multiple existence of sign changing solutions for coupled nonlinear schrodinger equations abstract in this paper we consider the multiple existence of sign changing solutions of coupled nonlinear schrodinger equations p u 1 u 1 u 3 v 2 u in r 3 v 2 v 2 v 3 u 2 v in r 3 where 1 2 1 2 are positive and 0

optimal liouville type theorems for noncooperative elliptic schrodinger systems and applications we study multi component elliptic schrodinger systems arising in nonlinear optics and bose einstein condensation phenomena we prove new liouville type nonexistence theorems as well as a priori bounds decay and singularity estimates this is shown under an optimal sobolev growth restriction on the nonlinearities thus improving on recent results of dancer et al and of tavares et al these systems are of non cooperative form and hence cannot be tackled by maximum principle methods such as moving planes instead we rely on a delicate combination of rellich pohozaev type identities sobolev and interpolation inequalities on sn 1 and feedback and measure arguments we also extend our results to a rather general class of gradient type systems

self similarity and asymptotic stability for coupled nonlinear schrodinger equations in high dimensions abstract this paper is concerned with systems of coupled schrodinger equations with polynomial nonlinearities and dimension n 1 we show the existence of global self similar solutions and prove that they are asymptotically stable in a framework based on weak l p spaces whose elements have local finite l 2 mass the radial symmetry of the solutions is also addressed

radial solutions and phase separation in a system of two coupled schrodinger equations we consider the nonlinear elliptic system left begin aligned delta u u u 3 beta v 2u 0 quad rm in mathbb b delta v v v 3 beta u 2v 0 quad rm in mathbb b u v 0 quad rm in mathbb b quad u v 0 quad rm on partial mathbb b end aligned right where n leqq 3 and mathbb b subset mathbb r n is the unit ball we show that for every beta leqq 1 and k in mathbb n the above problem admits a radially symmetric solution u v such that u v changes sign precisely k times in the radial variable furthermore as beta to infty after passing to a subsequence u w and v w uniformly in mathbb b where w w w has precisely k nodal domains and is a radially symmetric solution of the scalar equation w w w3 0 in mathbb b w 0 on partial mathbb b within a hartree fock approximation the result provides a theoretical indication of phase separation into many nodal domains for bose einstein double condensates with strong repulsion

bifurcation diagrams of coupled schrodinger equations radially symmetric solutions of many important systems of partial differential equations can be reduced to systems of special ordinary differential equations a numerical solver for initial value problems for such systems is developed based on matlab and numerical bifurcation diagrams are obtained according to the behavior of the solutions various bifurcation diagrams of coupled schrodinger equations from nonlinear physics are obtained which suggests the uniqueness of the ground state solution

brief paper adaptive observers for nonlinearly parameterized class of nonlinear systems in this paper one proposes adaptive observers for a class of uniformly observable mimo nonlinear systems with general nonlinear parameterizations the state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well defined persistent excitation condition moreover the gain of the observers involves a design function that has to satisfy a simple condition which is given different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function the theory is supported by simulation results related to the estimation of the biomass concentration and the contois model parameters in a bioreactor

online adaptive optimal control for continuous time nonlinear systems with completely unknown dynamics an online adaptive optimal control is proposed for continuous time nonlinear systems with completely unknown dynamics which is achieved by developing a novel identifier critic based approximate dynamic programming algorithm with a dual neural network nn approximation structure first an adaptive nn identifier is designed to obviate the requirement of complete knowledge of system dynamics and a critic nn is employed to approximate the optimal value function then the optimal control law is computed based on the information from the identifier nn and the critic nn so that the actor nn is not needed in particular a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier nn and critic nn simultaneously which converge to small neighbourhoods around their ideal values the closed loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the lyapunov theory the proposed ada

a sharp threshold of blow up for coupled nonlinear schrodinger equations this paper is concerned with the coupled supercritical nonlinear schrodinger equations which have applications in many physical problems especially in nonlinear optics two types of new invariant evolution flows are established a sharp threshold of blow up and global existence of solutions for the equations is derived it is shown that the main result obtained includes parts of those presented by fanelli and montefusco 2007 j phys a math theor 40 14139 50x

neural network observer based optimal control for unknown nonlinear systems using adaptive dynamic programming in this paper an observer based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming adp algorithm first a neural network nn observer is designed to estimate system states then based on the observed states a neuro controller is constructed via adp method to obtain the optimal control in this design two nn structures are used a three layer nn is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics and a critic nn is employed to approximate the value function the optimal control law is computed using the critic nn and the observer nn uniform ultimate boundedness of the closed loop system is guaranteed the actor critic and observer structures are all implemented in real time continuously and simultaneously finally simulation results are presented to demonstrate the effectiveness of the proposed control scheme

observer design for a class of mimo nonlinear systems a simple observer is proposed for a large class of mimo nonlinear systems which includes many physical models the main characteristic of the proposed observer lies in the easiness of its implementation and calibration indeed the gain of this observer does not necessitate the resolution of any dynamical system and its expression is given moreover its calibration is achieved through the choice of a single parameter a simulation example is given in order to illustrate the performance of the proposed observer

special set and solutions of coupled nonlinear schrodinger equations a special set of n coupled nonlinear schrodinger equations which consists of 2n interaction types each of which is characterized by a specific array of interaction parameters is presented it is shown that every lame function of order n n is a solution for one or more components for one or more interaction types of this special set simple rules that relate interaction and solution types and interesting features of these relationships are presented

observer design for nonlinear systems under unknown time varying delays the design of observers for nonlinear systems with unknown time varying bounded delays on both state and input still constitutes an open problem in this technical note we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a lyapunov krasovskii functional suitable choice sufficient conditions are provided to prove the practical stability of the observer it is shown that the observation error is bounded and depends on the size of two parameters the known upper bound delay of the unknown time varying function delay and the instantaneous state dynamic variation furthermore for the particular case of constant known time delay the convergence of the proposed observer becomes exponential the feasibility of the proposed strategy is illustrated by a numerical example

multiple positive solutions for linearly coupled nonlinear elliptic systems with critical exponent abstract this paper deals with the following system linearly coupled by nonlinear elliptic equations u 1 u u 2 2 u v x v 2 v v 2 2 v u x u v 0 on here is a smooth bounded domain in r n n 3 1 2 1 are constants 1 is the first eigenvalue of h 0 1 2 2 n n 2 is the sobolev critical exponent and r is a coupling parameter by variational method we prove that this system has a positive ground state solution for some 0 via a perturbation argument we show that this system also admits a positive higher energy solution when is small moreover the asymptotic behaviors of the positive ground state and higher energy solutions as 0 are analyzed

high gain predictor based output feedback control for time delay nonlinear systems this paper designs a high gain predictor for output feedback control of nonlinear systems in the presence of input output and state delays the high gain predictor realizes the states appearing in the output feedback control in terms of predictive state delayed state and current state the system includes internal and external dynamics and the closed loop system under state feedback is required to be asymptotically stable and locally exponentially stable positively invariant sets are found to verify boundedness exponential stability and performance recovery in the simulation a saturated sliding mode control is applied to demonstrate the performance recovery of the closed loop system and the fact that the high gain predictor parameter has a lower bound related to time delays

brief paper observer design and fault diagnosis for state retarded dynamical systems in this paper we propose a reduced order observer for state estimation in a class of state delayed dynamical systems driven by known as well as unknown inputs conditions for existence of the proposed observer plus the stability and convergence proof for the observer based on the razumikhin theorem are given additionally the proposed observer is utilized in an analytical redundancy based approach for sensor and actuator failure detection problem in the same class of time delay dynamical systems finally the applicability and effectiveness of the proposed fdi scheme is illustrated through numerical examples

joint state estimation and delay identification for nonlinear systems with delayed measurements the problem of state estimation for nonlinear systems with unknown state or measurement delays is still an open problem in this paper we consider the case of measurement delay and propose an approach that combines a delay identifier with a suitable high gain observer in order to achieve simultaneous estimation of state and delay we provide sufficient conditions that guarantee the exponential convergence to zero of the errors globally with respect to the system variables and locally with respect to the delay estimation we validate the method through an example concerning population models

exponential estimates for retarded time delay systems an lmi approach exponential estimates and sufficient conditions for the exponential stability of linear time delay systems are given the proof make use of lyapunov krasovskii functionals and the conditions are expressed in terms of linear matrix inequalities

segregated and synchronized vector solutions to linearly coupled systems of schrodinger equations in this paper we study the following linearly coupled system e2 ui pi x ui ui3 j in ijuj ui h1 r3 i 1 n where e 0 is a small parameter pi x are positive potentials and ij ji 0 i j are coupling constants for i j 1 n we investigate the effect of potentials to the structure of the solutions more precisely we construct multi spikes solutions concentrating near the local maximum point x0i of pi x when x0i x0j pi x0i pj x0j a i j i j 1 n the components have spikes clustering at the same point as e 0 when x0i x0j i j the components have spikes clustering at the different points as e 0

new existence and symmetry results for least energy positive solutions of schrodinger systems with mixed competition and cooperation terms abstract in this paper we focus on existence and symmetry properties of solutions to the cubic schrodinger system u i i u i j 1 d i j u j 2 u i in r n i 1 d where d 2 i i i 0 i j j i r for j i n 2 3 the underlying domain is either bounded or the whole space and u i h 0 1 or u i h rad 1 r n respectively we establish new existence and symmetry results for least energy positive solutions in the case of mixed cooperation and competition coefficients as well as in the purely cooperative case

sign changing solutions for coupled nonlinear schrodinger equations with critical growth abstract we consider the following nonlinear schrodinger system with critical growth u j j u j i 1 k i j u i 2 2 u j 2 2 2 u j in u j 0 on j 1 k where is a bounded smooth domain in r n 2 2 n n 2 0 j 1 j 1 k 1 is the first eigenvalue of with zero dirichlet boundary condition we consider the repulsive case namely j j 0 j 1 k i j j i 0 i j i j 1 k the existence of infinitely many sign changing solutions as bound states is proved provided n 7 by approximations of systems with subcritical growth and by the concentration analysis on approximating solutions

strong converse inequalities for meyer konig and zeller operators abstract in this paper we give the strong converse inequality of type b for meyer konig and zeller operators

high gain observer for a class of time delay nonlinear systems this article proposes a high gain observer design for a class of nonlinear systems with multiple known time varying delays intervening in the states and the inputs in the free delay case the class of systems under consideration coincides with a canonical form characterising a class of multi output nonlinear systems which are observable for any input the underlying high gain design has been mainly motivated by its inherent simplicity from both design and implementation points of view indeed the observer gain is determined from an explicit resolution of a time invariant lyapunov algebraic equation up to the specification of a single design parameter an academic observation problem is addressed to illustrate the effectiveness of the proposed observer

positive solutions to some systems of coupled nonlinear schrodinger equations abstract we study the existence of nontrivial bound state solutions to the following system of coupled nonlinear time independent schrodinger equations u j j u j j u j 3 k 1 k j n j k u j u k 2 u j w 1 2 r n j 1 n where n 1 2 3 j j 0 for j 1 n the coupling parameters j k k j r for j k 1 n j k precisely we prove the existence of nonnegative bound state solutions for suitable conditions on the coupling factors additionally with more restrictive conditions on the coupled parameters we show that the bound states founded are positive

sharp thresholds of blow up and global existence for the coupled nonlinear schrodinger system in this paper we establish two new types of invariant sets for the coupled nonlinear schrodinger system in the euclidean n space rn and derive two sharp thresholds of blow up and global existence for its solutions some analogous results for the nonlinear schrodinger system posed on the hyperbolic space hn and on the standard 2 sphere s2 are also presented our arguments and constructions are improvements of some previous works on this direction at the end we give some heuristic analysis about the strong instability of the solitary waves the relation between the two types of thresholds is a very interesting problem and we leave it as an open problem for further study

linear functional observers for systems with delays in state variables this paper is concerned with the design of linear functional state observers for systems with delays in state variables in particular the necessary and sufficient conditions for the existence of the rth order observers are given sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear matrix in equality formulation a systematic design method of these observers is presented numerical examples are given to illustrate this method

solitary and self similar solutions of two component system of nonlinear schrodinger equations conventionally to learn wave collapse and optical turbulence one must study finite time blow up solutions of one component self focusing nonlinear schrodinger equations nlse here we consider simultaneous blow up solutions of two component systems of self focusing nlse by studying the associated self similar solutions we prove two components of solutions blow up at the same time these self similar solutions may come from solitary wave solutions with multi bumps forming abundant geometric patterns which cannot be found in one component self focusing nlse our results may provide the first step to investigate optical turbulence in two component systems of nlse

blowup and solitary wave solutions with ring profiles of two component nonlinear schrodinger systems abstract blowup ring profiles have been investigated by finding non vortex blowup solutions of nonlinear schrodinger equations nlses cf fibich et al 2005 7 and fibich et al 2007 8 however those solutions have infinite l 2 norm so one may not maintain the ring profile all the way up to the singularity to find h 1 non vortex blowup solutions with ring profiles we study the blowup solutions of two component systems of nlses with nonlinear coefficients and j j 1 2 when 0 and 1 2 0 the two component system can be transformed into a multi scale system with fast and slow variables which may produce h 1 blowup solutions with non vortex ring profiles we use the localized energy method with symmetry reduction to construct these solutions rigorously on the other hand these solutions may describe steady non vortex bright ring solitons various types of ring profiles including m ring and ring ring profiles are presented by numerical solutions

delay identification for a class of nonlinear systems abstractthe problem of state estimation for nonlinear systems with unknown state delays is still an open problem in this paper we propose to add a delay identifier to suitable high gain observers in order to achieve simultaneous estimation of state and delay in the case of one constant delay in the state we provide sufficient conditions to guarantee the exponential convergence to zero of the errors globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation we validate the method through an example concerning chaotic oscillators

ground state of n coupled nonlinear schrodinger equations in mathbb r n n leq 3 we establish some general theorems for the existence and nonexistence of ground state solutions of steady state n coupled nonlinear schrodinger equations the sign of coupling constants ij s is crucial for the existence of ground state solutions when all ij s are positive and the matrix is positively definite there exists a ground state solution which is radially symmetric however if all ij s are negative or one of ij s is negative and the matrix is positively definite there is no ground state solution furthermore we find a bound state solution which is non radially symmetric when n 3

the strong converse inequality for bernstein kantorovich operators abstract we give a solution to a problem posed by totik at the 1992 texas conference concerning the strong converse inequality for approximation by bernstein kantorovich operators the approximation behaviour of these operators is characterized for 1 p by using an appropriate k functional which for 1 p is equivalent to a second order modulus and an extra term crucial in our approach are estimates for the derivatives of iterated kantorovich operators

symmetry properties in systems of semilinear elliptic equations abstract we investigate symmetry properties of solutions of systems of semilinear elliptic equations the two main tools we use consist of the maximum principle and the device of moving parallel planes to a critical position and then showing that the solution is symmetric about the limiting plane an application to the belousov zhabotinskii chemical reaction is given

positive ground state solutions and multiple nontrivial solutions for coupled critical elliptic systems in this study we consider the following coupled elliptic system with a sobolev critical exponent p u1 1u1 1u1p1 1 1u12 1 u12 2 1u22 2 x u2 2u2 2u2p2 1 2u22 1 u12 2u22 2 1 x u1 u2 0in u1 u2 0on where rn is a bounded smooth domain n 5 2 0 for j 1 2 and 1 is the first eigenvalue of with the dirichlet boundary condition we demonstrate the existence of a positive ground state solution for problem p when the coupling parameter 1 2 under some other conditions we show the nonexistence of positive solutions for p when n 3 we also construct multiple nontrivial solutions and sign changing solutions for the following system u1 1u1 1u13 u22u1 x u2 2u2 2u23 u12u2 x u1 u2 0on where rn is a bounded smooth domain and n 4

two component bose einstein condensates abstract recently coupled systems of nonlinear schrodinger equations have been used extensively to describe bose einstein condensates in this paper we study the structure of vortices of the coupled nonlinear equations for two component bose einstein condensates bec in a three dimensional space we show that vortices is 1 rectifiable set and give its mean curvature in particular we show that large interspecies scattering length causes vortices for two component bec

segregated and synchronized vector solutions for nonlinear schrodinger systems we consider the following nonlinear schrodinger system in mathbb r 3 left begin array ll delta u p x u mu u 2 u beta v 2u quad x in mathbb r 3 delta v q x v nu v 2 v beta u 2v quad x in mathbb r 3 end array right where p r and q r are positive radial potentials mu 0 nu 0 and beta in mathbb r is a coupling constant this type of system arises in particular in models in bose einstein condensates theory

symmetric ground state solutions of m coupled nonlinear schrodinger equations abstract we prove the existence of radial and radially decreasing ground states of an m coupled nonlinear schrodinger equation with a general nonlinearity

an observer design for linear time delay systems an observer design is proposed for linear systems with time delays the key to the design is to find a generalized coordinate change such that in the new coordinates all the time delay terms are injected by the system s output the existence of such a coordinate change is guaranteed by a rank condition on the observability matrix the novelty of the proposed design is clearly reflected in the multiple output case where a dimensional expansion in the coordinate change could become necessary and hence is allowed

multiplicity of localized solutions of nonlinear schrodinger systems for infinite attractive case abstract in this paper we consider the following nonlinear schrodinger system 2 u v 1 x u u v 2 in r n u h 1 r n 2 v v 2 x v u 2 v in r n v h 1 r n where n 3 0 1 v i c 1 r n r 0 inf x r n v i x sup x r n v i x i 1 2 and there exists a bounded open set r n with smooth boundary such that inf x min v 1 x v 2 x 0 we prove the existence of a given number of semi positive solutions localized in here we say u v is semi positive if either u 0 or v 0

note on ground states of a nonlinear schrodinger system abstract we give a sufficient condition for the existence of positive radial ground states of the time independent schrodinger system u 1 u 1 1 u 1 3 12 u 2 2 u 1 13 u 3 2 u 1 in r n u 2 u 2 12 u 1 2 u 2 2 u 2 3 23 u 3 2 u 2 in r n u 3 u 3 13 u 1 2 u 3 23 u 2 2 u 3 3 u 3 3 in r n u 1 x 0 u 2 x 0 u 3 x 0 as x where n 1 2 3 0 j 0 and i j 0 i j for i j 1 2 3 and in some special cases our conditions are also necessary

lyapunov stability analysis for nonlinear delay systems abstract sufficient conditions ensuring that a nonlinear system with disturbances having a delay is globally asymptotically stable independent of delay are given the proof carried out relies extensively on a characterization of the stability property in terms of lyapunov function the result is applied to some biological systems and neural networks a stabilizing memoryless controller for a second order system with state delay is also proposed

semi global observer for multi output nonlinear systems abstract we present an explicit form of nonlinear observers for a class of multi input multi output systems observer construction for multi output nonlinear systems is not a trivial extension of single output case especially when the global error convergence is of interest in this paper we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself and the overall system has a block triangular form for each subsystem hence the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed the construction is based on the saturation of some estimates which is originated by khalil and esfandiari for the use of semi global output feedback control

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example