positive periodic solutions of nonlinear differential systems with impulses abstract by using a fixed point theorem of strict set contraction sufficient conditions for the existence of positive periodic solutions of nonlinear differential systems with impulses are obtained as applications of our results the existence of positive periodic solutions are established for delay lotka volterra systems with impulses or without impulses

semi global practical asymptotic stability and averaging abstract we prove a generalized liapunov theorem which guarantees practical asymptotic stability based on this theorem we show that if the averaged system x f av x corresponding to x f x t is globally asymptotically stable then starting from an arbitrarily large set of initial conditions the trajectories of x f x t e converge uniformly to an arbitrarily small residual set around the origin when e 0 is taken sufficiently small in other words the origin is semi globally practically asymptotically stable

an averaging theorem for time periodic degree zero homogeneous differential equations abstract this paper considers the stability of the differential equation dot x ex t x e x r n where x t x e is a time periodic degree zero homogeneous vector field and e 0 is a parameter it is shown that asymptotic stability of the time averaged equation implies asymptotic stability of the original system for e sufficiently small

averaging results and the study of uniform asymptotic stability of homogeneous differential equations that are not fast time varying within the liapunov framework a sufficient condition for uniform asymptotic stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the v function taken along solutions of the system may have positive and negative values it is shown that the proposed condition is useful for the study of uniform asymptotic stability of homogeneous systems with order tau 0 in particular it is established that asymptotic stability of the averaged homogeneous system implies local uniform asymptotic stability of the original time varying homogeneous system this shows that averaging techniques play a prominent role in the study of homogeneous not necessarily fast time varying systems

existence results for abstract impulsive second order neutral functional differential equations abstract we establish the existence of mild solutions for a class of impulsive second order partial neutral functional differential equations with infinite delay in a banach space

existence and multiplicity of solutions for second order impulsive differential equations with dirichlet problems abstract in this paper we consider the existence and the multiplicity of solutions for second order impulsive differential equations with dirichlet boundary conditions some new existence results are obtained by critical point theory our results further improve some existing results

multiple positive solutions of dirichlet boundary value problems for second order impulsive differential equations abstract this paper is devoted to study the existence of multiple positive solutions for the second order dirichlet boundary value problem with impulse effects the main results here is the generalization of liu and li l liu f y li multiple positive solution of nonlinear two point boundary value problems j math anal appl 203 1996 610 625 for ordinary differential equations existence is established via the theory of fixed point index in cones

infinitely many periodic solutions for second order p q laplacian differential systems abstract some existence theorems are obtained for infinitely many periodic solutions for second order p q laplacian differential systems by using a general variational principle due to b ricceri

existence and multiplicity of solutions for some dirichlet problems with impulsive effects abstract in this paper we consider the existence and multiplicity of solutions for some dirichlet impulsive problems and some existence and multiplicity results are obtained the solutions are sought by means of lax milgram theorem and some critical theorems

solvability of second order hamiltonian systems with impulses via variational method in this paper a class of second order impulsive hamiltonian systems are considered some new existence results are obtained by using a variational method and critical point theorem due to tang and wu some recent results are extended three examples are presented to illustrate the feasibility and effectiveness of our results

multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations we study the existence behavior of positive solutions to a singular two point boundary value problem of second order impulsive equation with fixed moments proofs are based on combining a method of upper and lower solutions with fixed point index theorems on a cone

boundary value problems for a class of impulsive functional equations this paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions we study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times by the use of the monotone method some of the options included in this formulation are differential equations with maximum and integro differential equations in this paper we also prove that the lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval the corresponding results are established for the impulsive case the general formulation includes several types of functional dependence delay equations equations with maxima integro differential equations finally we consider the case of functional dependence which is given by nonincreasing and bounded functions

existence of solutions for a class of second order hamiltonian systems with impulsive effects abstract in this paper a class of second order hamiltonian systems with impulsive effects are considered we establish some sufficient conditions for the existence of solutions for the second order hamiltonian systems with impulsive effects u t f t u t a e t 0 t u 0 u t u 0 u t 0 u i t j u i t j u i t j i i j u i t j i 1 2 n j 1 2 p where t 0 0 t 1 t 2 t p t p 1 t u t u 1 t u 2 t u n t r n i i j r r i 1 2 n j 1 2 p are continuous and f 0 t r n r the solutions are sought by means of some critical point theorems finally two examples are presented to illustrate the feasibility and effectiveness of our results

on the simultaneous presence of unilateral and kinetic constraints in time dependent impulsive mechanics the simultaneous presence of unilateral and kinetic constraints acting on a mechanical system with a finite number of degrees of freedom is framed in the geometric context of left and right jet bundles of the classical space time bundle of the system the survey gives three main cases and several subcases some of which are mathematically correct but physically meaningless the existence of at least one frame of reference for which the whole set of constraints can be at rest is the criterion selecting the physically relevant systems for these systems the conservation of kinetic energy possibly together with a standard gauss s requirement on the impulsive reaction is shown to give a well posed criterion of ideality of the constraints the application of the criterion to several examples is presented and the corresponding results are critically analyzed

existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti periodic boundary conditions this paper describes the method of quasilinearization for first order nonlinear impulsive functional differential equations with anti periodic boundary conditions a monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand 2007 elsevier ltd all rights reserved

periodic boundary value problem for non lipschitzian impulsive functional differential equations we consider a class of first order impulsive functional differential equations where the functional dependence is not necessarily a lipschitzian function the new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented we give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution

averaging of nonsmooth systems using dither it was shown by zames and shneydor and later by mossaheb that a high frequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of lipschitz continuous feedback systems in this paper it is shown that also discontinuous nonlinearities of feedback systems can be narrowed using dither as long as the amplitude distribution function of the dither is absolutely continuous and has bounded derivative the averaged system is proven to approximate the dithered system with an error of the order of dither period

three solutions for a p laplacian boundary value problem with impulsive effects in this paper a p laplacian boundary value problem with impulsive effects is considered multiplicity of solutions is obtained by three critical points theorem an example is presented to illustrate main result

brief on exponential stability of nonlinear time varying differential equations within the liapunov framework a sufficient condition for exponential stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the liapunov function taken along solutions of the system may have positive and negative values verification of the conditions of the main theorem may be harder than in the classical case it is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time varying systems this sets the stability study by means of averaging in a liapunov context in particular it is established that exponential stability of the averaged system implies exponential stability of the original fast time varying system a comparison of our work with results taken from the literature is included

averaging criteria for asymptotic stability of time varying systems we establish averaging type sufficient conditions for local asymptotic stability for nonlinear time varying systems our main result is based on an extension of the averaging methodology employed in a recent paper by tsinias and stamati published in the same journal dealing with asymptotic stability for slow time varying systems

averaging techniques without requiring a fast time varying differential equation an averaging result is presented for local uniform asymptotic stability of nonlinear differential equations without requiring a fast time varying vectorfield the nonlinearity plays a crucial role close to the origin the trajectories vary slowly compared to the time dependence of the vectorfield the result generalises averaging results which prove stability properties for systems having a homogeneous vectorfield with positive order the result is illustrated with several examples

ii _ 1 factors with nonisomorphic ultrapowers we prove that there exist uncountably many separable ii1 factors whose ultrapowers with respect to arbitrary ultrafilters are nonisomorphic in fact we prove that the families of nonisomorphic ii1 factors originally introduced by mcduff are such examples this entails the existence of a continuum of nonelementarily equivalent ii1 factors thus settling a well known open problem in the continuous model theory of operator algebras

the multiplicity of solutions for perturbed second order hamiltonian systems with impulsive effects abstract in this paper we study the existence of multiple solutions for a class of second order impulsive hamiltonian systems we give some new criteria for guaranteeing that the impulsive hamiltonian systems with a perturbed term have at least three solutions by using a variational method and some critical points theorems of b ricceri we extend and improve on some recent results finally some examples are presented to illustrate our main results

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation