existence of sign changing solutions for nonlocal kirchhoff schrodinger type equations in r3 abstract in this paper we investigate the existence of sign changing solution for a class nonlocal kirchhoff schrodinger type equation a b r 3 u 2 d x u v x u f x u x r 3 where a and b are positive constants with the help of the constraint variational method and via a direct approach we show the existence of sign changing solution and prove that the sign changing solution has precisely two nodal domains this work can be regarded as the complement for some results of the literature

revisit to sign changing solutions for the nonlinear schrodinger poisson system in r3 abstract in this paper we investigate the existence of solutions for the nonlinear schrodinger poisson system with zero mass by introducing some new ideas we prove via the constraint variational method and the quantitative deformation lemma that the system has a sign changing solution

controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension the ultimate state of projective synchronization is hardly predictable a control algorithm is thus proposed to manipulate the synchronization in arbitrary dimension the control law derived from the lyapunov stability theory with the aid of slack variables is effective to any initial conditions the method allows us to amplify and reduce the synchronized dynamics in any desired scale with tiny control inputs applications are illustrated for seven and ten dimensional chaotic systems

structure of ground state solutions of singular semilinear elliptic equations abstract this paper deals with a class of singular semilinear elliptic equations in r n where the combined effects of a singular and a sublinear term allow us to establish some existence symmetry and uniqueness results for positive ground state solutions

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

an exact estimate result for singular p laplacian equations with sign changing potential abstract in this paper we study the multiplicity of positive solutions for a singular p laplacian problem with sign changing potential by the nehari method and some analysis techniques we obtain two positive solutions and point out one of the two positive solutions is a ground state solution moreover we provide an exact estimate to ensure the singular p laplacian problem has two positive solutions

existence of a positive solution to kirchhoff type problems without compactness conditions abstract the existence of a positive solution to a kirchhoff type problem on r n is proved by using variational methods and the new result does not require usual compactness conditions a cut off functional is utilized to obtain the bounded palais smale sequences

existence of solution for a class of nonvariational kirchhoff type problem via dynamical methods abstract in this paper we use dynamical methods to establish the existence of nontrivial solution for the following class of kirchhoff type problem p 1 b u 2 d x u f u h u u x u 0 x where r n n 2 3 is a smooth bounded domain b 0 f r r and h r r n 0 are c 1 functions that satisfy some technical conditions

brezis nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem abstract we study brezis nirenberg type theorems for the equation u g x u f x u in u 0 on where is a bounded domain in r n g x is increasing and f is a dissipative nonlinearity we apply such theorems for studying existence and multiplicity of positive solutions for the equation u u q u p in u 0 on where q 0 p 1 and 0

a galerkin neural network based design of guaranteed cost control for nonlinear distributed parameter systems this paper presents a galerkin neural network based guaranteed cost control gcc design for a class of parabolic partial differential equation pde systems with unknown nonlinearities a parabolic pde system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement motivated by this in the proposed control scheme galerkin method is initially applied to the pde system to derive an ordinary differential equation ode system with unknown nonlinearities which accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently parameterized by a multilayer neural network mnn with one hidden layer and zero bias terms then based on the neural model and a lure type lyapunov function a linear modal feedback controller is developed to stabilize the closed loop pde system and provide an upper bound for the quadratic cost function associated with the finite dimensional slow system for all admissible approximation errors of the network the outcome of the gcc problem is formulated as a linear matrix inequality lmi problem moreover by using the existing lmi optimization technique a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained finally the proposed design method is applied to the control of the temperature profile of a catalytic rod

module phase synchronization in complex dynamic system the concept of module phase synchronization was proposed the chaos synchronization between drive system and response system was achieved in module space and phase space respectively module phase synchronization different from the evolutions in real space there is no pseudorandom behavior in phase space when module phase synchronization achieve all the phases of complex state variables switched between two fixed values which are determined by initial values of drive system and the modules varied within a bounded field the theoretical analysis and the simulations were also given

existence and multiplicity of positive solutions for a class of kirchhoff type problems with singularity abstract in this work we study a class of kirchhoff type problems with singularity and nonlinearity and obtain the uniqueness and existence of positive solutions of those problems by the variational methods furthermore we obtain the multiplicity of positive solutions of those problems by the nehari method

existence and multiplicity of positive solutions for a class of kirchhoff laplacian type problems this paper deals with the existence and multiplicity of positive solutions for a class of kirchhoff laplacian type problems in whole r3 the multiplicity of solutions is established by variational methods and ljusternik schnirelmann theory

adaptive pinning control for the projective synchronization of drive response dynamical networks abstract this paper studies the projective synchronization of a drive response dynamical network of partially linear systems the coupling configuration matrix of the network is not necessarily symmetric two adaptive pinning control strategies are derived based on the barbalat s lemma in the first control strategy the pinning control gain is adaptively updated to realize the projective synchronization in the second control strategy both the pinning control gain and the coupling strength between nodes are adaptively updated numerical simulation results show that the coupling strength needed in the second control strategy is smaller than that in the first control strategy to achieve the projective synchronization of the network

projective synchronization in drive response dynamical networks abstract projective synchronization characterized by a scaling factor and its control have recently been well investigated in two coupled chaotic oscillators but it has not been realized yet in the case of more than two chaotic systems in this paper we study the projective synchronization in 1 n coupled chaotic systems by introducing a drive response dynamical networks model furthermore pinning control techniques are also adopted to direct the scaling factor onto the desired value it is also shown that the projection synchronization of the drive response dynamical networks can be realized by controlling only one node numerical simulations on the chaotic lorenz system are illustrated to verify the theoretical results

adaptive generalized hybrid function projective dislocated synchronization of new four dimensional uncertain chaotic systems based on projective synchronization and function projective synchronization a novel generalized hybrid function projective dislocated synchronization of new four dimensional uncertain chaotic systems is investigated according to the lyapunov stability theorem an adaptive hybrid controller for the synchronization of two different four dimensional chaotic systems is designed and some parameter update laws for estimating the unknown parameters of these systems are also gained the synchronization between memristor chaotic oscillator system and hyperchaotic lu system with linear scaling functions and periodic scaling functions are discussed to show the effectiveness of the proposed methods

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

positive solutions for a schrodinger poisson system with singularity and critical exponent abstract we study multiplicity of positive solutions for a class of schrodinger poisson system with singularity and critical exponent and obtain two positive solutions via the variational and perturbation methods

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

generalized projective synchronization of fractional order chaotic systems abstract in this paper based on the idea of a nonlinear observer a new method is proposed and applied to generalized projective synchronization for a class of fractional order chaotic systems via a transmitted signal this synchronization approach is theoretically and numerically studied by using the stability theory of linear fractional order systems suitable conditions for achieving synchronization are given numerical simulations coincide with the theoretical analysis

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

projective cluster synchronization in drive response dynamical networks abstract in this paper we study the projective cluster synchronization in a drive response dynamical network with 1 n coupled partially linear chaotic systems because the scaling factors characterizing the dynamics of projective synchronization remain unpredictable pinning control ideas are adopted to direct the different scaling factors onto the desired values it is also shown that the projection cluster synchronization can be realized by controlling only one node in each cluster numerical simulations on the chaotic lorenz system are illustrated to verify the theoretical results

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

lur e systems with multilayer perceptron and recurrent neural networks absolute stability and dissipativity sufficient conditions for absolute stability and dissipativity of continuous time recurrent neural networks with two hidden layers are presented in the autonomous case this is related to a lur e system with multilayer perceptron nonlinearity such models are obtained after parametrizing general nonlinear models and controllers by a multilayer perceptron with one hidden layer and representing the control scheme in standard plant form the conditions are expressed as matrix inequalities and can be employed for nonlinear h sub spl infin control and imposing closed loop stability in dynamic backpropagation

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

a special full state hybrid projective synchronization in symmetrical chaotic systems a special full state hybrid projective synchronization type is proposed in this paper the anti synchronization and complete synchronization can be achieved simultaneously in this new synchronization phenomenon we point out how to realize this synchronization in chaotic systems anti synchronization in symmetrical coordinate subspace and complete synchronization in its normal coordinate subspace two illustrative examples multi scroll chaotic system by the partial lyapunov stability theory and a four dimensional chaotic system by the invariance principle of differential equation are presented to exhibit this new synchronization

a uniqueness result for a nonlocal equation of kirchhoff type and some related open problem abstract we study the uniqueness of solution for the following boundary value problem involving a nonlocal equation of kirchhoff type a b u 2 d x u f u in u 0 here is a bounded open set in r n with smooth boundary a b are positive real numbers and f r r is a continuous function in particular we give an answer to an open problem recently proposed by b ricceri

synchronizing chaotic systems up to an arbitrary scaling matrix via a single signal abstract this paper introduces a novel type of synchronization where two chaotic systems synchronize up to an arbitrary scaling matrix in particular each drive system state synchronizes with a linear combination of response system states by using a single synchronizing signal the proposed observer based method exploits a theorem that assures asymptotic synchronization for a wide class of continuous time chaotic hyperchaotic systems two examples involving rossler s system and a hyperchaotic oscillator show that the proposed technique is a general framework to achieve any type of synchronization defined to date

combined effects of singular and critical nonlinearities in elliptic problems abstract in this paper we consider the existence and multiplicity of positive weak solutions for a class of elliptic problems with the nonlinearity containing both singular and critical terms by means of the concentration compactness principle due to lions and ekeland s variational principle two positive weak solutions are obtained

a dirichlet problem with singular and supercritical nonlinearities abstract following the approach of boccardo et al 1995 1 we prove the existence of positive solutions in w 0 1 2 l for a dirichlet problem with singular and supercritical nonlinearities

regularity of an elliptic problem with a singular nonlinearity we study a semilinear boundary value problem with the feature that the vanishing boundary value makes the equation singular we prove that the positive solution is in general holder continuous up to the boundary and has even better regularity in some special cases

multiplicity of positive solutions for a class of critical sobolev exponent problems involving kirchhoff type nonlocal term abstract we study a class of critical sobolev exponent problems involving kirchhoff type nonlocal term a b u 2 d x u u 5 g x u u q 1 x u 0 x where r 3 is a bounded domain a b 0 1 q 2 and g c r satisfies some conditions by the variational method we obtain two positive solutions moreover we prove that there exists a positive ground state solution by the nehari method

robust quasi lpv control based on neural state space models we derive a synthesis result for robust linear parameter varying lpv output feedback controllers for nonlinear systems modeled by neural state space models this result is achieved by writing the neural state space model on a linear fractional transformation lft form in a nonconservative way separating the system description into a linear part and a nonlinear part linear parameter varying control synthesis methods are then applied to design a nonlinear control law for this system since the model is assumed to have been identified from input output measurement data only it must be expected that there is some uncertainty on the identified nonlinearities the control law is therefore made robust to noise perturbations after formulating the controller synthesis as a set of linear matrix inequalities lmis with added constraints some implementation issues are addressed and a simulation example is presented

classical and weak solutions of a singular semilinear elliptic problem the singular semilinear elliptic equation u p x f u 0 is shown to have a unique positive classical solution inrnthat decays to zero at ifp x is simply a nontrivial nonnegative continuous function satisfying 0 t max x t p x dt providedfis a non increasing continuously differentiable function on 0 it is also shown that the equation has a unique weakh10 solution on a bounded domain provided e0 f s ds andp x l2

on a system involving a critically growing nonlinearity abstract this paper deals with the system u u q u 3 u in b r q u 5 in b r u 0 on b r we prove existence and nonexistence results depending on the value of

existence of positive solutions to the schrodinger poisson system without compactness conditions abstract in this paper we discuss the existence of a positive radial solution to a generalized schrodinger poisson system without compactness conditions by the method of the combination of a cut off function a monotonicity trick and a pohozaev type identity we obtain the boundedness of a palais smale sequence

a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems abstract an adaptive observer for a class of single input single output siso nonlinear systems is proposed using a generalized dynamic recurrent neural network drnn the neural network nn weights are tuned on line with no off line learning required no exact knowledge of non linearities in the observed system is required furthermore no linearity with respect to unknown system parameters is assumed the drnn observer does not assume that nonlinearities in the system are restricted to the system output only the overall adaptive observer scheme is shown to be uniformly ultimately bounded simulation results have verified the performance of the drnn observer

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

the existence and multiplicity of classical positive solutions for a singular nonlinear elliptic problem with any growth exponents a b s t r a c t in this paper we consider a class of singular elliptic boundary problems u u p x u u 0 in u 0 on with 1 0 1 and p c 0 0 1 we emphasize that there is no restriction on the boundedness of from above by means of the approximating variational arguments and truncation two classical positive solutions are obtained 2014 the authors published by elsevier ltd this is an open access article under the cc by nc nd license http creativecommons org licenses by nc nd 3 0

sign changing solutions for a class of kirchhoff type problem in bounded domains abstract we are interested in the existence of least energy sign changing solutions for a class of kirchhoff type problem in bounded domains because the so called nonlocal term b u 2 d x u is involving in the equation the variational functional of the equation has totally different properties from the case of b 0 combining constraint variational method and quantitative deformation lemma we prove that the problem possesses one least energy sign changing solution u b moreover we show that the energy of u b is strictly larger than the ground state energy finally we regard b as a parameter and give a convergence property of u b as b 0

sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems abstract this paper is concerned with nonlocal kirchhoff s equation a b u 2 u f x u in u 0 on via variational methods and invariant sets of descent flow we obtain existence of signed and sign changing solutions with asymptotically 3 linear bounded nonlinearity

input output stability theory for direct neuro fuzzy controllers in an input output i o setting we undertake a detailed theoretical investigation of the stability of a given direct static multiple input single output neuro fuzzy controller operating under feedback control dependent only on the functional gain of the plant to be controlled it is shown that various stability regions in weight space are convex and necessary and sufficient conditions are given for these stability regions to be open and bounded the convexity results coupled with the stability test give a practical method for constructing the stability regions we show that an adaptive neuro fuzzy controller is stable under feedback if we constrain the weights of the controller to lie within any compact set within the stability region combining a projection operator with any standard training law can thus give a stable adaptive controller

sign changing solutions of kirchhoff type problems via invariant sets of descent flow we obtain sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow

stable neural controllers for nonlinear dynamic systems in this paper a stability based approach is introduced to design neural controllers for nonlinear systems the requisite control input is generated as the output of a neural network which is trained off line such that the time derivative of a positive definite function of the state variables becomes negative at all points by using the successfully trained networks as controllers the closed loop system can be made stable the stability framework introduced permits the generation of more efficient algorithms that lead to a larger region of stability for a wide class of nonlinear systems

existence of multiple positive solutions to nonhomogeneous schrodinger poisson system in this paper we consider the existence of multiple solutions to the following nonhomogeneous generalized schrodinger poisson system u ku q f u g u h x in r 3 2 qf u in r 3 where q 0 is a parameter 0 h x h x l 2 r 3 and g is asymptotically linear or superliner at infinity we show that there exists q 0 0 such that the system has at least two positive radial solutions for q 0 q 0

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

an exact estimate result for a class of singular equations with critical exponents abstract we consider the singular boundary value problem u h x u u p 1 in u 0 on with p 2 n n 2 0 1 it is well known that there exists 0 such that the problem has a solution for all 0 and no solution for we obtain an exact result for p h

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

existence uniqueness and multiplicity of positive solutions for schrodinger poisson system with singularity abstract in this paper we consider the following schrodinger poisson system with singularity u u u r in u 2 in u 0 in u 0 on where r 3 is a smooth bounded domain with boundary 1 r 0 1 is a constant 0 is a parameter we obtain the existence and uniqueness of positive solution for 1 and any 0 by using the variational method the existence and multiplicity of solutions for the system are also considered for 1 and 0 small enough by using the method of nehari manifold

a neural approach for control of nonlinear systems with feedback linearization several schemes for feedback linearization using neural networks have been investigated and compared then an approach to design a neurocontroller in the sense of feedback linearization is introduced the contents include 1 full input output linearization when a system has relative degree n 2 partial input output linearization when a system has relative degree r r n and 3 approximate linearization when the involutivity condition does not hold corresponding programs and examples are given to illustrate the proposed methodology

lpv control and full block multipliers a novel construction of linear parameter varying controllers is presented for arbitrarily fast parameter variations it is shown how full block multipliers allow to considerably reduce conservatism various auxiliary results of independent interest are included

nonlinear system identification using neural state space models applicable to robust control design prediction error learning algorithms for neural state space models are developed both for the deterministic case and the stochastic case with measurement and process noise for the stochastic case a predictor with direct parametrization of the kalman gain by a neural net architecture is proposed expressions for the gradients are derived by applying narendra s sensitivity model approach finally a linear fractional transformation representation is given for neural state space models which makes it possible to use these models obtained from input output measurements on a plant in a standard robust performance control scheme

multiobjective algebraic synthesis of neural control systems by implicit model following the advantages brought about by using classical linear control theory in conjunction with neural approximators have long been recognized in the literature in particular using linear controllers to obtain the starting neural control design has been shown to be a key step for the successful development and implementation of adaptive critic neural controllers despite their adaptive capabilities neural controllers are often criticized for not providing the same performance and stability guarantees as classical linear designs therefore this paper develops an algebraic synthesis procedure for designing dynamic output feedback neural controllers that are closed loop stable and meet the same performance objectives as any classical linear design the performance synthesis problem is addressed by deriving implicit model following algebraic relationships between model matrices obtained from the classical design and the neural control parameters additional linear matrix inequalities lmis conditions for closed loop exponential stability of the neural controller are derived using existing integral quadratic constraints iqcs for operators with repeated slope restricted nonlinearities the approach is demonstrated by designing a recurrent neural network controller for a highly maneuverable tailfin controlled missile that meets multiple design objectives including pole placement for transient tuning h infin and h 2 performance in the presence of parameter uncertainty and command input tracking