nonresonance conditions for asymptotically positively homogeneous differential systems the fucik spectrum and its generalization in this article we propose how to define the fucik spectra for differential systems in rnwith jumping nonlinearities the propertyp a generalization of the non fucik spectra to positively homogeneous nonautonomous differential systems is also defined in the most general setting a quantitative estimate result concerning the parameterized completely continuous positively homogeneous perturbations of the identity in banach spaces is given in this article such a result is a generalization of one property in the spectrum theory for completely continuous linear operators using this estimate result we will give some significantly improved nonresonance results from the fucik spectra and propertypfor asymptotically positively homogeneous differential systems

solvability of some operator equations and periodic solutions of nonlinear functional differential equations on donne des conditions suffisantes pour la resolubilite d equations operateurs lx nx dans des espaces normes avec l operateur lineaire non inversible mais a noyau de dimension finie et n un operateur non lineaire

boundary controllability of a hybrid system consisting in two flexible beams connected by a point mass we consider a hybrid system consisting of two flexible beams connected by a point mass the constant of rotational inertia is assumed to be nonzero in a previous paper we have proved that in the presence of the point mass the system is well posed in asymmetric spaces in which solutions have one more degree of regularity to one side of the mass we are interested in the problem of controllability when the control acts on the free extreme of one of the beams we prove that when the control time is large enough the system is exactly controllable in an asymmetric space this result is sharp the proofs combine classical techniques from asymptotic analysis and the theory of nonharmonic fourier series

on the existence of periodic solutions of forced lienard differential equations on considere l existence des solutions t periodiques t 0 de l equation de lienard scalaire forcee x f x x g x h t ou f g h r r sont des fonctions continues et h est t periodique h 0

continuation theorems for periodic perturbations of autonomous systems it is first shown in this paper that whenever it exists the coincidence degree of the left hand member of an autonomous differential equation x g x 0 in the space of periodic functions with fixed period omega can be computed in terms of the brouwer degree of g this result provides efficient continuation theorems specially for omega periodic perturbations of autonomous systems extensions to differential equations in flow invariant enr s are also given

singularly perturbed higher order periodic boundary value problems abstract the existence of positive periodic solutions is proved for the higher order singular differential equation 0 1 x n a n 1 x n 1 a 1 x a 0 t x e t and for some generalizations including a class of differential systems with singular cyclic feedback

exact boundary controllability of a hybrid system of elasticity a hybrid control system is presented an elastic beam governed by a partial differential equation linked to a rigid body which is governed by an ordinary differential equation and to which control forces and torques are applied the entire system elastic beam plus rigid body is proved to be exactly controllable by smooth open loop controllers applied to the rigid body only and in arbitrarily short durations this system is modeled as a two dimensional space structure

periodic solutions of some fourth order nonlinear differential equations abstract in this paper using mawhin s continuation theorem we obtain existence results concerning t periodic solutions of fourth order nonlinear differential equations of the type u p u g t u e t where p r g r 2 r is continuous t periodic in t and e r r is continuous t periodic with mean value zero applications are given for the extended fisher kolmogorov and swift hohenberg equations with forcing term

on a periodic problem for higher order differential equations with a deviating argument for higher order nonautonomous linear and nonlinear differential equations with deviating arguments new sufficient conditions of existence and uniqueness of a periodic solution are found

a phase transition in the first passage of a brownian process through a fluctuating boundary with implications for neural coding finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple looking problem of vast practical importance in physics biology chemistry neuroscience economics and industrial engineering problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding such as neuronal integrators with irregular inputs and internal noise we show that the probability p t that a gauss markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary as measured by its holder exponent h the critical value occurs when the roughness of the boundary equals the roughness of the process so for diffusive processes the critical value is hc 1 2 for smoother boundaries h 1 2 the probability density is a continuous function of time for rougher boundaries h 1 2 the probability is concentrated on a cantor like set of zero measure the probability density becomes divergent almost everywhere either zero or infinity the critical point hc 1 2 corresponds to a widely studied case in the theory of neural coding in which the external input integrated by a model neuron is a white noise process as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs we argue that this transition corresponds to a sharp boundary between rate codes in which the neural firing probability varies smoothly and temporal codes in which the neuron fires at sharply defined times regardless of the intensity of internal noise

a partitioned scheme for fluid composite structure interaction problems we present a benchmark problem and a loosely coupled partitioned scheme for fluid structure interaction with composite structures the benchmark problem consists of an incompressible viscous fluid interacting with a structure composed of two layers a thin elastic layer with mass which is in contact with the fluid and modeled by the koiter membrane shell equations and a thick elastic layer with mass modeled by the equations of linear elasticity an efficient modular partitioned operator splitting scheme is proposed to simulate solutions to the coupled nonlinear fsi problem without the need for sub iterations at every time step an energy estimate associated with unconditional stability is derived for the fully nonlinear fsi problem defined on moving domains two instructive numerical benchmark problems are presented to test the performance of numerical fsi schemes involving composite structures it is shown numerically that the proposed scheme is at least first order accurate both in time and space this work reveals a new physical property of fsi problems involving thin interfaces with mass the inertia of the thin fluid structure interface regularizes solutions to the full fsi problem

nonlinear perturbations of differential operators with nontrivial kernel and applications to third order periodic boundary value problems this paper deals with the solvability of the nonlinear operator equations in normed spaces yx egx j where dp is a linear map with possible nontrivial kernel applications are given to the existence of periodic solutions for the thirdorder scalar differential equation x ax bx cx g t x p t under various conditions on the interaction of g t x x with spectral contigurations of a b and c

numerical integration of multiplicative noise stochastic differential equations a two stage runge kutta algorithm for vector ito and by transform also stratonovich stochastic differential equations with multiplicative noise has been developed the method is second order accurate but for vanishing drift the algorithm yields a martingale independent of step size several examples are included to illustrate our method a discussion of errors shows that sample size can be as important as truncation

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

an integral algorithm for numerical integration of one dimensional additive colored noise problems we present an integral closed algorithm for solving a langevin equation driven by an additive colored noise both the mean first passage time in a bistable system and the diffusion current in a titled periodic potential are calculated and the comparison with existing algorithms is carried out the dependence of the numerical results on the time steps is studied our algorithm is shown to have high accuracy and stability

wellposedness spectral analysis and asymptotic stability of a multilayered heat wave wave system abstract in this work we consider a multilayered heat wave system where a 3 d heat equation is coupled with a 3 d wave equation via a 2 d interface whose dynamics is described by a 2 d wave equation this system can be viewed as a simplification of a certain fluid structure interaction fsi pde model where the structure is of composite type namely it consists of a thin layer and a thick layer we associate the wellposedness of the system with a strongly continuous semigroup and establish its asymptotic decay our first result is semigroup well posedness for the fsi pde dynamics utilizing here a lumer phillips approach we show that the fluid structure system generates a c 0 semigroup on a chosen finite energy space of data as our second result we prove that the solution to the fsi dynamics generated by the c 0 semigroup tends asymptotically to the zero state for all initial data that is the semigroup of the fsi system is strongly stable for this stability work we analyze the spectrum of the generator a and show that the spectrum of a does not intersect the imaginary axis

a haar like construction for the ornstein uhlenbeck process the classical haar construction of brownian motion uses a binary tree of triangular wedge shaped functions this basis has compactness properties which make it especially suited for certain classes of numerical algorithms we present a similar basis for the ornstein uhlenbeck process in which the basis elements approach asymptotically the haar functions as the index increases and preserve the following properties of the haar basis all basis elements have compact support on an open interval with dyadic rational endpoints these intervals are nested and become smaller for larger indices of the basis element and for any dyadic rational only a finite number of basis elements is nonzero at that number thus the expansion in our basis when evaluated at a dyadic rational terminates in a finite number of steps we prove the covariance formulae for our expansion and discuss its statistical interpretation

uniform exponential long time decay for the space semi discretization of a locally damped wave equation via an artificial numerical viscosity we consider the finite difference space semi discretization of a locally damped wave equation the damping being supported in a suitable subset of the domain under consideration so that the energy of solutions of the damped wave equation decays exponentially to zero as time goes to infinity the decay rate of the semi discrete systems turns out to depend on the mesh size h of the discretization and tends to zero as h goes to zero we prove that adding a suitable vanishing numerical viscosity term leads to a uniform with respect to the mesh size exponential decay of the energy of solutions this numerical viscosity term damps out the high frequency numerical spurious oscillations while the convergence of the scheme towards the original damped wave equation is kept we discuss this problem in 1d and 2d in the interval and the square respectively our method of proof relies on discrete multiplier techniques

exact controllability and stabilization of a vibrating string with an interior point mass in this article we examine the problems of boundary control and stabilization for a one dimensional wave equation with interior point masses we show that singularities in waves are smoothed one order as they cross a point mass thus in the case of one interior point mass with e g l 2 dirichlet control at the left end the most general reachable space from 0 that one can expect is l 2 times h 1 to the left of the mass and h 1 times l 2 to the right of the mass we show that this is in fact the optimal result modulo certain compatibility conditions several related results for both control and stabilization of such systems are also given

numerical approximation schemes for multi dimensional wave equations in asymmetric spaces we develop finite difference numerical schemes for a model arising in multi body structures previously analyzed by h koch and e zuazua 13 constituted by two n dimensional wave equations coupled with a n 1 dimensional one along a flexible interface that model under suitable assumptions on the speed of propagation in each media is well posed in asymmetric spaces in which the regularity of solutions differs by one derivative from one medium to the other here we consider a flat interface and analyze this property at a discrete level for finite difference and mixed finite element methods on regular meshes parallel to the interface we prove that those methods are well posed in such asymmetric spaces uniformly with respect to the mesh size parameters and we prove the convergence of the numerical solutions towards the continuous ones in these spaces in other words these numerical methods that are well behaved in standard energy spaces preserve the convergence properties in these asymmetric spaces too these results are illustrated by several numerical experiments

multiple solutions of the periodic boundary value problem for some forced pendulum type equations if f x c 0 and e is a constant t then integrating 0 1 over 0 272 after multiplication of both members of the equation by x shows that the only possible solutions are constant and hence satisfy a sin x c consequently if we exclude the trivial translation by a multiple of 275 0 1 will have no solution if dj a one solution if lp a and two solutions if lc l a in 0th er t erms the intersection of the range of the operator d2 dt2 c d dt f u sin acting on zn periodic functions of class g with the subspace of constant functions in the space c o 2711 of real continuous functions on 0 27r is the closed interval a a whose interior points are images of two distinct solutions and boundary points of one we try to obtain similar results for the case where e is no more constant and

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

a fast algorithm for the first passage times of gauss markov processes with holder continuous boundaries even for simple diffusion processes treating first passage problems analytically proves intractable for generic barriers and existing numerical methods are inaccurate and computationally costly here we present a novel numerical method that is faster and has more tightly controlled accuracy our algorithm is a probabilistic variant of dichotomic search for the computation of first passage times through non negative homogeneously holder continuous boundaries by gauss markov processes these include the ornstein uhlenbeck process underlying the ubiquitous leaky integrate and fire model of neuronal excitation our method evaluates discrete points in a sample path exactly and refines this representation recursively only in regions where a passage is rigorously estimated to be probable e g when close to the boundary

boundary controllability of a linear semi discrete 1 d wave equation derived from a mixed finite element method in this article one discusses the controllability of a semi discrete system obtained by discretizing in space the linear 1 d wave equation with a boundary control at one extremity it is known that the semi discrete models obtained with finite difference or the classical finite element method are not uniformly controllable as the discretization parameter h goes to zero see 8 here we introduce a new semi discrete model based on a mixed finite element method with two different basis functions for the position and velocity we show that the controls obtained with these semi discrete systems can be chosen uniformly bounded in l 2 0 t and in such a way that they converge to the hum control of the continuous wave equation i e the minimal l 2 norm control we illustrate the mathematical results with several numerical experiments