on the existence of weak solutions of perturbated systems with critical growth sur un domaine borne de r n on considere le probleme de dirichlet pour le systeme elliptique a u g u f sur et u 0 ou a u est un operateur quasi lineaire et la perturbation g u depend de u et de d u on etudie des conditions suffisantes sur a u et sur g u pour l existence de solutions faibles

orbitally universal centers abstract in this paper we define when a polynomial differential system is orbitally universal and we show the relevance of this notion in the classical center problem i e in the problem of distinguishing between a focus and a center

local superlinearity and sublinearity for the p laplacian we study the existence nonexistence and multiplicity of positive solutions for a family of problems updelta p u f lambda x u u in w 0 1 p upomega where is a bounded domain in mathbb r n n p and 0 is a parameter the family we consider includes the well known nonlinearities of ambrosetti brezis cerami type in a more general form namely lambda a x u q b x u r where 0 leqslant q p 1 r leqslant p 1 here the coefficient a x is assumed to be nonnegative but b x is allowed to change sign even in the critical case preliminary results of independent interest include the extension to the p laplacian context of the brezis nirenberg result on local minimization in w 0 1 p text and c 0 1 a c 1 alpha estimate for equations of the form updelta p u h x u with h of critical growth a strong comparison result for the p laplacian and a variational approach to the method of upper lower solutions for the p laplacian

quasilinear elliptic problems with singular and homogeneous lower order terms abstract we deal with singular quasilinear elliptic equations namely u u x u q u q 1 f x in u 0 in u 0 on where is a bounded smooth domain of r n n 3 r 1 q 2 0 l and 0 f l p for some p n 2 we completely describe the set of values of the parameter for which the problem admits solution thus we study existence nonexistence and uniqueness of bounded weak solutions in both cases f 0 and f 0

existence of renormalized solutions to nonlinear elliptic equations with two lower order terms and measure data in this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is formula maths where is a bounded open subset of r n n 2 ap is the so called p laplace operator 1 p n is a radon measure with bounded variation on 0 p 1 0 p 1 and c and b belong to the lorentz spaces l p 1 r n p 1 r and l n 1 respectively in particular we prove the existence under the assumptions that p 1 c belongs to the lorentz space ln p 1 r n p 1 r and c n r is small enough

an algebraic approach to the classification of centers in polynomial lienard systems abstract we consider the second order lienard system x f x x g x 0 where f x and g x are polynomials which we rewrite in the equivalent two dimensional form x y y g x yf x we show that the local question of whether a critical point of this system is a center can be expressed in terms of global conditions on f and g using these results we give a simple classification of all such centers we also address the problem of the coexistence of centers foci and limit cycles for these systems systems with degenerate centers are also considered

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

solvability of perturbed elliptic equations with critical growth exponent for the gradient sur un domaine borne cr n on considere le probleme de dirichlet a u g u f u 0 ou a u t 1 n 1 d i a i x u d u definit un operateur pseudomonotone d un espace de sobolev h 0 1 p dans son espace dual et la perturbation g u g x u d u satisfait une condition de croissance

the successive derivatives of the period function of a plane vector field previously we provided an expression which generalized the classical melnikov function to any order for the first nonzero derivative of a return mapping our method relied on the decomposition of a 1 form associated to the relative cohomology of the perturbed hamiltonian with the same techniques we give a formula for the first nonzero derivative of a period function we focus on the particular example ofh 1 2 x2 y2 and then we define a class of hamiltonians for which the same computation remains valid finally we investigate relations with birkhoff normal form

existence results for some quasilinear parabolic equations on considere le probleme de cauchy pour une equation dont la partie principale est un operateur parabolique quasilineaire le terme non lineaire additionnel a au plus une croissance quadratique par rapport au gradient de la solution on demontre l existence d une solution bornee faible sous des hypotheses de regularite minimales en supposant l existence d une sous solution et d une supersolution pour le probleme

lower semicontinuity of functionals via the concentration compactness principle in this paper we show the weak lower semicontinuity of some classes of functionals using the concentration compactness principle of p l lions these functionals involve an integral term and we do not know whether it can be handled by the de giorgi theorem the semicontinuity result allows us to prove several existence results for quasilinear elliptic equations

homogenization of dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design in a previous paper we studied the homogenization of a sequence of parabolic linear dirichlet problems when the coefficients and the domains vary arbitrarily here we improve the convergence result given in this paper by showing the strong convergence in l2 every time this is applied to obtain an existence result for control problems in optimal design written in a relaxed form the control variables are the material and the shape

nonlinear filters for bayesian estimation of pulse arrival time in additive white gaussian noise bayesian estimation of the arrival time of a single pulse is considered in the presence of a white noise the employed model is a stochastic process consisted of a randomly delayed causal pulse and an additive white gaussian noise where the prior density of the delay is known the history of this stochastic process is given at every point in time and the problem is to obtain the conditional expectation of an arbitrary function of the arrival time the paper adopts a stochastic differential equation approach to develop nonlinear filters to efficiently compute this estimation the filtering problem is resolved for a number of pulse shapes which allow for a finite dimensional solution these pulse shapes include step exponential and rectangular functions as well as a piecewise constant function which well approximates a broad class of waveforms the application of this filtering problem in real time pulse arrival detection is discussed the task of this operation is to report the event of pulse arrival as soon after occurrence as possible the performance of nonlinear filtering is numerically verified for this application

existence and non existence of positive solutions for nonlinear elliptic singular equations with natural growth abstract in this paper we analyze the existence non existence and uniqueness of positive solutions of some nonlinear elliptic equations containing singular terms and natural growth in the gradient term we use an adequate sub super solution method to prove the existence of solutions the characterization of eigenvalues and the integrability of the term u 2 u 2 for the non existence and results from arcoya segura de leon for the uniqueness

asymptotic behaviour of linear dirichlet parabolic problems with variable operators depending on time in varying domains abstract we study the asymptotic behaviour of the solutions of linear parabolic dirichlet problems when the coefficients and the domains where the problems are posed vary simultaneously in the limit problem it appear the h limit of the operators and as it is usual in the homogenization of dirichlet problems a new term of order zero we also obtain a corrector result

regularizing effect for some p laplacian systems abstract we study existence and regularity of weak solutions for the following p laplacian system p u a 1 u r 2 u f u w 0 1 p p u r w 0 1 p where is an open bounded subset of r n n 2 p v div v p 2 v is the p laplacian operator for 1 p n a 0 r 1 0 p 1 and f belongs to a suitable lebesgue space in particular we show how the coupling between the equations in the system gives rise to a regularizing effect producing the existence of finite energy solutions

ground states of degenerate quasilinear schrodinger equation with vanishing potentials abstract in this paper we study the existence of nontrivial ground state solutions for the following class of p laplacian type equation div a x u v x x p u p 2 u k x x p f u in r n where 1 p n n 3 n p p e 1 d 1 e p p e n p n d p critical hardy sobolev exponent f has a quasicritical growth v and k are nonnegative potentials the function a satisfies a x u c 0 x p h 0 x u p 1 c 0 1 x p h 1 x u p 1 for any r n a e x r n for any two positive functions h 1 l l o c r n h 0 l p p 1 r n with p p

shape optimisation problems governed by nonlinear state equations the purpose of this paper is to give a compactness continuity result for the solution of a nonlinear dirichlet problem in terms of its domain variation the topology in the family of domains is given by the hausdorff metric and continuity is obtained under capacity conditions a generalisation of sverak s result in iv dimensions is deduced as a particular case

frequency domain interpretation of the cramer rao bound for carrier and clock synchronization the cramer rao bound is a fundamental lower bound on the variance of unbiased estimates applied to carrier phase and clock phase synchronization for digital communications it is shown that the corresponding bounds can be derived from the power density spectrum of the transmitted signal irrespective of the particular modulation scheme this allows the localization of the available information about the parameters in the frequency domain if the incoming signal is only partly exploited the resulting performance loss is now easily attainable

a simple solution of some composition conjectures for abel equations abstract trigonometric abel differential equations appear in the study of the number of limit cycles and the center focus problem for certain families of planar polynomial systems the composition centers are a class of centers for trigonometric abel equations which have been widely studied during last years we characterize this type of centers as the ones given by couples of trigonometric polynomials for which all the generalized moments vanish they also coincide with the strongly and the highly persistent centers our result gives a simple and self contained proof of the so called composition conjecture for trigonometric abel differential equations we also prove a similar version of this result for abel equations with polynomial coefficients

the problem of center for resonant singular points of polynomial vector fields we generalize the notion of center to the case of a p q resonant singular point of a polynomial vector field in 2 and to some other situations resonant node saddle node non elementary singular point of vector field and resonant fixed point of one dimensional complex diffeomorphism we show some similarities and differences with the classical case in particular the analogue of bautin s theorem does not hold four small amplitude limit cycles can bifurcate from the center after quadratic perturbation of a quadratic vector field with resonant center

center conditions at infinity for abel differential equations an abel differential equation y p x y 2 q x y 3 is said to have a center at a set a a 1 a r of complex numbers if y a 1 y a 2 y a r for any solution y x with the initial value y a 1 small enough the polynomials p q are said to satisfy the polynomial composition condition on a if there exist polynomials p q and w such that p p and q q are representable as p x p w x q x q w x and w a 1 w a 2 w a r we show that for wide ranges of degrees of p and q restricted only by certain assumptions on the common divisors of these degrees the composition condition provides a very accurate approximation of the center one up to a finite number of configurations not accounted for to our best knowledge this is the first general i e not restricted to small degrees of p and q or to a very special form of these polynomials result in the center problem for abel equations as an important intermediate result we show that at infinity according to an appropriate projectivization of the parameter space the center conditions are given by a system of the moment equations of the form as a1 p k q 0 s 2 r k 0 1

existence results for some nonlinear elliptic system with lack of compactness abstract we are interested in existence of solutions for some typical elliptic systems governed by two pseudo laplacian operators with critical sobolev exponents we show this result by a local minimization for an adapted variational problem a concentration compactness principle allows us to obtain some convergence results

algebraic particular integrals integrability and the problem of the center in this work we clarify the global geometrical phenomena corresponding to the notion of center for plane quadratic vector fields we first show the key role played by the algebraic particular integrals of degrees less than or equal to three in the theory of the center these curves control the changes in the systems as parameters vary the bifurcation diagram used to prove this result is realized in the natural topological space for the situation considered namely the real four dimensional projective space next we consider the known four algebraic conditions for the center for quadratic vector fields one of them says that the system is hamiltonian a condition which has a clear geometric meaning we determine the geometric meaning of the remaining other three algebraic conditions i ii iii

non autonomous perturbations for a class of quasilinear elliptic equations on r abstract this paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on r involving the p laplacian with a non autonomous perturbation the first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain pass argument the special features of the problem here is the complex structure of the linear part which in particular oblige to work into the space w 1 p r then one faces problems in the convergence of the sequences of derivatives u n u

on the center problem for ordinary differential equations we study the center problem for equations v i 1 a i x v i 1 this problem is closely connected to the classical poincare center focus problem about the characterization of planar polynomial vector fields whose integral trajectories are closed curves with interiors containing a fixed point a center

a lower bound for the error variance of maximum likelihood delay estimates of discontinuous pulse waveforms a new lower bound is developed for the error variance of maximum likelihood time delay estimation when the received signal is a square pulse corrupted by additive white gaussian noise the bound is generated by combining concepts previously developed for a special class of stochastic processes induced by the signal model for moderate signal to noise ratios the new bound is significantly tighter than previously known ones

homogenization of dirichlet parabolic systems with variable monotone operators in general perforated domains we consider the homogenization of parabolic systems with dirichlet boundary conditions when the operators and the domains in which the problems are posed vary simultaneously we assume the operators do not depend on t then we show that the corrector obtained in a previous paper for the elliptic problem still gives a corrector for the parabolic one from this result we easily obtain the limit problem in the parabolic case

optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a hardy potential abstract we deal with the following parabolic problem u t u u p u x 2 f u 0 in 0 t u x t 0 on 0 t u x 0 u 0 x x where r n n 3 is a bounded regular domain such that 0 or r n p 1 0 and f 0 u 0 0 are in a suitable class of functions there are deep differences with respect to the heat equation 0 the main features in the paper are the following if 0 there exists a critical exponent p such that for p p there is no nontrivial local solution p is optimal in the sense that if p p there exists solution for suitable data if we consider the cauchy problem i e r n we find the same phenomenon about the critical power p as above moreover there exists a fujita type exponent f p in the sense that independently of the initial datum for 1 p f any solution blows up in a finite time respect to an integral norm this is a major difference with respect to the heat equation 0

non autonomous equations related to polynomial two dimensional systems periodic solutions of certain one dimensional non autonomous differential equations are investigated equation 1 4 the independent variable is complex the motivation which is explained in the introductory section is the connection with certain polynomial two dimensional systems several classes of coefficients are considered in each case the aim is to estimate the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients in particular we need to know when there is a full neighbourhood of periodic solutions we give a number of sufficient conditions and investigate the implications for the corresponding two dimensional systems

the p dirichlet to neumann operator with applications to elliptic and parabolic problems abstract in this paper we investigate the dirichlet to neumann operator associated with second order quasi linear operators of p laplace type for 1 p which acts on the boundary of a bounded lipschitz domain in r d for d 2 we establish well posedness and holder continuity with uniform estimates of weak solutions of some elliptic boundary value problems involving the dirichlet to neumann operator by employing these regularity results of weak solutions of elliptic problems we show that the semigroup generated by the negative dirichlet to neumann operator on l q enjoys an l q c 0 smoothing effect and the negative dirichlet to neumann operator on the set of continuous functions on the boundary of the domain generates a strongly continuous and order preserving semigroup moreover we establish convergence in large time with decay rates of all trajectories of the semigroup and in the singular case 1 e 2 d d 2 p 2 for some e 0 we give upper estimates of the finite time of extinction

a gradient estimate to a degenerate parabolic equation with a singular absorption term the global quenching phenomena we prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term we also show the global quenching phenomena for l1 initial datums moreover the free boundary problem is considered in this paper

universal centres and composition conditions in this paper we characterize the universal centers of the ordinary differential equations d d i 1 ai i 1 where ai are trigonometric polynomials in terms of the composition conditions these centers are closely related with the classical poincare center problem for planar analytic differential systems additionally we show that the notion of universal center is not invariant under changes of variables and we also provide different families of universal centers finally we characterize all the universal centers for the quadratic polynomial differential systems

an explicit expression for the first return map in the center problem abstract the classical center focus problem posed by h poincare in 1880 s asks about the characterization of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point a center in this paper we present a method allowing for the first time to obtain an explicit expression for the first return map in the center problem

existence of a continuum of solutions for a quasilinear elliptic singular problem abstract in this paper we study the existence of positive solution u h 0 1 for some quasilinear elliptic equations having lower order terms with quadratic growth in the gradient and singularities whose model is u x u 2 u u u p f 0 x x 0 0 p using topological methods we obtain the existence of an unbounded continuum of solutions in the case x is constant we derive the existence of solution for every 0 if 1 2 for any and p 1 even more for l we prove this result if 1 and p 2