oscillation criteria of first order linear difference equations with delay argument abstract this paper presents new sufficient conditions for the oscillation of all proper solutions of the first order linear difference equation with delay argument u k p k u k 0 k n where u k u k 1 u k p n r n n and lim k k examples illustrating the results are given it is to be pointed out that this is the first paper dealing with the oscillatory behaviour of the equation in the case of a general delay argument k

oscillations of difference equations with non monotone retarded arguments consider the first order retarded difference equation x n p n x n 0 n n 0 where p n n 0 is a sequence of nonnegative real numbers and n n 0 is a sequence of integers such that n n 1 n 0 and lim n n under the assumption that the retarded argument is non monotone a new oscillation criterion involving lim inf is established an example illustrates the case when the result of the paper implies oscillation while previously known results fail

identification of time delays using a polynomial identification method abstract an algorithm for the exact least squares identification of an approximate continuous time time delay system is derived and its operation verified by simulation

existence of multiple solutions to nonlinear elliptic equations of nondivergence form abstract in this paper by means of a priori estimates and topological degree theory we prove the existence of two or more solutions to nonlinear elliptic equations of nondivergence form

oscillations of delay difference equations with oscillating coefficients abstract in this paper we establish sufficient conditions for the oscillation of all solutions of the delay difference equation y n 1 y n p n y n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer an open problem in ladas in international conference on differential equations stability and control dekker new york 1990 is solved

an oscillation criterion for a delay difference equation by using the method of yu zhang and qian in j s yu b g zhang x z qian oscillation of delay difference equations with oscillating coefficients j math anal appl 177 1993 432 444 we prove another oscillation criterion for all solutions of the following linear delay difference equation x n 1 x n p nx n k 0 n 0 1 2 where p n is a sequence of real numbers and k is a positive integer

useful redundancy in parameter and time delay estimation for continuous time models in this paper we propose an algorithm to estimate the parameters including time delay of continuous time systems based on instrumental variable identification methods to overcome the multiple local minima of the cost function associated with the estimation of a time delay system we utilize the useful redundancy technique specifically the cost function is filtered through a set of low pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem numerical examples are presented to demonstrate the effectiveness of the proposed algorithm

new oscillation criteria for delay difference equations abstract this paper is concerned with the oscillation of all solutions of the delay difference equations and where pn and pi n are sequences of nonnegative real numbers an k and ki are positive integers new oscillation criteria of the forms for equation and for equation are obtained where lim infn 1 k n 1i n k pi and c is the the best possible function of in some sense

oscillation criteria for delay and difference equations with non monotone arguments consider the first order linear delay differential equation 1 x t p t x t t 0 t t 0 where p email protected c t 0 r t t t 0 and lim t email protected t and the discrete analogue difference equation 1 dx n p n x t n 0 n 0 1 2 where d denotes the forward difference operator dx n x n 1 x n p n is a sequence of nonnegative real numbers and t n is a sequence of integers such that t n 0 and lim n email protected n the state of the art on the oscillation of all solutions to these equations are established especially in the case of non monotone arguments examples illustrating the results are given

existence of positive solutions for the p laplacian with p gradient term abstract in this paper we study the existence of positive solutions for the p laplacian involving a p gradient term due to the non variational structure and the fact that the nonlinearity may be critical or supercritical the variational method is no longer valid taking advantage of global c 1 estimates and the liouville type theorems we employ the blow up argument to obtain the a priori estimates on solutions and finally obtain the existence result based on the krasnoselskii fixed point theorem

oscillations of delay difference equations consider the delay difference equation n 1 n pn n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer new oscillation criteria for this equation are established an extension of the results to difference equations with several delays is also presented

a necessary and sufficient condition for the oscillation of first order linear difference equations with several delay arguments abstract in this article we discuss the oscillation of all solutions of a first order linear delay difference equation with several delay arguments and obtain some new oscillation criteria under more relaxed conditions in particular we establish a necessary and sufficient condition only based on the coefficient functions and delay arguments when the coefficient functions are non negative examples and tables are given to illustrate our results

optimal finite dimensional recursive identification in a polynomial output mapping class abstract a time varying polynomial output equation expressing an implicit dependence of the observed signal on the parameter vector admits a finite dimensional recursive representation for the optimal on line estimator both continuous and discrete observations result in the differential systems which give the estimate deterministic exponentially weighted least squares is applied exponential stability of the identifier and convergence to the true parameter value are shown two examples are presented a continuous application originates in a ph control process the discrete identification is applied in a dynamic arma type model which is quadratic in the parameter

new oscillation criteria for second order linear difference equations with positive and negative coefficients the oscillation of second order neutral difference equations with positive and negative coefficients of the form d 2 x n la nx n t p nx n d q nx n s 0 l 1 is investigated we obtain many new results using the comparison between both first order and second order difference equations an example is given to show the strength of the obtained results

periodic solutions for extended fisher kolmogorov and swift hohenberg equations by truncature techniques abstract combining truncature techniques with a variational approach we establish an existence result for nontrivial periodic solutions for a class of fourth order ordinary differential equations involving extended fisher kolmogorov and swift hohenberg equations

brief paper identification of continuous time systems with multiple unknown time delays by global nonlinear least squares and instrumental variable methods this paper considers the identification problem of multiple input single output miso continuous time systems with unknown time delays of the inputs from sampled input output data an iterative global separable nonlinear least squares gsepnls method which estimates the time delays and transfer function parameters separably is derived to significantly reduce the possibility of convergence to a local minimum by using the stochastic global optimization techniques furthermore the gsepnls method is modified to a novel global separable nonlinear instrumental variable gsepniv method to remove the biases of the estimates in the presence of high measurement noise simulation results show that the proposed algorithms work quite well

on oscillation of differential and difference equations with non monotone delays abstract for the delay differential equation x t p t x h t 0 p t 0 h t t t 0 lim t h t we demonstrate that the inequality limsup t h t t p u d u 1 is not sufficient for oscillation moreover for any a 0 the relation limsup t h t t p u d u a generally does not imply oscillation a similar result is obtained for difference equations in terms of the maximal argument new sufficient oscillation conditions are presented for differential and difference equations

adaptive parameter identification of linear siso systems with unknown time delay abstract an adaptive online parameter identification is proposed for linear single input single output siso time delay systems to simultaneously estimate the unknown time delay and other parameters after representing the system as a parameterized form a novel adaptive law is developed which is driven by appropriate parameter estimation error information consequently the identification error convergence can be proved under the conventional persistent excitation pe condition which can be online tested in this paper a finite time ft identification scheme is further studied by incorporating the sliding mode scheme into the adaptation to achieve ft error convergence the previously imposed constraint on the system relative degree is removed and the derivatives of the input and output are not required comparative simulation examples are provided to demonstrate the validity and efficacy of the proposed algorithms

identification of time delays in linear stochastic systems abstract this paper presents a new approach to the explicit identification of an input time delay in continuous time linear systems the system model is converted to a discrete time version assuming that a digital computer is to be used for time delay estimation and control a recursive identification algorithm based on parallel kalman filtering and bayes estimation is developed the sampling rate is adapted during the time delay estimation process using the most recent estimate of the time delay this method assures that the estimate of the time delay approaches the true value with each successive iteration the proposed method also has the advantage of a fast convergence rate because prior knowledge of the delay if available can be effectively utilized

digital parameter adaptive control of processes with unknown dead time simultaneous estimation of process parameters and process time delay is achieved by applying a modification of the recursive least squares method for an extended process model the order of the numerator polynomial is increased by an upper limit of the time delay the estimation of the actual time delay email protected and the calculation of the final process model is done in every step by fitting the impulse response of a model with an assumed order email protected and time delay email protected to the impulse response of the estimated extended process model by combining this method with a feedback control algorithm parameter adaptive control algorithms result and they can be applied to processes with unknown parameters and unknown constant or time varying time delays

positive and negative solutions of a quasi linear elliptic equation by a mountain pass method and truncature techniques abstract the existence of a positive and a negative solution of a problem of the type u f x u u 0 in u 0 on is proved when f has a growth at infinity depending both on u and on u the techniques are based on an iterative scheme of mountain pass approximated solutions and the use of a suitable truncature method

recursive estimation of time delay in sampled systems abstract this paper presents a new identification method based on standard recursive least squares for the estimation of time delay in linear sampled systems the algorithm relies on the fact that if the continuous time model has a delay or anticipation shorter than one sampling time then a real negative zero arises in the corresponding sampled system by inspection of the phase contribution of this zero the value of the delay is recursively updated a frequency domain analysis is also performed to examine the characteristics of the algorithm simulation results illustrate the performances of the time delay estimation algorithm

quasilinear equations with dependence on the gradient via mountain pass techniques in rn abstract we consider the quasilinear problem p u u p 2 u f u u p 2 u in r n where 1 p n and f is a nonlinearity depending also on the gradient of the solution the existence of a positive solution is stated through an iterative method based on mountain pass techniques