second order initial value problems with non absolute integrals in ordered banach spaces abstract in this paper we derive the existence and comparison results for second order initial value problems in ordered banach spaces the considered problems can be implicit singular functional discontinuous and nonlocal the main tools are fixed point results in ordered spaces and the theory of locally hl integrable vector valued functions

minimal order observer designs for linear time varying multivariable systems this note presents two simple approaches for the design of minimal order observer for linear time varying systems both techniques rely on canonical transformations of the given system as a consequence simple expressions are obtained which permit the observer constraint equation to be solved effectively the observers possess the desirable property of having a time invariant observer coefficient matrix with arbitrary eigenvalues a comparison is made between the proposed methods from which conclusions are drawn an illustrative example is also included

existence results for urysohn integral inclusions involving the henstock integral this paper presents two existence results for urysohn integral inclusions in banach spaces the set valued integral involved being the henstock integral in particular the existence of continuous solutions for integral inclusions of volterra and of hammerstein type is obtained our results extend the existence theorems given in literature in the single or set valued case under bochner or pettis integrability hypothesis the compactness of solutions set is also studied

a class of the first order impulsive dynamic equations on time scales abstract in this paper the first order impulsive dynamic equations on time scales is considered the existence and uniqueness of solution for a class of nonlinear impulsive dynamic equations on time scales is proved

differential equations on variable time scales abstract we introduce a class of differential equations on variable time scales with a transition condition between two consecutive parts of the scale conditions for existence and uniqueness of solutions are obtained periodicity boundedness and stability of solutions are considered the method of investigation is by means of two successive reductions b equivalence of the system e akalin m u akhmet the principles of b smooth discontinuous flows computers and mathematics with applications 49 2005 981 995 m u akhmet perturbations and hopf bifurcation of the planar discontinuous dynamical system nonlinear analysis 60 2005 163 178 m u akhmet n a perestyuk the comparison method for differential equations with impulse action differential equations 26 9 1990 1079 1086 on a variable time scale to a system on a time scale a reduction to an impulsive differential equation m u akhmet perturbations and hopf bifurcation of the planar discontinuous dynamical system nonlinear analysis 60 2005 163 178 m u akhmet m turan the differential equations on time scales through impulsive differential equations nonlinear analysis 65 2006 2043 2060 appropriate examples are constructed to illustrate the theory

on the existence of a kazantzis kravaris luenberger observer we state sufficient conditions for the existence on a given open set of the extension to nonlinear systems of the luenberger observer as it has been proposed by kazantzis and kravaris we prove it is sufficient to choose the dimension of the system giving the observer less than or equal to 2 twice the dimension of the state to be observed we show that it is sufficient to know only an approximation of the solution of a pde needed for the implementation we establish a link with high gain observers finally we extend our results to systems satisfying an unboundedness observability property

adaptive control of linear multivariable systems using dynamic regressor extension and mixing estimators removing the high frequency gain assumptions abstract in this paper it is shown that using the recently introduced dynamic regressor extension and mixing parameter estimation technique it is possible to remove the key assumption of prior knowledge on the high frequency gain imposed in model reference adaptive control of linear time invariant multivariable systems for the case of scalar systems this is tantamount to removing the requirement of known sign of this coefficient the proposed controller is not certainty equivalent in the sense that the parameters generated by the new estimator are not directly applied to the controller but they are modified adding a shifting and a scaling factor under the weak assumption of interval excitation parameter convergence in finite time of the modified parameters is achieved ensuring good robustness of the proposed controller

existence theorems of global solutions for nonlinear volterra type integral equations in banach spaces in this paper first a new fixed point theorem is established and then by the use of it the existence theorems of global solutions for nonlinear volterra type integral equations in banach spaces are investigated the results obtained in this paper generalize and improve the results corresponding to those obtained by others

existence results for dynamic inclusions on time scales with nonlocal initial conditions this paper is mainly concerned with the existence of solutions for first order dynamic inclusions on time scales with nonlocal initial conditions by using bohnenblust karlin s fixed point theorem and leray schauder nonlinear alternative for multivalued maps some sufficient conditions are established an example is also included to illustrate our results

initial value problems for nonlinear second order impulsive integro differential equations in banach spaces in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of initial value problems for nonlinear second order impulsive integro differential equations in banach spaces

almost periodic solutions for abstract impulsive differential equations this paper studies the existence and uniqueness of exponentially stable almost periodic solutions for abstract impulsive differential equations in banach space the investigations are carried out by means of the fractional powers of operators we construct an example to illustrate the feasibility of our results

extremal solutions for nonresonance impulsive functional dynamic equations on time scales in this paper we give an existence theorem for extremal solutions of a class of first order nonresonance impulsive dynamic equations on time scales with a periodicity condition

convergence theorems for hl integrable vector valued functions with applications abstract in this paper we prove dominated and monotone convergence theorems for hl integrable banach valued functions these results and a fixed point theorem in ordered spaces are then applied to prove existence and comparison results for integral equations of fredholm type in ordered banach spaces involving kurzweil integrals or improper integrals results are used also to solve concrete second order functional boundary value problems involving discontinuities and singularities

mean curvature flow of entire graphs in a half space with a free boundary we study the mean curvature flow of graphs with prescribed contact angle on a fixed smooth hyperplane in euclidean space we obtain long time existence and convergence to a self similar solution of the mean curvature flow orthogonal to the fixed hyperplane

on singular functional nonsmooth and implicit phi laplacian initial and boundary value problems in this paper we apply fixed point results for mappings in partially ordered spaces to derive existence results for extremal solutions of phi laplacian initial and boundary value problems the considered problems can be singular functional discontinuous nonlocal and implicit concrete examples are also solved

solution tube method for impulsive periodic differential inclusions of first order abstract the aim of this paper is to obtain an existence result for impulsive differential inclusions of first order with boundary conditions in hilbert spaces under a hypothesis of integrability in the henstock lebesgue sense for the multifunction on the right hand side the proof is based on the assumption that there exists a solution tube for the inclusion taken under consideration this novel concept which generalizes the extensively used notions of upper and lower solution was adapted to the present setting finally a compactness property is proved

henstock kurzweil delta and nabla integrals we will study the henstock kurzweil delta and nabla integrals which generalize the henstock kurzweil integral many properties of these integrals will be obtained these results will enable time scale researchers to study more general dynamic equations the henstock kurzweil delta nabla integral contains the riemann delta nabla and lebesque delta nabla integrals as special cases c 2005 elsevier inc all rights reserved

a note on differential and integral equations in the spaces of functions of λ bounded variation abstract in this paper we examine mainly some nonlinear integral equations in the spaces of functions of bounded variation establishing the existence and uniqueness results for that purpose we also examine a convolution operator as well as a nonlinear superposition operator in these spaces

non parametric mean curvature evolution with boundary conditions soit un domaine borne de r n n 2 de frontiere lisse et soit a l operateur de surface minimale donne par a d i a i p a i p i 1 p 2 1 2 on considere des surfaces dont la vitesse en direction de leur normale unite est egale a la courbure moyenne on etudie l equation d evolution qui en resulte u 1 du 2 1 2 au 0 dans 0 t

differential and integral equations with henstock kurzweil integrable functions abstract in this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing henstock kurzweil integrable functions

existence theory for functional p laplacian equations with variable exponents in this paper we consider the solvability of equations of the form d dt t u u t u t f t u u t u t for a e t i a b subject to a general type of functional boundary conditions which cover dirichlet and periodic boundary data as particular cases our approach is that of upper and lower solutions together with growth restrictions of nagumo s type an example is provided where a p laplacian with variable p is shown to have a solution between given upper and lower solutions

impulsive retarded differential equations in banach spaces via bochner lebesgue and henstock integrals t f t xt xt0 1 1 where is a given continuous function from r 0 r 0 to a banach space x and f is a continuous map from an open set r c r 0 x to x given a continuous function x t0 r t0 a x a 0 t0 r we follow 11 to deane xt r 0 x by xt x t r 0 t t0 t0 a the initial value problem 1 1 is equivalent to the integral equation

on kurzweil generalized ordinary differential equations on etudie sous quelles conditions une equation differentielle generalisee de kurzweil est equivalente a une equation differentielle

the differential equations on time scales through impulsive differential equations in this paper we investigate differential equations on certain tim es cales with transition conditions detc on the basis of reduction to the impulsive differential equations ide detc are in some sense more general than dynamic equations on time scales m bohner a peterson dynamic equations on

differential equations with non absolutely integrable functions in ordered banach spaces abstract in this paper we derive existence and comparison results for initial value problems in ordered banach spaces the considered problems can be implicit singular functional discontinuous and nonlocal the main tools are fixed point results in ordered spaces and theory of hl integrable vector valued functions concrete examples are presented and solved

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

performance enhancement of parameter estimators via dynamic regressor extension and mixing a new procedure to design parameter estimators with enhanced performance is proposed in the technical note for classical linear regression forms it yields a new parameter estimator whose convergence is established without the usual requirement of regressor persistency of excitation the technique is also applied to nonlinear regressions with partially monotonic parameter dependence giving rise again to estimators with enhanced performance simulation results illustrate the advantages of the proposed procedure in both scenarios

a new result on impulsive differential equations involving non absolutely convergent integrals in this paper we obtain as an application of a darbo type theorem global solutions for differential equations with impulse effects under the assumption that the function on the right hand side is integrable in the henstock sense we thus generalize several previously given results in literature for ordinary or impulsive equations

impulsive nonlocal differential equations through differential equations on time scales abstract we propose a non standard approach to impulsive differential equations in banach spaces by embedding this type of problems into differential dynamic problems on time scales we give an existence result for dynamic equations and as a consequence we obtain an existence result for impulsive differential equations

well posedness results for differential and integral equations containing henstock kurzweil integrable vector valued functions abstract in this paper we prove existence uniqueness and comparison results for solutions of differential and integral equations in banach spaces containing henstock kurzweil integrable functions from a compact real interval to an ordered banach space

on functional observers for linear time varying systems the technical note deals with existence conditions of a functional observer for linear time varying systems in the case where the order of the observer is equal to the number of observed variables constructive procedures for the design of such a linear functional observer are deduced from the existence conditions as a specific feature the proposed procedures do not require the solution of a differential sylvester equation some examples illustrate the presented results

unbounded solutions of the singular boundary value problems for second order differential equations on the half line this paper presents some results on the existence of multiple unbounded solutions for the boundary value problems for second order differential equations on half line and on the uniqueness of unbounded solution

monotone convergence theorems for henstock kurzweil integrable functions and applications abstract in this paper we prove monotone convergence theorems for henstock kurzweil integrable functions from a compact real interval to an ordered banach space these theorems are then applied to prove existence results for solutions of a discontinuous functional integral equation containing henstock kurzweil integrable functions

on dynamic regressor extension and mixing parameter estimators two luenberger observers interpretations dynamic regressor extension and mixing is a new technique for parameter estimation with guaranteed performance improvement with respect to classical gradient or least squares estimators that has proven instrumental in the solution of several open problems in system identification and adaptive control in this brief note we give two interpretations of this parameter estimator in terms of the recent extensions to the cases of nonlinear systems and observation of linear functionals for time varying systems of the classical luenberger s state observers

contracting convex hypersurfaces in riemannian manifolds by their mean curvature which shrink towards the center of the initial sphere in finite time it was shown in 3 that this behaviour is very typical if the initial hypersurface m o o r 1 is uniformly convex then the surfaces m t contract smoothly to a single point in finite time and the shape of the surfaces becomes spherical at the end of the contraction if the ambient space n is a general riemannian manifold the curvature of n will interfere with the mot ion of the surfaces m r we want to show here that the contract ion first to a small sphere and then to a single point is still

existence results for second order boundary value problem of impulsive dynamic equations on time scales abstract in this paper schaefer s fixed point theorem and nonlinear alternative of leray schauder type are used to investigate the existence of solutions for second order boundary value problem for impulsive dynamic equations on time scales

on improper integrals and differential equations in ordered banach spaces in this paper we study the existence of improper integrals of vector valued mappings the so obtained results combined with fixed point results in partially ordered functions spaces are then applied to derive existence and comparison results for least and greatest solutions of initial and boundary value problems in ordered banach spaces the considered problems can be singular functional nonlocal implicit and discontinuous concrete examples are also solved

on the solution of dydx ap f x y abstract we prove a substantial extension of picard s theorem on the solvability of the ordinary differential equation dy dx f x y and also obtain a generalization of the result in terms of approximate derivative dy dx ap the results are illustrated by suitable examples

existence and comparison results for operator and differential equations in abstract spaces in this paper we apply the chain methods developed in heikkila and lakshmikantham 1994 to obtain new fixed point theorems and new existence and comparison results for operator equations in partially ordered sets these results are then applied to discontinuous implicit functional differential equations in ordered banach spaces

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

closure properties for integral problems driven by regulated functions via convergence results abstract in this paper we give necessary and sufficient conditions for the convergence of kurzweil stieltjes integrals with respect to regulated functions using the notion of asymptotical equiintegrability one thus generalizes several well known convergence theorems as applications we provide existence and closure results for integral problems driven by regulated functions both in single and set valued cases in the particular setting of bounded variation functions driving the equations we get features of the solution set of measure integrals problems

existence results for second order impulsive boundary value problems on time scales abstract in this paper using a fixed point theorem due to krasnoselskii and zabreiko and the leggett williams fixed point theorem respectively we investigate the existence of one solution and three nonnegative solutions to second order impulsive equations on time scales

weak solutions for the dynamic cauchy problem in banach spaces abstract this paper is devoted to unify and extend the results of the existence of the weak solutions of continuous and discrete cauchy problem in banach spaces we offer the existence of the weak solution of dynamic cauchy problem on an infinite time scale the measure of weak noncompactness and the fixed point theorem of kubiaczyk are used to prove the main result

second order three boundary value problem in banach spaces via henstock and henstock kurzweil pettis integral abstract existence theorems and some properties of solutions set of three boundary value second order differential equations and inclusions in banach spaces are obtained under henstock respectively henstock kurzweil pettis integrability assumptions our results extend those obtained by azzam castaing and thibault in the bochner integrability setting and in the pettis integrability one the continuity of the unique solution with respect to a parameter in the single valued case is also studied

on functional improper volterra integral equations and impulsive differential equations in ordered banach spaces in this paper we derive existence and comparison results for discontinuous improper functional integral equations of volterra type in an ordered banach space which has a regular order cone for this purpose we prove dominated and monotone convergence theorems for improper integrals the obtained results are then applied to first order impulsive differential equations concrete examples are also solved by using symbolic programming

on positive solutions of boundary value problems for second order functional differential equations on infinite intervals we study the existence of positive solutions for the following boundary value problem on infinite interval for second order functional differential equations x t px t qx t f t xt 0 t 0 x t x t t t 0 limt x t 0 and x t px t qx t f t xt x t 0 t 0 x t x t t t 0 limt x t 0 where p 0 2 2 0 and q 0 the fixed point theorem on cone is used

boundary value problems on the half line with impulses and infinite delay this paper presents some results on the existence and uniqueness of solutions for the boundary value problems on the half line with impulses and infinite delay moreover an existence theorem of multiple solutions is obtained also the problems may be singular at the boundary

existence results for operator equations in abstract spaces and an application in this paper we apply the recursion method presented in heikkila and lakshmikantham 1994 to derive fixed point theorems and existence results for operator equations in partially ordered sets the obtained results combined with related results of heikkila 2002 are then applied to operator equations in ordered hilbert spaces and to a functional elliptic boundary value problem

difference equations in banach spaces difference equations which discretely approximate boundary value problems for second order ordinary differential equations are analysed it is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and even if solutions to the discrete problem are guaranteed they may be unrelated and inapplicable to the continuous problem analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense an example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated the earlier results are applied to show the existence of a solution the sufficient estimates on the step size are presented c 2003 elsevier science ltd all rights reserved

observers for linear time varying systems we give characterizations and necessary and sufficient existence conditions for tracking and asymptotic observers for linear functions of the state of a linear finite dimensional time varying state space system we specialize the results to affine parameter varying systems and bilinear control systems