a priori bounds and existence of positive solutions for semilinear elliptic systems abstract we provide a priori l bounds for classical positive solutions of semilinear elliptic systems in bounded convex domains when the nonlinearities are below the power functions v p and u q for any p q lying on the critical sobolev hyperbola our proof combines moving planes method and rellich pohozaev type identities for systems our analysis widens the known ranges of nonlinearities for which classical positive solutions of semilinear elliptic systems are a priori bounded using these a priori bounds and local and global bifurcation techniques we prove the existence of positive solutions for a corresponding parametrized semilinear elliptic system

on the coupled systems of second and fourth order elliptic equations in this paper by the variational method we discuss the existence and uniqueness of solutions for a coupled system of second and fourth order elliptic equations in the cases where the perturbation is zero sublinear and superlinear respectively

robust relative stability of time invariant and time varying lattice filters we consider the relative stability of time invariant and time varying unnormalized lattice filters first we consider a set of lattice filters whose reflection parameters spl alpha sub i obey spl alpha sub i spl les spl delta sub i and provide necessary and sufficient conditions on the spl delta sub i that guarantee that each time invariant lattice in the set has poles inside a circle of prescribed radius 1 spl rho 1 spl rho

bifurcation for an elliptic system coupled in the linear part we study linearly coupled elliptic systems without any assumption on the signs of the coefficients of the linear part we derive first the leray schauder degree of the associated linear system then we obtain sufficient conditions on the nonlinear terms for having bifurcation to coexistence states our results include the sublinear case keys words linearly coupled elliptic systems bifurcation to positive solutions coexistence states leray schauder degree email jfleck cict fr rpardo sunma4 mat ucm es

a structural view of stability in adaptive iir filters this correspondence deals with the stability issue in adaptive iir filters from a structural view a new condition under which the bounded input bounded output bibo stability of the filters can be ensured is derived based on this result a normal state space realization for second order iir filters is proposed it is shown that the adaptive iir filter realized with such a structure is bibo stable no matter it is implemented with infinite or finite precision this property is very important for real time applications though both the proposed and the normalized lattice based structures are bibo stable the former is simpler and has minimal pole sensitivities two adaptive iir filter structures are developed based on a cascade form of second order filters the first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters simulations are given to demonstrate the performance of the proposed structures

maximum principles for a coupled system of second and fourth order elliptic equations and an application in this paper we obtain a maximum principle for the coupled system of second and fourth order elliptic equations using an abstract result in a recent paper by correa and souto nonlinear anal 26 1996 and an application of the maximum principle is given

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

nonconstant radial positive solutions of elliptic systems with neumann boundary conditions let br be the ball of radius r in rn with n 2 we consider the nonconstant radial positive solutions of elliptic systems of the form u u f u v inbr v v g u v inbr u v 0on br where f and g are nondecreasing in each component with few assumptions on the nonlinearities we apply bifurcation theory to show the existence of at least one nonnegative nonconstant and nondecreasing solution

a martingale study of the beurling ahlfors transform inrn abstract we apply the theory of martingale transforms to study the beurling ahlfors transform s in dimensions n 2 this operator reveals a rich structure through its representation as a martingale and we obtain new results concerning the operator norm of s acting on the class of differential forms having l p coefficients in particular we show that its norm is independent of the dimension when restricted to k forms and we present new essen type norm inequalities related to this martingale structure finally we suggest a purely analytic method to further investigate these norms which up to now has been lacking

a new normalized relatively stable lattice structure this paper proposes a new lattice filter structure that has the following properties when the filter is linear time invariant lti it is equivalent to the celebrated gray markel lattice when the lattice parameters vary with time it sustains arbitrary rates of time variations without sacrificing a prescribed degree of stability provided that the lattice coefficients are magnitude bounded in a region where all lti lattices have the same degree of stability we also show that the resulting ltv lattice obeys an energy contraction condition this structure thus generalizes the normalized gray markel lattice which has similar properties but only with respect to stability as opposed to relative stability

a note on the stability of linear discrete systems and lyapunov method in a publication by y p harn and c t chen 1 a proof of a discrete stability test by using the lyapunov method was given in this note the main results obtained by the author in this direction in 1965 6 7 and the extensions and applications obtained partially with other authors since then and published in different journals 8 10 are surveyed the similarity to the results in 1 is obvious

variational elliptic problems which are nonquadratic at infinity p co if n 1 2 then it is well known that the weak solutions u e h 2 of p are the critical points of the c functional j u ulvul dx jcf x u dx where f x s jif x t dt in this variational setting the literature usually distinguishes between two situations for prob lem p the subquadratic situation where the potential f satisfies lim suplsl f x s s2 i c m and the superquadratic situation where f satisfies limlsl m f x s s2 00 the main goal of this paper is to present a unified approach to both situations by means of a condition of nonquadraticity at infinity on f more precisely our hypotheses are as follows

spatially inhomogeneous steady state solutions for systems of equations describing interacting populations for x e i2 and t 0 where 0 is a bounded region in r n 1 2 3 and a denotes the laplacian models the interaction of two species co existing in q the densities of the species at time t and at the point x e q are given by u x t and v x t the constants d dz 0 give the rates at which the species diffuse the constants a and b give if positive the birth rates and if negative the mortality rates of the species so that system 1 1 has a unique solution we must specify initial conditions i e u x 0 and li x 0 and boundary conditions we shall be interested in the case of dirichlet boundary conditions i e in the case where u x f and t x t are specified functions of x on x co existing populations may interact in various ways e g they may compete or co operate with each other or one may be a predator preying on the other the nature of the interaction is reflected by the properties of the terms f u tl and g u c for example if the 1 population preys on the ii population an increase in l would lead to a decrease in u and so it would be natural to assume that zf k 0 throughout we shall assume that

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

exponential asymptotic stability of time varying inverse prediction error filters it is a classical result of linear prediction theory that as long as the minimum prediction error variance is nonzero the transfer function of the optimum linear prediction error filter for a stationary process is minimum phase and therefore its inverse is exponentially stable here extensions of this result to the case of nonstationary processes are investigated in that context the filter becomes time varying and the concept of transfer function ceases to make sense nevertheless we prove that under mild condition on the input process the inverse system remains exponentially stable we also consider filters obtained in a deterministic framework and show that if the time varying coefficients of the predictor are computed by means of the recursive weighted least squares algorithm then its inverse remains exponentially stable under a similar set of conditions