an orlicz space approach to superlinear elliptic systems in this paper we study superlinear elliptic systems in hamiltonian form using an orlicz space setting we extend the notion of critical growth to superlinear nonlinearities which do not have a polynomial growth existence of nontrivial solutions is proved for superlinear nonlinearities which are subcritical in this generalized sense

boundary blow up solutions to elliptic systems of competitive type abstract we consider the elliptic system u u p v q v u r v s in where p s 1 q r 0 and r n is a smooth bounded domain subject to different types of dirichlet boundary conditions f u v i u v and sf u v on where 0 under several hypotheses on the parameters p q r s we show existence and nonexistence of positive solutions uniqueness and nonuniqueness we further provide the exact asymptotic behaviour of the solutions and their normal derivatives near some more general related problems are also studied

existence of nonnegative solutions for a class of semilinear elliptic systems with indefinite weight abstract we prove the existence of nonnegative solutions to the system u a x f v in v b x g u in u 0 v on where is a bounded domain in r n with a smooth boundary is a positive parameter by the method of monotone iteration and schauder fixed point theorem we prove the existence of a nonnegative solution to the above system for sufficiently small in this study we do not restrict the sign of a and b

stabilization of solutions of a degenerate nonlinear diffusion problem i 4 u f u in l l x r u tl t o in r u x 0 uo x in l l where m 1 is a parameter f is locally lipschitz continuous f 0 0 and u is bounded problems of this form arise in a number of areas of science for instance in models for gas or fluid flow in porous media 2 and for the spread of certain biological populations 13 161 this paper is divided into two parts in part i we consider what may be called the motivating example problem i which consists of problem i with the special choice f u u 1 u u a 1 for suitably restricted parameters a we begin by describing in detail the set l of nonnegative equilibrium solutions of problem i clearly 8 l contains the trivial solution u 0 for all l 0 write 8 l e l o in the description of z l there are two critical parameter values lo and l1 with 0 lo l1 j we show that i g l 4 for 0 l lo

a quasilinear hyperbolic integrodifferential equation related to a nonlinear string we discuss global existence boundedness and regularity of solu tions to the integrodifferential equation h t x u t x 0 mo 0 for all a 0

yosida approximation and nonlinear hyperbolic equation we are concerned with the initial value problem for nonlinear evolution equations of the form u t m a 1 2 u t 2 au t u t f t on 0 u 0 u o u o u 1 here a is a nonnegative selfadjoint operator in a real hilbert space h 0 is a constant and m is a c 1 class function satisfying m r m o 0 for r 0 with m o constant the equation has its motivation in the mathematical description of small amplitude vibrations of an elastic string

switching relay and complementarity systems a tutorial on their well posedness and relationships this paper reviews the relationships between switching systems defined from a partition of the state space into convex cells and relay or complementarity dynamical systems which are other classes of discontinuous systems well posedness results i e results on the existence and the uniqueness of solutions for different classes of relay and complementarity systems which are also switching systems are presented the reverse issue when can a switching system be rewritten equivalently as a relay or a complementarity system is also tackled many examples from mechanics circuits and biology illustrate the developments throughout the paper the paper focuses on systems with continuous solutions i e with no state jumps convexity is the central property

equilibria of continuous time recurrent fuzzy systems abstract unlike static fuzzy systems recurrent fuzzy systems allow representing knowledge based dynamic processes that can be stated in the form of if then rules making it possible to model systems that can only be described qualitatively further possible applications exist in the case where the dynamics of a system are quantitatively known but only in certain mesh points the interpolating character of the fuzzy system between the dynamics of the mesh points yields a complete dynamic model based on discrete time recurrent fuzzy systems this article presents first steps towards the theory of continuous time recurrent fuzzy systems and provides criteria for the investigation of the dynamics of this class of systems

piecewise linear quadratic optimal control the use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control lower bounds on the optimal control cost are obtained by semidefinite programming based on the bellman inequality this also gives an approximation to the optimal control law an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law a compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

existence and uniqueness of solutions of piecewise nonlinear systems abstract in this paper we consider the existence and the uniqueness of solutions of piecewise nonlinear systems we will present some necessary and sufficient conditions for the existence and the uniqueness of solutions of this class of systems

an existence result on positive solutions for a class of semilinear elliptic systems consider the system where is a positive parameter and is a bounded domain in r n we prove the existence of a large positive solution for large when lim x f mg x x 0 for every m 0 in particular we do not need any monotonicity assumptions on f g nor any sign conditions on f 0 g 0

structure and control of piecewise linear systems elementary algebraic topology is used in the study of the structure and optimal control of piecewise linear and non linear systems

a mathematical analysis of blowup for thermal reactions the spatially nonhomogeneous case the equations describing the induction period process for a super critical high activation energy thermal explosion in a bounded domain are studied a formal proof based on comparison techniques is used to show that the temperature perturbation becomes unbounded as t to t b leqq infty for values of the frank kamenetski parameter delta greater than the critical value upper and lower bound estimates for t b are found by using specified comparison equations a comparison of these bounds with values of t b obtained from numerical solutions of the basic equations shows that the estimates provide an excellent prediction of the escape time when delta is greater than 2 3 times the critical value for smaller values of delta where heat loss is more significant a better comparison equation is required

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

well posedness of piecewise linear systems with multiple modes and multiple criteria the results of a previous paper imura and van der schaft 2000 are generalized to obtain necessary and sufficient conditions for the well posedness of piecewise linear systems with multiple modes and multiple criteria to check the necessary and sufficient conditions we present algorithmic procedures by making use of the fourier motzkin elimination technique

characterization of well posedness of piecewise linear systems one of the basic issues in the study of hybrid systems is the well posedness existence and uniqueness of solutions problem of discontinuous dynamical systems the paper addresses this problem for a class of piecewise linear discontinuous systems under the definition of solutions of caratheodory the concepts of jump solutions or of sliding modes are not considered here in this sense the problem to be discussed is one of the most basic problems in the study of well posedness for discontinuous dynamical systems first we derive necessary and sufficient conditions for bimodal systems to be well posed in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions next its extensions to the multimodal case are discussed as an application to switching control in the case that two state feedback gains are switched according to a criterion depending on the state we give a characterization of all admissible state feedback gains for which the closed loop system remains well posed

on positive solutions for a second order differential system with indefinite weight in this paper we consider the existence of positive solutions for a second order differential system u a t u h t f u 0 t 1 b t u 0 t 1 u 0 u 1 0 0 1 0 where a t b t h t change sign the proof is based on the well known fixed point theorem of cone expansion and compression

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates

decomposition property of fuzzy systems and its applications this paper presents the decomposition property of fuzzy systems using a simple constructive decomposition procedure that is by properly dividing the input space into sub input spaces a general fuzzy system is decomposed into several sub fuzzy systems which are the simplest fuzzy systems in the sub input spaces based on the decomposition property of fuzzy systems the analysis of fuzzy systems can be divided into two steps first analyze the properties of the simplest fuzzy systems and then use the decomposition property to extend the results to general fuzzy systems using this idea two applications of the decomposition property are given the first is the application to the representation capability analysis of fuzzy systems the second is the application to the analysis of a class of nonlinear control systems then based on the piecewise affine fuzzy system model the existence condition and the design of a stable control for a class of single input single output siso nonlinear systems are presented