on aspects of boundary damping for a rectangular plate in this paper the vibrations are studied of a rectangular plate with two opposite sides simply supported to the other two sides of the plate linear springs and dampers are attached by using the recently developed adapted version of the method of separation of variables the relationship between the plate parameters and the damping rates is obtained analytically

a qualitative explanation of the origin of torsional instability in suspension bridges abstract we consider a mathematical model for the study of the dynamical behavior of suspension bridges we show that internal resonances which depend on the bridge structure only are the origin of torsional instability we obtain both theoretical and numerical estimates of the thresholds of instability our method is based on a finite dimensional projection of the phase space which reduces the stability analysis of the model to the stability of suitable hill equations this gives an answer to a long standing question about the origin of torsional instability in suspension bridges

positive solutions of singular boundary value problems for systems of nonlinear fourth order differential equations abstract in this paper we study the singular boundary value problems for systems of nonlinear fourth order differential equations u 4 t a 1 t f 1 t u t v t u t v t b 1 t g 1 t u t v t u t v t v 4 t a 2 t f 2 t u t v t u t v t b 2 t g 2 t u t v t u t v t 0 t 1 u 0 u 1 v 0 v 1 0 1 u 0 1 u 0 0 1 u 1 1 u 1 0 2 v 0 2 v 0 0 2 v 1 2 v 1 0 under some weaker conditions we show the existence of single and multiple positive solutions of the above problem by applying the fixed point theorem of cone expansion and compression type due to krasnosel skill

uniform compact attractors for the coupled suspension bridge equations in this paper we investigate the uniformly absorbing set for the coupled suspension bridge equations with a new class of external forces and then prove the existence of the uniform attractors for the family of process corresponding to the equations

the existence of global attractors for the norm to weak continuous semigroup and application to the nonlinear reaction diffusion equations abstract in this paper first we introduce a new concept called the norm to weak continuous semigroup in a banach space and give a technical theorem to verify this notion of continuity then we establish a general method which is necessary and sufficient to obtain the existence of the global attractor for this kind of semigroup as an application we obtain the existence of the global attractor for a nonlinear reaction diffusion equation with a polynomial growth nonlinearity of arbitrary order and with some weak derivatives in the inhomogeneous term the global attractors are obtained in l p h 0 1 and h 2 h 0 1 respectively a new a priori estimate method called asymptotic a priori estimate has been introduced since the solutions of the equation has no higher regularity and the semigroup associated the solutions is not continuous in l p h 0 1 and h 2 h 0 1 the results in this part are new and appear to be optimal

periodic solutions of the second order damped systems with singularities and deviating arguments in this paper we study the existence of periodic solutions of the second order damped systems with singularities and deviating arguments x p 1 t x q 1 t x f 1 t y t 1 t e 1 t y p 2 t y q 2 t y f 2 t x t 2 t e 2 t where p i q i i e i l 1 r are t periodic f i car r i r r i 1 2 are t periodic with the first variable and have singularities at the origin we prove that the singularities of f i enable the existence of periodic solutions by using schauder s fixed point theorem

existence of strong solutions and global attractors for the suspension bridge equations abstract in this paper we show the existence of strong solutions for the suspension bridge equations furthermore the existence of strong global attractors is investigated using a new semigroup scheme

on the existence of geodesics on stationary lorentz manifolds with convex boundary abstract in this paper we consider the problem of the existence and multiplicity for geodesics not touching the boundary of a stationary lorentz manifold having convex boundary a physical example of a stationary and nonstatic lorentz manifold having convex boundary is the stationary axisymmetric asymptotically flat gravitational field outside a rotating massive object whenever its angular speed is small and its mean radius is close to the schwarzschild radius

asymptotic behaviour of solutions to cable stayed bridge equations asymptotic behaviour of solutions to the nonlinear variational equations of the two basic types of cable stayed bridges is studied the equations describe vertical and torsional oscillations of the center span which is the part of road bed between pylons due to damping amplitude and velocity of oscillations remain bounded if wind force is bounded as well moreover the solution to the nonlinear equations converges to the solution of the steady state problem if wind drops if the center span has certain aerodynamical properties and the initial state is near to the solution of the steady state problem then the solution converges to the steady state solution even if the forces representing wind do not vanish

long time behavior of a suspension bridge equations with past history in this paper we study a suspension bridge equation with memory effects for the suspension bridge equation without memory there are many classical results existing results mainly devoted to existence and uniqueness of a weak solution energy decay of solution and existence of global attractors however the existence of global attractors for the suspension bridge equation with memory was no yet considered the object of the present paper is to provide some results on the well posedness and long time behavior to the suspension bridge equation when the unique damping mechanism is given by the memory term

multiple nontrivial solutions for a floating beam equation via critical point theory abstract we study periodic flexings of a floating beam via critical point theory the beam is described by the nonlinear equation with free end boundary conditions described in the introduction we give a theorem of existence of two nontrivial solutions and a theorem of existence of four nontrivial solutions depending on the position of a suitable parameter with respect to the eigenvalues of the linear part

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

multiplicity results for some fourth order elliptic equations abstract this paper deals with some fourth order elliptic equations with navier boundary condition by using the variational method some existence and multiplicity results are established

nonlinear models of suspension bridges nonlinear variational equations describing one type of suspension bridges are proposed and studied the variational equations describe the behaviour of road bed main cables and cable stays the road bed is described by two functions connected with vertical and horizontal deformation of any cross section the main cable is considered to be perfectly flexible and inextensible the cable stays only resist tensile forces the variational equations are derived from the principle of minimum potential energy the existence of solution is based on the brouwer fixed point theorem the local uniqueness and continuous dependence on the data represented by gravitational forces acting on the road bed are studied the local results are based on the implicit function theorem for banach spaces a certain stability criterion for suspension bridges is formulated and this criterion indicates how to influence the stability of suspension bridges

spectral theory of certain unbounded jacobi matrices abstract using the conjugate operator method of mourre we study the spectral theory of a class of unbounded jacobi matrices we especially focus on the case where the off diagonal entries a n n 1 o 1 and diagonal ones b n n 1 o 1 with 0 r

existence of strong solutions and global attractors for the coupled suspension bridge equations abstract in this paper we show the existence of the strong solutions for the coupled suspension bridge equations furthermore existence of the strong global attractors is investigated using a new semigroup scheme since the solutions of the coupled equation have no higher regularity and the semigroup associated with the solutions is not continuous in the strong hilbert space the results are new and appear to be optimal

on nonlinear oscillations in a suspension bridge system in this paper we study nonlinear oscillations in a suspension bridge system governed by two coupled nonlinear partial differential equations by applying the leray schauder degree theory it is proved that the suspension bridge system has at least two solutions one is a near equilibrium oscillation and the other is a large amplitude oscillation

initial boundary value problem for the nonlinear string beam system this paper deals with a nonlinear string beam system describing the torsional vertical oscillations of a suspension bridge we consider the initial boundary value problem and study the existence and uniqueness question we assume time independent right hand sides but allow quite general nonlinear terms using the faedo galerkin method we prove the existence of a unique solution on an arbitrary large time interval

mathematical analysis of dynamic models of suspension bridges in this paper we present some mathematical analysis of dynamic pde models of suspension bridges as proposed by lazer and mckenna our results are illustrated by numerical simulation with physical interpretation

asymptotic dynamics of nonlinear coupled suspension bridge equations abstract in this paper we study the long term dynamics of a doubly nonlinear abstract system which involves a single differential operator to different powers for a special choice of the nonlinear terms the system describes the motion of a suspension bridge where the road bed and the main cable are modeled as a nonlinear beam and a vibrating string respectively and their coupling is carried out by nonlinear springs the set of stationary solutions turns out to be nonempty and bounded as the external loads vanish the null solution of the system is proved to be exponentially stable provided that the axial load does not exceed some critical value finally we prove the existence of a bounded global attractor of optimal regularity in connection with an arbitrary axial load and quite general nonlinear terms

periodic solutions for dynamical systems on non complete riemannian manifolds abstract we look for periodic solutions in a dynamical system on a non complete riemannian manifold if the potential is bounded and suitable convexity assumptions hold the existence of infinitely many solutions can be proved by means of variational methods penalization arguments and classical ljusternik schnirelman theory

positive solutions of singular sub linear boundary value problems for fourth order and second order differential equation systems abstract this paper investigates the existence of positive solutions of singular sub linear boundary value problems for fourth order and second order differential equation systems first of all we establish some important lemmas then we define a partial ordering in c 2 a b c 4 a b c a b c 2 a b and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c 2 0 1 c 0 1 positive solutions as well as c 3 0 1 c 1 0 1 positive solutions our nonlinearity f t x 1 x 2 x 3 g t x 1 x 2 may be singular at x 1 0 x 2 0 x 3 0 t 0 and or t 1

closed geodesies on compact lorentzian manifolds of splitting type in this paper we consider the problem of the existence of a spacelike closed geodesic on compact lorentzian manifolds tipler and galloway proved that under suitable topological properties of the manifold there exists a closed timelike geodesic in their proofs they use the hypothesis that the time coordinate of one timelike geodesic has derivative always different from zero this clearly fails for spacelike geodesies using variational methods and applying the relative category theory we prove the existence of a closed spacelike geodesic on a compact manifold of splitting type observe that thanks to the previous results the existence of at least two geometrically distinct closed geodesies on follows

the investigation of free vibrations for an asymmetric beam equation using category theory we investigate free vibrations for an asymmetric beam equation we find them by applying linking inequalities and the limit relative category theory

pullback d attractors for non autonomous suspension bridge equations abstract in this paper we prove the existence of a pullback d attractor in v h for the non autonomous suspension bridge equations

high energy solutions of modified quasilinear fourth order elliptic equations with sign changing potential abstract in the present paper we consider the following modified quasilinear fourth order elliptic equation 1 1 2 u u v x u 1 2 u 2 u f x u for x r n u x h 2 r n where 2 is the biharmonic operator v c r n r and f c r n r r n 5 are allowed to be sign changing two main theorems on the existence of nontrivial solutions and infinitely many high energy solutions for eq 1 1 are obtained via variational methods

maximum principles for a coupled system of second and fourth order elliptic equations and an application in this paper we obtain a maximum principle for the coupled system of second and fourth order elliptic equations using an abstract result in a recent paper by correa and souto nonlinear anal 26 1996 and an application of the maximum principle is given

multiple critical points for indefinite functionals and applications abstract in this paper we prove a multiplicity result for critical points of an indefinite functional on a manifold by using a generalization of the ljusternik schnirelman category the abstract result is applied to prove the existence of multiple timelike trajectories for lorentzian manifolds of splitting type

periodic orbits and subharmonics of dynamical systems on non compact riemannian manifolds where dt x t is the covariant derivative of x along the direction of x and r the riemannian gradient has been studied when m is a noncontractible manifold see 2 8 9 14 assuming if m is non compact the existence of a function on m convex at infinity when v is bounded the difficulties arise from the lack of compactness of m indeed in this case the action functional does not satisfy the palais smale compactness condition on the other side if v is unbounded the action functional is unbounded both from below and from above therefore neither min max methods and linking arguments can be used since the loop space is not linear nor the ljusternik schnirelmann category theory can be applied although m has a non trivial topology article no 0136

a variational approach to subquadratic perturbations of elliptic systems abstract we consider subquadratic perturbations of semilinear elliptic systems which are in variational form a unified approach to both the cooperative and noncooperative problems is presented and a condition of nonquadraticity at infinity is introduced to treat the resonant cases through minimax techniques

positive solutions for singular boundary value problems of a coupled system of differential equations by using fixed point theorem of cone expansion and compression this paper investigates the existence of multiple positive solutions for singular boundary value problems of a coupled system of nonlinear ordinary differential equations

on the coupled systems of second and fourth order elliptic equations in this paper by the variational method we discuss the existence and uniqueness of solutions for a coupled system of second and fourth order elliptic equations in the cases where the perturbation is zero sublinear and superlinear respectively

random attractors for the coupled suspension bridge equations with white noises the paper is devoted to the investigation of the existence of a compact random attractor for the random dynamical system generated by the coupled suspension bridge equations with white noises

geodesics in stationary spacetimes and classical lagrangian systems abstract we state a fundamental correspondence between geodesics on stationary spacetimes and the equations of classical particles on riemannian manifolds accelerated by a potential and a magnetic field by variational methods we prove some existence and multiplicity theorems for fixed energy solutions joining two points or periodic of the above described riemannian equation as a consequence we obtain existence and multiplicity results for geodesics with fixed energy connecting a point to a line or periodic trajectories in standard stationary spacetimes

random attractors for the extensible suspension bridge equation with white noise this paper is devoted to the dynamical behavior of a stochastic extensible suspension bridge equation with white noise for a deterministic suspension bridge equation there are many classical results such as existence and uniqueness of a solution and long term behavior of solutions to the best of our knowledge the existence of attractors for the suspension bridge equation with white noise was not yet considered we intend to investigate these problems we first obtain the dissipativeness of a solution in higher energy spaces h 3 h 2 h 0 1 this implies that the random dynamical system generated by the equation has a random attractor in h 2 h 0 1 l 2 which is a tempered random set in the space in h 3 h 2 h 0 1

stochastic initial boundary value problems subject to distributed and boundary noise and their optimal control abstract in this paper we consider a class of stochastic evolution equations arising from initial boundary value problems with both boundary and distributed noise we prove existence and regularity of mild solutions then we consider a controlled version of the model and prove the existence of optimal controls and develop the necessary conditions of optimality for partially observed problems using relaxed controls

mountain pass solutions for the coupled systems of second and fourth order elliptic equations abstract in this paper by the mountain pass theorem we give an existence theorem of nontrivial solutions for a coupled system of second and fourth order elliptic equations

orthogonal polynomials spectral measures and absolute continuity abstract this paper studies the measure of orthogonality for a system of polynomials corresponding to an unbounded self adjoint jacobi matrix with finite row sums techniques of operator theory and functional analysis are used to study the spectral measure of this operator which gives the measure of orthogonality for the system of polynomials with a view toward obtaining results on absolute continuity

spectral theory of a class of block jacobi matrices and applications abstract we develop a spectral analysis of a class of block jacobi operators based on the conjugate operator method of mourre we give several applications including scalar jacobi operators with periodic coefficients a class of difference operators on cylindrical domains such as discrete wave propagators and certain fourth order difference operators

existence of global attractors for the coupled system of suspension bridge equations a mathematical model of the suspension bridge describes the vibration of the road bed in the vertical plain and that of the main cable we show the existence of an absorbing set for the solution of the problem furthermore the global attractors of the coupled system of suspension bridge are studied by a new semigroup approach

absolute continuity for unbounded jacobi matrices with constant row sums we investigate the spectral properties of a class of jacobi matrices in which the subdiagonal entries are quadratics and the row sums are constants

periodic trajectories on stationary lorentzian manifolds in this paper we present an existence and multiplicity result for periodic trajectories on stationary lorentzian manifolds possibly with boundary whose proof is based on a morse theory approach see 5 we recall that a lorentzian manifold is a smooth connected nite dimensional manifold m equipped with a 0 2 tensor eld g such that for any z m g z is a nondegenerate symmetric bilinear form on the tangent space tzm having exactly one negative eigenvalue moreover relativistic spacetimes are a particular class of lorentzian manifolds of dimension four

existence of strong global attractors for hyperbolic equation with linear memory we prove that the existence of global attractors of strong solutions for the hyperbolic equations with linear memory using the semigroup approach

periodic solutions of a nonlinear suspension bridge equation with damping and nonconstant load abstract the paper is concerned with the existence of periodic solutions for the lazer mckenna suspension bridge equation with damping and nonconstant load by using the lyapunov schmidt reduction methods the author discuss the relationship between the sign changing solutions and the source terms the result answers partly the open problem in lazer and mckenna siam rev 32 1990 537 578