the hamiltonian

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 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 a class of second order hamiltonian systems abstract a new result for existence of homoclinic orbits is obtained for the second order hamiltonian systems u t l t u t w 1 t u t w 2 t u t f t where t r u r n and w 1 w 2 c 1 r r n r and f c r r n are not necessary periodic in t this result generalizes and improves some existing results in the literature

homoclinics for asymptotically quadratic and superquadratic hamiltonian systems abstract in this paper we find new conditions which are different from those used in previous related studies to ensure the existence of infinitely many homoclinic orbits for the second order hamiltonian systems of the form q v q t q here we assume that v t q depends periodically on t and assume on q that v t q is asymptotically quadratic at q 0 and is as q either asymptotically quadratic or superquadratic as well as the new conditions

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

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

superfiber bundle structure of gauge theories with faddeev popov fields in this work the mathematical structure of principal superfiber bundle ps is used to give a geometrical description of gauge theories the base space of ps is an s4 2 supermanifold xs four commuting and two anticommuting variables and the structure group an sn 0 supergroup gs where n is the dimension of the gauge group for the classical theory the body of ps is the usual principal fiber bundle p of gauge theories gauge and faddeev popov fields arise as superfields components of the connections in ps in a local coordinate system brs becchi rouet and stora and anti brs transformations are gauge transformations in ps of parameters the ghost and antighost superfields respectively in the case of soul flat connections which are connections in ps coming from connections in p the brs and anti brs transformations are finite translations along the anticommuting directions of xs and generate an s0 2 supergroup

homoclinics and heteroclinics for a class of conservative singular hamiltonian systems abstract we consider an autonomous hamiltonian system u v u 0 where the potential v r 2 r has a strict global maximum at the origin and a singularity at some point 0 under some compactness conditions on v at infinity and around the singularity we study the existence of homoclinic orbits to 0 winding around we use a sufficient and in some sense necessary geometrical condition on v to prove the existence of infinitely many homoclinics each one being characterized by a distinct winding number around moreover under the condition there exists a minimal non contractible periodic orbit and we establish the existence of a heteroclinic orbit from 0 to this connecting orbit is obtained as the limit in the c 1 loc topology of a sequence of homoclinics with a winding number larger and larger

geometrical interpretation of brst symmetry in topological yang mills higgs theory we study the topological yang mills higgs theories in two and three dimensions and the topological yang mills theory in four dimensions in a unified framework of superconnections in this framework we first show that a classical action of topological yang mills type can provide all three classical actions of these theories via appropriate projections then we obtain the becchi rouet stora tyutin brst and anti brst transformation rules encompassing these three topological theories from an extended definition of curvature and a geometrical requirement of the bianchi identity this is an extension of perry and teo s work in the topological yang mills case finally comparing this result with our previous treatment in which we used the modified horizontality condition we provide a meaning of the bianchi identity from the brst symmetry viewpoint and thus interpret the brst symmetry in a geometrical setting

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

connecting orbits for some classes of almost periodic lagrangian systems abstract the existence is proved by means of variational arguments of infinitely many heteroclinic solutions connecting possibly degenerate equilibria for a class of almost periodic lagrangian system an analogous multiplicity result is then established for homoclinic solutions of systems with an almost periodic singular potential

periodic and homoclinic solutions of extended fisher kolmogorov equations in this paper we study the existence of periodic solutions of the fourth order equations uiv pu a x u b x u3 0 and uiv pu a x u b x u3 0 where p is a positive constant and a x and b x are continuous positive 2l periodic functions the boundary value problems p1 and p2 for these equations are considered respectively with the boundary conditions u 0 u l u 0 u l 0 existence of nontrivial solutions for p1 is proved using a minimization theorem and a multiplicity result using clark s theorem existence of nontrivial solutions for p2 is proved using the symmetric mountain pass theorem we study also the homoclinic solutions for the fourth order equation uiv pu a x u b x u2 c x u3 0 where p is a constant and a x b x and c x are periodic functions the mountain pass theorem of brezis and nirenberg and concentration compactness arguments are used

existence and exponential decay of homoclinics in a nonperiodic superquadratic hamiltonian system abstract this paper deals with existence and exponential decay of homoclinic orbits in the first order hamiltonian system z j h z t z where the hamiltonian function h t z is nonperiodic in t r and superquadratic in z r 2 n with certain mild conditions we obtain the solutions via variational methods for strongly indefinite problems

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

on uniqueness in the general inverse transmisson problem in this paper we demonstrate uniqueness of a transparent obstacle of coefficients of rather general boundary transmission condition and of a potential coefficient inside obstacle from partial dirichlet to neumann map or from complete scattering data at fixed frequency the proposed transmission problem includes in particular the isotropic elliptic equation with discontinuous conductivity coefficient uniqueness results are shown to be optimal hence the considered form can be viewed as a canonical form of isotropic elliptic transmission problems proofs use singular solutions of elliptic equations and complex geometrical optics determining an obstacle and boundary conditions i e reflecting and transmitting properties of its boundary and interior is of interest for acoustical and electromagnetic inverse scattering for modeling fluid structure interaction and for defects detection

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

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

generic type results for chaotic dynamics in equations with periodic forcing terms abstract we prove that a class of equations containing the classical periodically forced pendulum problem displays the main features of chaotic dynamics for a set of forcing terms open and dense in suitable spaces the approach is based on global variational methods

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

geometrical structure of faddeev popov fields and invariance properties of gauge theories let pn be the trivial principal bundle with structural group g and base space pn 1 p1 being the usual fiber bundle of gauge theories in order to give a geometrical interpretation to the faddeev popov fields as well as to the becchi rouet and stora transformations we need to use the fiber bundle p3 the gauge fields and the faddeev popov ghost and antighost fields appear as part of certain 1 forms defined on the base space p2 the anticommuting character of the ghost and antighost fields is essentially due to their identification with 1 forms the becchi rouet and stora transformations are identified with generalized infinitesimal gauge transformations on p3 of parameters related to the ghost fields we obtain a further invariance of the action given by a similar generalized infinitesimal gauge transformation on p3 related to the antighost fields

homoclinic orbits in reversible systems and their applications in mechanics fluids and optics abstract this survey article reviews the theory and application of homoclinic orbits to equilibria in reversible continuous time dynamical systems where the homoclinic orbit and the equilibrium are both reversible the focus is on even order reversible systems in four or more dimensions local theory generic argument and global existence theories are examined for each qualitatively distinct linearisation several recent results such as coalescence caused by non transversality and the reversible orbit flip bifurcation are covered a number of open problems are highlighted applications are reviewed to systems arising from a variety of disciplines with the aid of numerical methods three examples are presented in detail one of which is infinite dimensional

first order elliptic systems and the existence of homoclinic orbits in hamiltonian systems and h r x r 2 r is smooth by a homoclinic or a doubly asymptotic orbit to y where y is a periodic solution of 1 we mean a solution x y of 1 such that i x 0 y t l 0 as i tl oo finding homoclinic orbits in systems like 1 can be quite difficult in the case when y is a hyperbolic orbit this is equivalent to showing that the stable and unstable manifold of y intersect in some situation this can be done by melnikov s method recently some progress has been made by applying variational methods coti zelati and ekeland showed in 3 using dual variational methods that 1 has at least one homoclinic orbit if h satisfies some convexity and growth assumptions in their proof the convexity assumption enters in a crucial way already in the set up of the variational problem variational methods have been used by benci and giannoni 2 who studied homoclinic orbits on compact riemannian manifolds and by p rabinowitz in 9 who proved existence of heteroclinic orbits on the n dimensional torus as well as their multiplicity in 2 and 9 only special hamiltonian of lagrangian type are studied the associated variational problem is then at least semi definite the

topological yang mills theory from non commutative geometry it will be shown that the topological yang mills theory of witten can be induced from the usual yang mills theory of the second rank antisymmetric tensor field when the matrix derivative of non commutative geometry proposed by connes is incorporated in the superconnection framework it is done by identifying consistently the antisymmetric tensor field b with the usual field strength f by b f

existence and multiplicity results of homoclinic solutions for fractional hamiltonian systems abstract in this paper by the critical point theory we consider the existence and multiplicity of solutions for the following fractional differential equation t d d t u t l t u t w t u t t r where 1 2 1 d t and t d are left and right liouville weyl fractional derivatives of order on the whole axis r respectively u r n l t is positive definite symmetric matrix for all t r and w r r n r is a suitably chosen function

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

multibump solutions for quasilinear elliptic equations abstract the current paper is concerned with constructing multibump type solutions for a class of quasilinear schrodinger type equations including the modified nonlinear schrodinger equations our results extend the existence results on multibump type solutions in coti zelati and rabinowitz 1992 17 to the quasilinear case our work provides a theoretic framework for dealing with quasilinear problems which lack both smoothness and compactness by using more refined variational techniques such as gluing techniques morse theory lyapunov schmidt reduction etc

multibump solutions for quasilinear elliptic equations with critical growth the current paper is concerned with constructing multibump solutions for a class of quasilinear schrodinger equations with critical growth this extends the classical results of coti zelati and rabinowitz commun pure appl math 45 1217 1269 1992 for semilinear equations as well as recent work of liu wang and guo j funct anal 262 4040 4102 2012 for quasilinear problems with subcritical growth the periodicity of the potentials is used to glue ground state solutions to construct multibump bound state solutions

supermanifolds and brs transformations we use a supermanifold formalism to support a geometrical interpretation of a recently proposed superfield formulation of brs becchi ronet stora and anti brs transformations

homoclinic orbits for a singular second order neutral differential equation using critical point theory and an approximation method we study the existence of homoclinic orbits for a singular second order neutral differential difference equations

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

homoclinic orbits on compact manifolds abstract under a suitable assumption on the potential energy v we prove the existence of a homoclinic orbit of the equation dt x t grad v x t 0 x m where m is a compact riemannian manifold our assumption is satisfied for instance if the function v has a unique nondegenerate maximum point

determining a magnetic schrodinger operator from partial cauchy data in this paper we show in dimension n 3 that knowledge of the cauchy data for the schrodinger equation in the presence of a magnetic potential measured on possibly very small subsets of the boundary determines uniquely the magnetic field and the electric potential we follow the general strategy of 7 using a richer set of solutions to the dirichlet problem that has been used in previous works on this problem

some remarks on brs transformations anomalies and the cohomology of the lie algebra of the group of gauge transformations we show that ghosts in gauge theories can be interpreted as maurer cartan forms in the infinite dimensional group of gauge transformations we examine the cohomology of the lie algebra of and identify the coboundary operator with the brs operator we describe the anomalous terms encountered in the renormalization of gauge theories triangle anomalies as elements of these cohomology groups

singular solutions of elliptic equations and the determination of conductivity by boundary measurements abstract we improve some results on uniqueness and stability in the determination of the coefficient a in the equation i div a grad u 0 in when all possible pairs of dirichlet and neumann data on are known we also treat cases of anisotropic equations our method relies on the construction of solutions to i having an isolated singularity with prescribed asymptotic behaviour

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

global uniqueness for a two dimensional semilinear elliptic inverse problem for a general class of nonlinear schrodinger equations au a x u 0 in a bounded planar domain 2 we show that the function a x u can be recovered from knowledge of the corresponding dirichlet to neumann map on the boundary dq

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

topological yang mills theory with scalar and vector fields in two and three dimensions we study the topological yang mills theory of scalar and vector fields in two and three dimensions in the superconnection framework we modify the horizontality condition in such a way that we can take care of the topological symmetry of the a type as well as the usual gauge symmetry of the a d c type we then obtain a complete set of brst and anti brst transformation rules of the component fields in a systematic way

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

infinitely many stationary solutions of discrete vector nonlinear schrodinger equation with symmetry in this paper we study the existence of stationary solutions for the following discrete vector nonlinear schrodinger email protected email protected email protected email protected f email protected email protected n jf n f n f n where f n is a sequence of 2 component vector j 0110 email protected email protected n email protected n email protected nis the discrete laplacian in one spatial dimension and sequence t n is assumed to be n periodic in n i e t n email protected n we prove the existence of infinitely many nontrivial stationary solutions for this system by variational methods the same method can also be applied to obtain infinitely many breather solutions for single discrete nonlinear schrodinger equation