multiple normalized standing wave solutions to the scalar non linear klein gordon equation with two competing powers abstract in this work we prove the existence of standing wave solutions to the scalar non linear klein gordon equation in dimension one and the stability of the ground state the set which contains all the minima of the energy constrained to the manifold of the states sharing a fixed charge for non linearities which are combinations of two competing powers we prove that standing waves in the ground state are orbitally stable we also show the existence of a degenerate minimum and the existence of two positive and radially symmetric minima having the same charge

model reduction of systems with zeros interlacing the poles the problem of reducing a system with zeros interlacing the poles zip on the real axis is considered it is proved that many model reduction methods such as the balanced truncation balanced residualization suboptimal and optimal hankel approximations inherit the zip property properties of the hankel singular values of zip systems are also listed

radial solutions of δu f u 0 with prescribed numbers of zeros u 0 0 u r f 0 as r 03 1 2 here n 1 is a real parameter and the function f satisfies the following hypotheses f 1 f r r is locally lipschitz continuous f2 uf u 0 and j 0 such that f u 0 on 0 pi f u 0 on uc 0 f u 0 on b 01 f u 0 on a pi where f u f r f s ds f4 f u k u jujp u g u where

uniqueness and nondegeneracy of positive solutions of delta s u u u p rm in mathbb r n when s is close to 1 we consider the equation delta s u u u p with s in 0 1 in the subcritical range of p we prove that if s is sufficiently close to 1 the equation possesses a unique minimizer which is nondegenerate

sharp upper bound on the blow up rate for the critical nonlinear schrodinger equation we consider the critical nonlinear schrodinger equation iu t delta u u 4 n with initial condition u 0 x u0

quadratic optimal controller to stabilise symmetrical systems it is considered a controller design in order to stabilize a control system the technique that is used for designing the controller includes a linear regulator and an asymptotical estimator which form the controller the linear regulator is designed by state estimators feedback for symmetrical systems minimizing a quadratic performance index computing the gain matrix of optimal feedback is solved by riccati s equation whilst the gain estimator matrix is computed by making use of symmetrical systems properties the symmetrical systems properties allow us to find the solution for riccati s dual equation without needing to solve two equations one for the feedback and other for the estimator using the controllability and observability matrices can be found a symmetrical and invertible matrix which can be used for computing the riccati s dual solution having the regulator and the estimator gain matrices we proceed to compute the transfer function of the controller based on estimator then we use this m

uniqueness of positive radial solutions of δu f u 0 in ℝ n ii we prove a uniqueness result for the positive solution of u f u 0 in r n which goes to 0 at the result applies to a wide class of nonlinear functions f including the important model case f u u u p 1 p n 2 n 2 the result is proved by reducing to an initial boundary problem for the ode u n 1 r f u 0 and using a shooting method

exact multiplicity for degenerate two point boundary value problems with p convex nonlinearity the exact number of positive solutions of a degenerate quasilinear two point boundary value problem is investigated for the generalization of earlier results concerning the nondegenerate case with convex nonlinearity suitably defined p convex nonlinearities are considered strictly p convex c2 functions having a non negative root are classified according to the shape of the bifurcation diagram of positive solutions versus the length of the interval we have uniqueness when f 0 0 and 0 1 or 2 solutions when f 0 0 similarly to the non degenerate case provided that the number of solutions is finite however now there may also occur a continuum of solutions connected to a dead core type phenomenon the proof of our results relies on the shooting method for the characterization of the shape of the time map in contrast to the non degenerate case the shooting method does not determine directly the number of solutions owing to the lack of uniqueness of the corresponding ivp exact conditions on the uniqueness of the ivp and in the case of non uniqueness the number and types of its local solutions are given based on this all the positive solutions of the bvp can be compiled

some quantum estimates for hermite hadamard inequalities in this paper we establish quantum analogue of classical integral identity using this identity we derive some quantum estimates for hermite hadamard inequalities for q differentiable convex functions and q differentiable quasi convex functions results obtained present refinement and improvement of the known results the ideas and techniques of this paper may stimulate further research

paper low order control design for lmi problems using alternating projection methods computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities lmis in particular we concentrate on the stabilization and the suboptimal h output feedback control design problems these problems can be described by a pair of lmis and an additional coupling condition this coupling condition is convex for the full order control design problem but convexity is lost for the control problem of order strictly less than the plant order we formulate these problems as feasibility problems with matrix constraint sets of simple geometry and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets full order and low order controllers are designed using alternating projection methods for the full order controller case global convergence of the alternating projection methods to a feasible solution is guaranteed however for the low order control case only local convergence is guaranteed an example is provided to illustrate the use of these methods for the full order and the low order controller design

uniqueness of positive radial solutions of δu f u 0 in rn n 2 abstract we study the uniqueness of radially symmetric ground states for the semilinear elliptic partial differential equation u f u 0 in r n n 2 assuming that f t 0 t f s d s is negative in 0 u 1 and positive in u 1 u we obtain the uniqueness of nonnegative solutions with u 0 sup u 0 u in the case where s u u f u f u is monotonically decreasing in u 1 u

on weighted q cebysev gruss type inequalities in this paper weighted q cebysev gruss type inequalities are established by using the weighted q integral montgomery identity some applications are also obtained

stable standing waves of nonlinear klein gordon equations in this paper we give sufficient conditions for the stability of the standing waves of least energy for nonlinear klein gordon equations

uniqueness of positive radial solutions for δu u up 0 on an annulus abstract we prove uniqueness of positive radial solutions to the semilinear elliptic equation u u u p 0 p 1 subject to the dirichlet boundary condition on an annulus in r n n 3 as a by product our argument also provides a much simpler if not the simplest new proof for the uniqueness of positive solutions to the same problem in a finite ball or in the whole space r n

comments on dissipative analysis and control of state space symmetric systems automatica 45 2009 1574 1579 we show that some results presented by meisami azad mohammadpour and grigoriadis meisami azad m mohammadpour j grigoriadis k m 2009 dissipative analysis and control of state space symmetric systems automatica 45 1574 1579 are erroneous first we present a counterexample contradicting the necessary and sufficient condition of lemma 5 then we point out that lemma 4 which is a key instrumental lemma in the proof of theorem 6 is also erroneous and we propose a new lemma that corrects and completes the proof of theorem 6 finally we show that h norm formulations claimed by theorems 6 7 and 8 are inaccurate which is also sustained by previously published results as well as numerical examples taken from the commented paper

damping parameter design optimization in structural systems using an explicit h norm bound abstract this paper examines the damping parameter design optimization problem for structural systems with collocated measurements and inputs so that h norm bound constraints are satisfied we utilize a particular solution of the bounded real lemma that provides an explicit upper bound on the h norm of a collocated structural system using this upper bound result the damping design is formulated as a linear matrix inequality lmi optimization problem with respect to the damping coefficients of the structural system the formulation is particularly useful for large scale structural systems where existing methods are computationally prohibitive numerical examples demonstrate the benefits and computational advantages of the proposed damping parameter design method

uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations in this article we are concerned with the semilinear elliptic equation where n 2 p 1 and k lxl 0 in r n the correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived in addition we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on k and p furthermore based on the pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions we obtain the whole structure of radial solutions depending on various situations

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

gruss type inequalities for double integrals on time scales we prove some gruss type inequalities for double integrals on time scales and unify the corresponding continuous and discrete versions from the literature we also apply our results to the quantum calculus case

existence and multiplicity of stable bound states for the nonlinear klein gordon equation abstract we are interested in the problem of existence of soliton like solutions for the nonlinear klein gordon equation in particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge we remark that the conditions we consider can be easily verified moreover we show that multiplicity of solitons of the same charge is guaranteed by the shape of the nonlinear term for equations on r n hence without appealing to topological or geometrical properties of the domain

instability of nonlinear bound states we establish a sharp instability theorem for the bound states of lowest energy of the nonlinear klein gordon equation utt u f u 0 and the nonlinear schrodinger equation iut u f u 0

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

the inequalities for some types of q integrals using the restriction of the q integral over a b to a finite sum and q integral of riemann type we establish new integral inequalities of q chebyshev type q gruss type q hermite hadamard type and cauchy buniakowsky type some inequalities which include the boundaries of functions are also indicated

technical communique dissipative analysis and control of state space symmetric systems the paper addresses the problem of analysis and static output feedback control synthesis for strict quadratic dissipativity of linear time invariant systems with state space symmetry as a particular case of dissipative systems we consider the mixed h and positive real performance criterion and we develop an explicit expression for calculating the h norm of these systems subsequently an explicit parametrization of the static output feedback control gains that solve the mixed h and positive real performance problem is obtained numerical examples demonstrate the use and computational advantages of the proposed explicit solutions

uniqueness of positive radial solutions for quasilinear elliptic equations in an annulus abstract extending a previous result of tang 1 we prove the uniqueness of positive radial solutions of p u f u 0 subject to dirichlet boundary conditions on an annulus in r n with 2 p n under suitable hypotheses on the nonlinearity f this argument also provides an alternative proof for the uniqueness of positive solutions of the same problem in a finite ball see 9 in the complement of a ball or in the whole space r n see 10 3 11

an application of hayashi s inequality for differentiable functions abstract in this paper we offer an application of hayashi s generalization of steffensen s inequality for differentiable functions as well as its connections with the celebrated hermite hadamard s integral inequality for convex functions some applications for special means are also given

existence and orbital stability of standing waves for nonlinear schrodinger systems abstract in this paper we investigate the existence of solutions in h 1 r n h 1 r n for nonlinear schrodinger systems of the form u 1 1 u 1 1 u 1 p 1 2 u 1 r 1 u 1 r 1 2 u 1 u 2 r 2 u 2 2 u 2 2 u 2 p 2 2 u 2 r 2 u 1 r 1 u 2 r 2 2 u 2 under the constraints r n u 1 2 d x a 1 0 r n u 2 2 d x a 2 0 here n 1 0 i 0 r i 1 2 p i 2 4 n for i 1 2 and r 1 r 2 2 4 n this problem is motivated by the search of standing waves for an evolution problem appearing in several physical models our solutions are obtained as constrained global minimizers of an associated functional note that in the system 1 and 2 are unknown and will correspond to the lagrange multipliers our main result is the precompactness of the minimizing sequences up to translation assuming the local well posedness of the associated evolution problem we then obtain the orbital stability of the standing waves associated to the set of minimizers

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

a positive bound state for an asymptotically linear or superlinear schrodinger equation abstract we establish existence of a positive solution to the stationary nonlinear schrodinger equation u v x u f u u h 1 r n in situations where this problem does not have a ground state we consider general superlinear nonlinearities and asymptotically linear ones as well

integral inequalities in q calculus abstract in this paper q calculus analogues of some classical and some recent integral inequalities are found applications to estimation of sums of some convergent series are also given

some quantum integral inequalities via preinvex functions in this paper we obtain some new quantum analogues of hermite hadamard and iyengar type inequalities for some classes of preinvex functions some special cases are also discussed

on positive realness negative imaginariness and h control of state space symmetric systems this paper studies positive realness and negative imaginariness of state space symmetric systems first a necessary and sufficient condition is provided for a state space symmetric system to be respectively positive real and negative imaginary then an explicit formulation for the infimum of h norm under a mixed h and negative imaginary performance and an explicit solution for the associated optimal static output feedback control gain are developed based on symmetric negative imaginary theorem finally three examples are provided to illustrate the main results of the paper

some inequalities for the q beta and the q gamma functions via some q integral inequalities some new inequalities for the q gamma the q beta and the q analogue of the psi functions are established via some q integral inequalities

model reduction for state space symmetric systems in this paper the model reduction problem for state space symmetric systems is investigated first it is shown that several model reduction methods such as balanced truncation balanced truncation which preserves the dc gain optimal and suboptimal hankel norm approximations inherit the state space symmetric property furthermore for single input and single output siso state space symmetric systems we prove that the h norm of its transfer functions can be calculated via two simple formulas moreover the siso state space symmetric systems are equivalent to systems with zeros interlacing the poles zip under mild conditions

structure of the sets of regular and singular radial solutions for a semilinear elliptic equation abstract this paper is concerned with the structure of the set of radially symmetric solutions for the equation u f u 0 on r n 0 with n 2 here the nonlinear term f is assumed to be a smooth function of u that is positive for u 0 and is equal to 0 for u 0 then any radial solution u u r r x of the equation is shown to be classified into one of several types according to its behavior as r 0 and r under the assumption that f is supercritical for small u 0 and is subcritical for large u 0 we clarify the entire structure of the set of solutions of various types the pohozaev identity plays a crucial role in the investigation of the structure

the existence and uniqueness of bound state solutions of a semi linear equation we investigate the existence and uniqueness of bounded radially symmetric solutions in r3 of uf u 0 where f u is continuous piecewise linear and has three distinct real zeros we give a detail

on problems involving eigenvalues for uncertain matrices by structured singular values this technical note considers problems that involve eigenvalues of uncertain matrices expressed in linear fractional form using the structured singular value mu and the skewed structured singular value nu in particular positive definiteness conditions maximum and minimum eigenvalues and generalized eigenvalues of uncertain matrices are expressed using mu and nu the obtained results allow us to acquire information of an uncertain matrix efficiently by the existing computational tools that provide practically useful approximations to the values of mu and nu

bernstein schurer kantorovich operators based on q integers in this paper we introduce a new kantorovich type generalization of the q bernstein schurer operators defined in muraru 2011 first we give the basic convergence theorem and then obtain the local direct results for these operators estimating the rate of convergence by using the modulus of smoothness and the lipschitz type maximal function respectively we also obtain a voronovskaja type theorem and investigate the statistical approximation properties of these operators with the help of a korovkin type statistical approximation theorem given in duman 2008

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

stabilization and h control of symmetric systems an explicit solution abstract in this paper we address the h control analysis the output feedback stabilization and the output feedback h control synthesis problems for state space symmetric systems using a particular solution of the bounded real lemma for an open loop symmetric system we obtain an explicit expression to compute the h norm of the system for the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state space symmetric systems for the h control synthesis problem we derive an explicit expression for the optimally achievable closed loop h norm and the optimal control gains extension to robust and positive real control of such systems are also examined these results are obtained from the linear matrix inequality formulations of the stabilization and the h control synthesis problems using simple matrix algebraic tools

some applications of small gain theorem to interconnected systems based on small gain theorem decentralized control of interconnected systems is studied linear matrix inequality conditions are given for stabilizability of interconnected systems interconnections can be used to improve system robustness in the sense of small gain theorem an example is given to illustrate the results finally interconnected systems composed of symmetric subsystems are studied