adaptive parallel cascade truncated volterra filters this paper studies adaptive truncated volterra filters employing parallel cascade structures parallel cascade realizations implement higher order volterra systems as a parallel connection of multiplicative combinations of lower order truncated volterra systems a normalized lms adaptive filter is developed and its performance capabilities are evaluated using a series of simulation experiments the experimental results indicate that the normalized lms adaptive parallel cascade volterra filter has superior convergence properties over several competing structures this paper also includes an experiment that demonstrates the capability of the parallel cascade adaptive system to reduce its implementation complexity by using fewer than the maximum number of branches required for the most general realization of the system

existence of solutions for a p x kirchhoff type equation this paper is concerned with the existence and multiplicity of solutions to a class of p x kirchhoff type problem with dirichlet boundary data by means of a direct variational approach and the theory of the variable exponent sobolev spaces we establish conditions ensuring the existence and multiplicity of solutions for the problem

a factorization method for identification of volterra systems a factorization method is proposed for identification of volterra systems of order n and analyses the stability of the systems constructed by this method an optimization method is also suggested to generate optimal systems which minimize system response energy

existence and multiplicity of solutions for a nonlocal problem with critical sobolev exponent abstract in this work we are interested in considering the following nonlocal problem a b u 2 d x u u 2 2 u u q 2 u x u 0 x where r n n 4 is a smooth bounded domain a 0 b 0 1 q 2 0 and 2 2 n n 2 is the critical sobolev exponent by using the variational method and the critical point theorem some existence and multiplicity results are obtained

nontrivial solutions of kirchhoff type problems via the yang index abstract we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the yang index and critical groups

the critical problem of kirchhoff type elliptic equations in dimension four abstract we study the following kirchhoff type elliptic problem p a b u 2 d x u u q u 3 u 0 in u 0 on where r 4 is a bounded domain with smooth boundary moreover we assume a 0 b 0 and 1 q 3 in this paper we prove the existence of solutions of p our tools are the variational method and the concentration compactness argument for ps sequences

positive solutions for kirchhoff type equations with critical exponent in rn abstract in this paper we study the following nonlinear kirchhoff type equation 0 1 a b r n u 2 d x u u 2 2 u h x x r n u d 1 2 r n where a 0 b 0 n 3 2 2 n n 2 0 and h l 2 2 1 r n 0 is nonnegative by using the variational method we obtain the existence of positive solutions for eq 0 1 under some assumptions on a b

on the problem of tracking for a class of linear systems with delays and sliding modes this paper applies the block control technique to design a sliding mode regulator that guarantees asymptotic reference tracking for a class of linear delayed systems with disturbances this class of systems are those presented in so called block controllable form with delay the block control technique is used to derive a sliding manifold on which the motion of the closed loop system is stable and the tracking error is zeroed examples of the application of the proposed control strategy and observer design are illustrated

existence of soliton solutions for a quasilinear schrodinger equation involving critical exponent in rn abstract mountain pass in a suitable orlicz space is employed to prove the existence of soliton solutions for a quasilinear schrodinger equation involving critical exponent in r n these equations contain strongly singular nonlinearities which include derivatives of the second order such equations have been studied as models of several physical phenomena the nonlinearity here corresponds to the superfluid film equation in plasma physics

multiple solutions for quasilinear schrodinger equations involving critical exponent by using lions second concentration compactness principle and concentration compactness principle at infinity to prove that the ps condition holds locally and by minimax methods and the krasnoselski genus theory we establish the multiplicity of solutions for a class of quasilinear schrodinger equations arising from physics

memoryless stabilization of uncertain dynamic delay systems riccati equation approach the authors present a procedure for obtaining the memoryless linear state feedback control of uncertain dynamic delay systems the uncertainties are time varying and within a given compact set this method is an extension of the riccati equation approach proposed by i r petersen and c v hollot 1986 the extension is straightforward also the uncertainties do not need to satisfy the matching conditions

multiple positive solutions for kirchhoff type of problems with singularity and critical exponents abstract in this paper we study multiplicity of positive solutions for a class of kirchhoff type of equations with the nonlinearity containing both singularity and critical exponents we obtain two positive solutions via the variational and perturbation methods

dynamical realizations of finite volterra series in this paper realizations of finite volterra series are viewed as nonlinear analytic input output systems with state space described by an analytic manifold for a minimal realization guaranteed by h j sussmann the state space which is unique up to diffeomorphism is shown to have the homogeneous space structure of a nilmanifold the quotient of two nilpotent lie groups the structure of nilmanifolds as described by a malcev is used to show that for these systems the state space has a vector space structure as a consequence of this result it is shown that a minimal realization of a finite volterra series can be described as a cascade of linear subsystems with polynomial link maps in which the dimension o f each linear subsystem is independent of the realization considered

on the fractional schrodinger kirchhoff equations with electromagnetic fields and critical nonlinearity abstract in this paper we consider the fractional schrodinger kirchhoff equations with electromagnetic fields and critical nonlinearity e 2 s m u s a e 2 a e s u v x u u 2 s 2 u h x u 2 u x r n u x 0 as x where a e s is the fractional magnetic operator with 0 s 1 2 s 2 n n 2 s m r 0 r is a continuous nondecreasing function v r n r 0 and a r n r n are the electric and magnetic potentials respectively by using the fractional version of the concentration compactness principle and variational methods we show that the above problem i has at least one solution provided that e e and ii for any m n has m pairs of solutions if e e m where e and e m are sufficiently small positive numbers moreover these solutions u e 0 as e 0

global bifurcation and positive solution for a class of fully nonlinear problems in this paper we study global bifurcation phenomena for the following kirchhoff type problem m u x 2 d x u f x u in u 0 on where m is a continuous function under some natural hypotheses we show that 1 a m 0 0 is a bifurcation point and there is a global continuum c emanating from 1 a m 0 0 where 1 a denotes the first eigenvalue of the above problem with f x s a x s as an application of the above result we study the existence of positive solution for this problem with asymptotically linear nonlinearity

infinitely many positive solutions for kirchhoff type problems abstract this paper is concerned with the existence of infinitely many positive solutions to a class of kirchhoff type problem a b u 2 d x u f x u in and u 0 on where is a smooth bounded domain of r n a b 0 0 and f r r is a caratheodory function satisfying some further conditions we obtain a sequence of a e positive weak solutions to the above problem tending to zero in l with f being more general than that of k perera z zhang nontrivial solutions of kirchhoff type problems via the yang index j differential equations 221 2006 246 255 z zhang k perera sign changing solutions of kirchhoff type problems via invariant sets of descent flow j math anal appl 317 2006 456 463

study of a nonlinear kirchhoff equation with non homogeneous material abstract in this paper we study a non homogeneous elliptic kirchhoff equation with nonlinear reaction term we analyze the existence and uniqueness of positive solution the main novelty is the inclusion of non homogeneous term making the problem without a variational structure we use mainly bifurcation arguments to get the results

a critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations abstract for an even functional on a banach space the symmetric mountain pass lemma gives a sequence of critical values which converges to zero under the same assumptions on the functional this paper establishes a new critical point theorem which provides a sequence of critical points converging to zero the theorem is applied to sublinear elliptic equations then a sequence of solutions converging to zero is obtained

soliton solutions to kirchhoff type problems involving the critical growth in rn abstract in this article we study the existence of multiple soliton solutions for kirchhoff type problems involving the critical growth by using of the concentration compactness principle and minimax methods we obtain infinitely many solutions which tend to zero for suitable positive parameters

tensor product basis approximations for volterra filters the paper studies approximations for a class of nonlinear filters known as volterra filters although the volterra filter provides a relatively simple and general representation for nonlinear filtering it is often highly overparameterized due to the large number of parameters the utility of the volterra filter is limited the overparameterization problem is addressed in the paper using a tensor product basis approximation tpba in many cases a volterra filter may be well approximated using the tpba with far fewer parameters hence the tpba offers considerable advantages over the original volterra filter in terms of both implementation and estimation complexity furthermore the tpba provides useful insight into the filter response the paper studies the crucial issue of choosing the approximation basis several methods for designing an appropriate approximation basis and error bounds on the resulting mean square output approximation error are derived certain methods are known to be nearly optimal

on a p kirchhoff equation via fountain theorem and dual fountain theorem abstract in this paper we show the existence of infinite solutions to the kirchhoff type quasilinear elliptic equation m u p x u p d x p 1 p u x u p 2 u f x u in a smooth bounded domain r n with nonlinear boundary condition u p 2 u u p 2 on the method we used here is based on fountain theorem and dual fountain theorem

multiplicity of solutions to the generalized extensible beam equations with critical growth abstract in this paper by variational methods we study the multiplicity of solutions to the following fourth order elliptic equations of kirchhoff type with critical nonlinearity in r n 2 u m r n u 2 d x u v x u k x u q 2 u u 2 2 u x r n where 2 u u is the biharmonic operator m r r is a continuous function 0 is a parameter v r n r is a potential function and k x is a nonnegative continuous real valued function satisfying some conditions the compactness condition is proved by the lions second concentration compactness principle and concentration compactness principle at infinity

identification of structurally constrained second order volterra models continuing advances in industrial control hardware and software have increased interest in the identification of nonlinear dynamic models from chemical process data two practically important issues are those of nonlinear model structure selection and input sequence design for adequate model identification while the general nonlinear model identification problem is intractably complex we may obtain useful insights into both of these issues by restricting our attention to special cases building incrementally on our linear intuition we consider the special case of second order volterra models focusing on the effects of structural restrictions and non gaussian input sequences on the model identification problem the results presented build on the work of powers and his co workers who considered the unconstrained gaussian problem certain constrained special cases e g the hammerstein model and identification using non i i d input sequences besides extending these results to a wider class of model structure constraints and input sequences the results presented yield some useful insights into the issue of input sequence design

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

on ground state solutions for a kirchhoff type equation with critical growth in this paper with the aid of variational method and concentration compactness principle a positive ground state solution is obtained for a class of kirchhoff type equations with critical growth a b r 3 u 2 d x u u 5 k x u q 1 x r 3 u d 1 2 r 3 where 0 is a parameter 2 q 6 and k satisfies some conditions

robust stability of uncertain time delay systems and its stabilization by variable structure control in this paper two main results for uncertain time delay systems are derived the first result is the presentation of a new robust stability criterion for uncertain time delay systems the second result is the successful application of the concept of variable structure control to the stabilization problem of uncertain time delay systems the robustness and stability degree of perturbed systems in the sliding mode are also discussed last some examples are included to illustrate our results

on multiple solutions of a singular quasilinear equation on unbounded domain abstract variational methods are used to prove existence and multiplicity of solutions for the following quasilinear partial differential equation p u x s u p s 2 u k x u r 2 u in where 0 s p r n may be unbounded in particular r n is permitted

a critical kirchhoff type problem involving a nonlocal operator abstract in this paper we show the existence of non negative solutions for a kirchhoff type problem driven by a nonlocal integrodifferential operator that is m u z 2 l k u f x u u 2 2 u in u 0 in r n where l k is an integrodifferential operator with kernel k is a bounded subset of r n m and f are continuous functions z is a functional norm and 2 is a fractional sobolev exponent

existence and multiplicity of solutions for fourth order elliptic equations of kirchhoff type with critical growth in ℝn in this paper we deal with the existence and multiplicity of solutions for fourth order elliptic equations of kirchhoff type with critical nonlinearity e 4 2 u e 4 a b r n u 2 d x u v x u u 2 2 u h x u t x n by using lions second concentration compactness principle and concentration compactness principle at infinity to prove that ps condition holds locally and by variational method we prove that it has at least one solution and for any m it has at least m pairs of solutions

existence results for kirchhoff equations with hardy littlewood sobolev critical nonlinearity abstract in this paper we study a class of kirchhoff equations with hardy littlewood sobolev critical nonlinearity in r n more precisely we consider a b r n u 2 d x u a u 2 u i u p u p 2 u i u 2 2 u 2 2 2 u where a 0 b 0 n 3 0 4 n 3 n 4 2 n n p 2 2 n n 2 0 and i is a riesz potential we prove the existence and multiplicity of solutions for the equation by variational methods together with concentration compactness principle

multiplicity results for stationary kirchhoff problems involving fractional elliptic operator and critical nonlinearity in rn in this paper we study a class of stationary kirchhoff problems involving a fractional elliptic operator and critical nonlinearity in rn g u s2 su k x u q 2u u 2s 2u by using a fractional version of lions second concentration compactness principle and concentration compactness principle at infinity to prove that the ps c condition holds locally and by minimax methods and krasnoselskii genus theory we establish the multiplicity of solutions for suitable positive parameters

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

multiplicity of solutions for p x polyharmonic elliptic kirchhoff equations abstract in this paper we establish the existence of an unbounded sequence of solutions for a class of quasilinear elliptic p x polyharmonic kirchhoff equations including the new delicate degenerate case not yet covered in the literature the main tool is the symmetric mountain pass theorem of ambrosetti and rabinowitz

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

efficient algorithms for volterra system identification in this paper nonlinear filtering and identification based on finite support volterra models are considered the volterra kernels are estimated via input output statistics or directly in terms of input output data it is shown that the normal equations for a finite support volterra system excited by zero mean gaussian input have a unique solution if and only if the power spectral process of the input signal is nonzero at least at m distinct frequencies where m is the memory of the system a multichannel embedding approach is introduced a set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format efficient algorithms for the estimation of the volterra parameters are derived for batch as well as for adaptive processing an efficient order recursive method is presented for the determination of the volterra model structure the proposed methods are illustrated by simulations

i i r volterra filtering with application to bilinear systems a new nonlinear filtering technique by means of infinite impulse response iir volterra functionals is developed it yields the projection onto the closed class of finite volterra series with separable kernels of arbitrary degree k such an optimal estimator is finitely realizable as a bilinear system with parameters that are computable off line moreover if the original system model is itself bilinear this computation is finitely recursive through higher moments of degree 2 k two simple illustrating examples are developed i estimation of the covariance of the internal white noise driving a linear system and ii filtering of a non gaussian linear system driven by a poisson process the robustness with respect to the observation noise distribution is finally examined

existence and multiplicity of solutions for a superlinear kirchhoff type equations with critical sobolev exponent in r n abstract in this article we consider a class of superlinear kirchhoff type equations with critical growth a b r n u 2 d x u u 2 1 k x u q 1 x r n u d 1 2 r n where 0 n 4 2 q 2 2 2 n n 2 a b 0 and a b 0 k satisfies some conditions by using the variational method the multiplicity of positive solutions and infinitely many pairs of solutions are obtained

solutions for a class of quasilinear choquard equations with hardy littlewood sobolev critical nonlinearity abstract in this article we consider the quasilinear choquard equation with critical nonlinearity in r n e 2 u v x u e 2 u u 2 r n u 2 2 x y d y u 2 2 2 u h x u u where 0 n n 3 2 2 n n 2 is the critical exponent in the sense of hardy littlewood sobolev inequality e is a real parameter by using a change of variables the quasilinear equations are reduced to a semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem under suitable assumptions on v and h we investigate the existence and multiplicity of solutions for the above problem by using the mountain pass theorem and index theory in order to overcome the lack of compactness we apply the concentration compactness principle