control lyapunov razumikhin functions and robust stabilization of time delay systems motivated by control lyapunov functions and razumikhin theorems on stability of time delay systems we introduce the concept of control lyapunov razumikhin functions clrf the main reason for considering clrfs is construction of robust stabilizing control laws for time delay systems most existing universal formulas that apply to clfs are not applicable to clrfs it turns out that the domination redesign control law applies achieving global practical stability and under an additional assumption global asymptotic stability this additional assumption is satisfied in the practically important case when the quadratic part of a clrf is itself a clrf for the jacobian linearization of the system the clrf based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin while in general construction of clrfs is an open problem we show that for several classes of time delay systems a clrf can be constructed in a systematic way

global stabilization of high order nonlinear time delay systems by state feedback abstract we consider the problem of global stabilization by state feedback for a class of high order nonlinear systems with time delay by developing a novel dynamic gain based backstepping approach a state feedback controller independent of the time delay is explicitly constructed with the help of appropriate lyapunov krasovskii functionals the precise knowledge even the upper bound of the time delay is not required it is proved that the states of the nonlinear time delay systems can be regulated to the origin while all the closed loop signals are globally bounded finally both physical and academic examples are given to illustrate the applications of the proposed scheme

multiplicity of positive solutions for the kirchhoff type equations with critical exponent in rn abstract in this work we study the existence and multiplicity of solutions to the following kirchhoff type problem with critical nonlinearity in r n a b r n u p d x p u u p 1 f x u x r n u d 1 p r n where n 2 p a b 0 and the nonlinearity f x u satisfies certain subcritical growth conditions by using topological and variational methods infinitely many positive solutions are obtained

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

validity of the formal edgeworth expansion when the underlying distribution is partly discrete validity of the formal edgeworth expansion for the distribution of the statistic ng x n n y n n is considered here x n is a continuous variate and y n is a discrete variate in general if x n y n resemble the sum of i i d variables and the partial derivative of g with respect to the first variable has full rank it is possible to establish an edgeworth expansion

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

multiple existence of solutions for a nonhomogeneous elliptic problem with critical exponent on rn abstract let n 3 2 2 n n 2 our purpose in this paper is to consider the existence and multiplicity of solutions of the problem u u 2 2 u f on r n u h 1 r n where f l 2 2 1 r n l r n f 0 and f 0

edgeworth expansions of suitably normalized sample mean statistics for atomic markov chains this paper is devoted to the problem of estimating functionals of type f fd from observations drawn from a positive recurrent atomic markov chain open image in new window with stationary distribution the properties of different estimators are studied beyond an accurate estimation of their bias the estimation of their asymptotic variance is considered we also show that the results of malinovskii 1987 on the validity of the formal edgeworth expansion for sample mean statistics of type t n n 1 n i 1 f x i extend to their studentized versions normalized by the asymptotic variance estimates we consider

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

existence of positive ground state solutions for a critical kirchhoff type problem with sign changing potential abstract in this work we are interested in studying the following kirchhoff type problem a b u 2 d x u f x u 2 2 u g x u q 1 u x u 0 x where r n n 3 is a smooth bounded domain 2 2 n n 2 is the critical sobolev exponent 0 q 1 0 and f l with the set x f x 0 of positive measures and g l with g x 0 g 0 by the nehari method and variational method the existence of positive ground state solutions is obtained

nonsmooth feedback control of time delay nonlinear systems a dynamic gain based approach this technical note addresses the problem of global control for a class of time delay nonlinear systems under a smoothness condition on the system nonlinearities a delay independent non smooth dynamic state compensator is constructed by developing a dynamic gain based design method with the help of appropriate lyapunov krasovskii functionals it is shown that all the states of the time delay nonlinear system can be regulated to the origin while maintaining boundedness of the closed loop system a benchmark example is given to illustrate the effectiveness of the proposed non smooth feedback controller

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

bounded state solution of degenerate kirchhoff type problem with a critical exponent abstract in the present paper we investigate the following degenerate kirchhoff type problem b r n u 2 d x u v x u u 2 2 u in r n u d 1 2 r n where b is a positive constant v l n 2 r n is a given nonnegative function and 2 is the critical exponent quite a few papers have been published about the degenerate kirchhoff type problem with a critical exponent moreover this degenerate problem in r n n 5 has never been considered so far we obtain some sufficient conditions on the existence of bounded state solution for this degenerate problem as to the cases where n 5 it is the first time to consider the degenerate problem

multiple positive solutions to a kirchhoff type problem involving a critical nonlinearity abstract in this paper we investigate a class of kirchhoff type problem involving a critical nonlinearity 1 b u 2 d x u u u 4 u u h 0 1 where b 0 1 1 is the principal eigenvalue of h 0 1 with the help of the nehari manifold we obtain the multiplicity of positive solutions for in a small right neighborhood of 1 and prove that one of the solutions is a positive ground state solution which is different from the result of brezis nirenberg in 1983 this paper can be regarded as the complementary work of naimen 2015

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

delay adaptive control for nonlinear systems we present a systematic delay adaptive prediction based control design for nonlinear systems with unknown long actuator delay our approach is based on the representation of the constant actuator delay as a transport partial differential equation pde in which the convective speed is inversely proportional to the unknown delay we study two different frameworks assuming first that the actuator state is measured and relaxing afterward for the full state feedback case we prove global asymptotic convergence of the proposed adaptive controller while in the second case replacing the actuator state by its adaptive estimate we prove local regulation the relevance of the obtained results are illustrated by simulations of a biological activator repressor system

the nehari manifold for a kirchhoff type problem involving sign changing weight functions abstract this paper examines a class of kirchhoff type equations that involve sign changing weight functions using nehari manifold and fibering map the existence of multiple positive solutions is established

remarks on an elliptic equation of kirchhoff type abstract we present a short survey on the nonlocal elliptic boundary value problem m u 2 d x u f x u in u 0 on where is a smooth bounded domain of r n m is a positive function and f has subcritical growth

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

fractional kirchhoff type equation with hardy littlewood sobolev critical exponent abstract in this paper we consider the following fractional kirchhoff type equation a b r n r n u x u y 2 x y n 2 s d x d y s u i u 2 h u 2 h 2 u in r n where n 3 s 0 1 a 0 b 0 0 n and 2 h n n 2 s is the hardy littlewood sobolev critical exponent and i is the riesz potential we establish the existence nonexistence and multiplicity of nontrivial solutions to above equation

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

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

is the improved likelihood ratio statistic really improved in the discrete case summary on the basis of some numerical studies we argue that bartlett adjustment of the likelihood ratio statistic for discrete data does not in general yield an improvement in the asymptotic error rate of the chi squared approximation also we argue that the small sample effect of the bartlett adjustment is unclear and that it is in no way comparable with the improvement obtained for continuous data

the existence of nontrivial solutions for the critical kirchhoff type problem in rn abstract in this paper we study the problem 0 1 a b r n u 2 d x u v x u f u g x u 2 1 in r n where n 3 a b 0 when n 3 and 0 is small under suitable conditions on v f and g we prove 0 1 has two nontrivial solutions when n 4 and g x 1 we also obtain the existence and non existence results

existence and multiplicity of solutions for critical kirchhoff type p laplacian problems abstract in this paper we deal with the existence multiplicity and asymptotic behavior of solutions for the following stationary kirchhoff problems involving the p laplacian m u p d x p u f x u u p 2 u in u 0 on where is a bounded smooth domain of r n m r 0 r 0 is a continuous function satisfying some extra assumptions by using the mountain pass theorem the existence of solutions is obtained by applying an abstract critical point theorem based on the cohomological index we prove the existence of multiple solutions for the above problem when parameter belongs to some left neighborhood of the eigenvalue of the nonlinear operator u 1 p p where p n p p we also investigate the asymptotic behavior of solutions when converges to infinity the main feature as well as the main difficulty of our problem is the fact that the kirchhoff term m could be zero at zero i e the problem is degenerate

positive solutions for a critical p laplacian problem with a kirchhoff term abstract in this article the following p laplacian problem with kirchhoff term and critical exponent is studied a b r n u p d x p u u p 1 h x x r n u d 1 p r n where a 0 b 0 1 p n p n p n p p u d i v u p 2 u and h l p p 1 r n is nonzero and nonnegative when 0 with the help of the recent result of b sciunzi adv math 291 2016 12 23 infinitely many positive solutions are obtained by some analysis techniques while 0 by the variational method some results about positive solutions are obtained

existence of a positive solution for a kirchhoff problem type with critical growth via truncation argument abstract in this paper we shall show an existence result of a positive solution for a kirchhoff problem type in a bounded domain of r n that is for the problem m u 2 d x u f x u u 2 2 u in u 0 on we shall study the asymptotic behavior of this solution when converges to infinity our approach is based on the variational method an appropriated truncated argument and a priori estimates to obtain the solution

global asymptotic stabilization for chains of integrators with a delay in the input the problem of the global uniform asymptotic stabilization by bounded feedback of a chain of integrators with a delay in the input is solved no limitation on the size of the delay is imposed to validate the approach a third order example is presented

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

infinitely many positive solutions for a p x kirchhoff type equation this paper is concerned with the existence of infinitely many positive solutions to a class of p x kirchhoff type problem by means of a direct variational approach and the theory of the variable exponent sobolev spaces we establish the existence of infinitely many distinct positive solutions whose w1 p x norms and l norms tend to zero under suitable hypotheses about nonlinearity

existence results of positive solutions of kirchhoff type problems abstract in the present paper we use variational methods to prove two existence results of positive solutions of the following kirchhoff type problems a b u 2 u f x u in u 0 on one deals with the asymptotic behaviors of f near zero and infinity and the other deals with 4 superlinear of f at infinity

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

adaptive control of nonlinearly parameterized systems the smooth feedback case studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization using a parameter separation technique and the tool of adding a power integrator we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation in contrast to the existing results in the literature a key feature of our adaptive regulator is its minimum order property namely no matter how big the number of unknown parameters is the order of the dynamic compensator is identical to one and is therefore minimal as a consequence global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one dimensional adaptive controllers without imposing any extra e g convex concave conditions on the unknown parameters

non degeneracy of positive solutions of kirchhoff equations and its application abstract a non degeneracy theorem for positive solutions of the standard kirchhoff model is proved in all cases except for n 5 and b r n q 2 d x 2 n 4 n 4 2 n 2 n 2 2 in particular for dimensions n 5 and b r n q 2 d x 2 n 4 n 4 2 n 2 n 2 2 we show that there exist two non degenerate positive solutions of the kirchhoff equations which seem to be completely different from the result of the standard schrodinger equation the effects of the non local term on the positive solution set are also studied we show that the non local term has no effect on the structure of the positive solution set for dimensions 1 n 3 and the effects eventually appear for dimensions n 4 with the non degeneracy property of positive solutions of the limit problem we construct concentrated solutions of a singularly perturbed kirchhoff problem via the well known lyapunov schmidt reduction method for dimensions n 5 the existence result of concentrated solutions is completely new and is not implied by the main result of g m figueiredo et al in 19 where a generalized singularly perturbed kirchhoff problem was considered

global stabilization of cascade systems by c sup 0 partial state feedback this paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization and the notion and properties of the input to state stability lyapunov function can be effectively coupled resulting in globally stabilizing c sup 0 partial state feedback controllers for a class of cascade systems which may not be smoothly stabilizable even locally

the critical neumann problem of kirchhoff type in this paper we study the critical neumann problem of kirchhoff type by using the variational method and the concentration compactness argument the existence and multiplicity of nontrivial solutions are obtained

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

sign changing and multiple solutions of kirchhoff type problems without the p s condition abstract the existence of nontrivial solutions of kirchhoff type equations is an important nonlocal quasilinear problem in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4 superlinear kirchhoff type problems without the p s condition one concerning the existence of a nontrivial solution and the other one concerning the existence of sign changing solutions and multiple solutions a b u 2 u f x u in u 0 on

existence and multiplicity of solutions for kirchhoff type equations abstract in this paper the existence and multiplicity of weak solutions are obtained for a class of kirchhoff type problems with dirichlet boundary value conditions by using the mountain pass theorem the local linking theorem the fountain theorem and the symmetric mountain pass lemma in critical point theory

a continuous feedback approach to global strong stabilization of nonlinear systems we present a continuous feedback approach to the problem of global strong stabilization for genuinely nonlinear systems that may not be stabilized even locally by any smooth feedback we describe conditions under which it is possible to prove while no smooth controllers exist the existence of continuous state feedback control laws that achieve global strong stability gss in the sense of kurzweil 1956 the proof is constructive and carried out by developing a machinery which combines the theory of homogeneous systems with the idea of adding a power integrator for the explicit construction of globally stabilizing continuous controllers we then illustrate by means of examples how this machinery can be used to overcome the topological obstruction caused by smooth feedback and hence resulting in new solutions to a variety of open control problems including global stabilization of an underactuated unstable two degree of freedom mechanical system

liouville theorems for kirchhoff equations in rn this paper is devoted to the nonexistence of nontrivial weak solutions for the kirchhoff equation a b rn u 2 dx u x qf u in rn we prove that the equation has no weak solution if a 0 b 0 q 2 and f is a positive convex nondecreasing function if only b 0 and f is a non negative function we establish the nonexistence of weak solutions u satisfying lim infr r1 n2 br x qf u dx 0 this implies that the equation has no weak solution when n 2 and f is a positive function we also show that the equation has no stable weak solution in dimension n 0

standardized log likelihood ratio statistics for mixtures of discrete and continuous observations on considere des cas ou la statistique exhaustive minimale est partiellement discrete et partiellement continue en particulier on considere des problemes de test associes avec des durees de vie exponentielles censurees

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

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

a priori bounds for positive solutions of kirchhoff type equations abstract let be a bounded smooth domain in r n assume that 0 2 1 2 a 0 and b 0 we consider the following dirichlet problem of kirchhoff type equation 0 1 a b u 2 2 u u p 1 u h x u u in u 0 on with p 0 2 1 where 2 for n 2 and 2 n 2 n 2 for n 3 under suitable conditions of h x u u see a h 1 and h 2 in section 3 we get a priori estimates for positive solutions to problem 0 1 by making use of these estimates and the continuous method we further get some existence results for positive solutions to problem 0 1 when 0 p 1 or 2 1 p 2 effects of the term a b u 2 2 on the solution set of problem 0 1 can be seen in an example given in section 2