multipath time delay detection and estimation a transmitted and known signal is observed at the receiver through more than one path in additive noise the problem is to estimate the number of paths and for each of them the associated attenuation and delay we propose a deconvolution approach with an additive regularization term built around an l sub 1 norm the underlying optimization problem is transformed into a quadratic program and is thus easily and quickly solved by standard programs the procedure is able to handle more severe conditions than previous methods

the beginning of the fucik spectrum for the p laplacian has a nontrivial solution u here 1 p 2p u div u p 2 u u max u 0 u uu in 1 1 denoting by 1 2 the first two eigenvalues of 2p on w 1 p 0 0 cf the end of this introduction 7p clearly contains in particular 1 1 2 2 and the two lines 1 r and r 1 this generalized notion of spectrum was introduced for p 2 i e in the linear case in the 1970s by fuc ik 21 and dancer 15 in connection article id jdeq 1999 3645 available online at http www idealibrary com on

multiple solutions for p laplacian type problems with asymptotically p linear terms via a cohomological index theory abstract the aim of this paper is investigating the existence of weak solutions of the quasilinear elliptic model problem div a x u u p 2 u 1 p a t x u u p f x u in u 0 on where r n is a bounded domain n 2 p 1 a is a given function which admits partial derivative a t x t a t x t and f is asymptotically p linear at infinity under suitable hypotheses both at the origin and at infinity and if a x is even while f x is odd by using variational tools a cohomological index theory and a related pseudo index argument we prove a multiplicity result if p n in the non resonant case

nontrivial solutions for a class of quasilinear problems with jumping nonlinearities via a cohomological local splitting abstract we establish the existence of a nontrivial solution for a class of quasilinear elliptic boundary value problems with jumping nonlinearities by means of variational arguments and a cohomological local splitting

multiplicity of solutions for a fourth order quasilinear nonhomogeneous equation we consider a fourth order quasilinear nonhomogeneous equation which is equivalent to a nonhomogeneous hamiltonian system the purpose of this work is to prove the existence of at least two solutions for such equation when a certain parameter is small enough furthermore under an additional hypothesis on positiveness of the nonhomogeneous part we prove that our solutions are positive

sign changing and nontrivial solutions for a class of kirchhoff type problems abstract in this paper we study the existence of sign changing nodal and nontrivial solutions for the nonlinear kirchhoff type equation a b u 2 d x u u u 3 in u 0 on where r are two real parameters with the help of nodal nehari set we first provide a description of a two dimensional set in the plane which corresponds to the nonexistence and existence of sign changing solutions for the above kirchhoff type equation and then we establish the existence result of nontrivial solutions via the minimax methods

adaptive iterative algorithms for spiky deconvolution considering the joint detection estimation character that spiky deconvolution problems have an adaptively contracted projection selection operator is introduced to detect the nonzero values of the solution which can be combined with iterative algorithms to offer very efficient schemes for solving these problems a number of gradient type algorithms based on this principle are described and their performance is illustrated through simulation examples the approach is based on the idea of reducing the noise and defining the signal in an iterative form another possibility is to define the signal and reduce the overall energy outside its domain also in an iterative form this algorithm is more expensive from a computational point of view however simulations indicate that it has somewhat different properties it seems to be slightly less robust against the noise while it offers better resolution and even more accurate amplitude estimates

sign changing solutions for some fourth order nonlinear elliptic problems in this paper we consider the existence and multiplicity of sign changing solutions for some fourth order nonlinear elliptic problems and some existence and multiple are obtained the weak solutions are sought by means of sign changing critical theorems

variational identities and applications to differential systems j serrin 1 introduction in the work of ponos p and in recent work of pucci serrin ps variational identities are discussed which are useful for solving various ques tions about elliptic differential equations and particular elliptic systems here we obtain a number of further applications of these identities to systems it was noted in ps that these identities are closely related to noether s theorem for variational problems by working out the divergence term arising in noether s theorem and making some simplifications one obtains a general identity for variational problems if a variational integral has a symmetry group g with the following infinitesimal generator

existence of a non trivial solution for the p laplacian equation with fucik type resonance at infinity abstract we prove the existence of a non trivial weak solution for the equation p u a u p 1 b u p 1 f x u in u 0 on by variational methods we consider the case where a 1 or b 1 1 denotes the first eigenvalue of p or the case where a is close to b while the nonlinearity f belongs to a class that contains for example u q 2 u 1 q p

existence of infinitely many weak solutions for the p laplacian with nonlinear boundary conditions abstract in this paper we deal with the existence of weak solutions for quasilinear elliptic problem involving a p laplacian of the form p u x u p 2 u f x u in u p 2 u u p 2 u on we consider the above problem under several conditions on f for f superlinear and subcritical with respect to u we prove the existence of infinitely many solutions of the above problem by using the fountain theorem and the dual fountain theorem respectively for the case where f is critical with a subcritical perturbation namely f x u u p 2 u u r 2 u we show that there exists at least a nontrivial solution when p r p and there exist infinitely many solutions when 1 r p by using the mountain pass theorem and the concentration compactness principle respectively

on a property of the nodal set of least energy sign changing solutions for quasilinear elliptic equations in this note we prove the payne type conjecture about the behaviour of the nodal set of least energy sign changing solutions for the equation delta p u f u in bounded steiner symmetric domains omega subset of r n under the zero dirichlet boundary conditions the nonlinearity f is assumed to be either superlinear or resonant in the latter case least energy sign changing solutions are second eigenfunctions of the zero dirichlet p laplacian in omega we show that the nodal set of any least energy sign changing solution intersects the boundary of omega the proof is based on a moving polarization argument

multiple solutions for asymptotically p 1 homogeneous p laplacian equations we consider a nonlinear elliptic equation driven by the p laplacian and with a reaction term which exhibits a p 1 homogeneous growth both near and near zero using critical point theory with truncation techniques the method of upper lower solutions and morse theory we show that the problem has five nontrivial smooth solutions four of which have constant sign two positive and two negative

eigenvalues of the p x laplacian steklov problem abstract consider steklov eigenvalue problem involving the p x laplacian on a bounded domain the open subset of r n with n 2 as follows p x u u p x 2 u in u p x 2 u u p x 2 u on where p x constant we prove that the existence of infinitely many eigenvalue sequences unlike the p laplacian case for a variable exponent p x constant there does not exist a principal eigenvalue and the set of all eigenvalues is not closed under some assumptions finally we present some sufficient conditions for the infimum of all eigenvalues is zero and positive respectively

existence of three nontrivial solutions for asymptotically p linear noncoercive p laplacian equations abstract we consider a nonlinear elliptic problem driven by the p laplacian where the right hand side nonlinearity exhibits a p linear behavior near infinity and the euler functional of the problem need not be coercive and in fact can be indefinite using a combination of minimax arguments with truncation techniques and morse theory we show that the problem has at least three nontrivial smooth solutions two of which have a constant sign our method of proof uses some results on critical groups and the spectrum of the p laplacian due to perera and dancer perera

numerical methods for computing nonlinear eigenpairs part i iso homogeneous cases with a rayleigh quotient formulation a local minimax method is developed to solve a class of iso homogeneous nonlinear eigenpair problems for multiple solutions in banach spaces following their instability order the algorithm is implemented to compute weighted eigenpairs of the p laplacian numerical eigenfunctions are illustrated by their graphics several interesting phenomena have been observed and are open for further investigation mathematical analysis related to convergence and instability order of computed eigenfunctions etc is also presented

multiplicity of nontrivial solutions for quasilinear elliptic equation two nontrivial solutions are obtained by the reduction method for the nonautonomous semilinear elliptic dirichlet boundary value problem some well known multiplicity results are generalized

resonance problems for the p laplacian systems abstract two existence theorems of the solutions are obtained for the p laplacian systems at resonance under a landesman lazer type condition by critical point theory

perturbation of the p laplacian by vanishing nonlinearities in one dimension abstract we treat the quasi linear spectral problem p u p 2 u u p 2 u h x u 0 x a u 0 u a 0 at resonance with vanishing nonlinearity h x u g u f x g u 0 as u and f l 0 a f 0 satisfying certain orthogonality related hypotheses 1 p 3 p 2 the parameter r takes an arbitrary resonant value we first establish the boundedness of the set of all weak solutions in the sobolev space w 0 1 p 0 a which then enables us to obtain an existence result by the leray schauder degree theory the boundedness is obtained from a very precise asymptotic estimate valid for large solutions to p which can be applied thanks to a sufficiently fast rate of decay g u 0 as u

the feasible solution in signal restoration the feasible solution to the signal restoration problem is defined as the one which satisfies all constraints which can be imposed on the true solution a very important set of constraints can be obtained by examining the statistics of the noise these and other constraints can be described as closed convex sets thus projection onto closed convex sets is the numerical method used to obtain a feasible solution examples of this method demonstrate its usefulness in one and two dimensional signal restoration the limitations of the method are discussed

on the non commutative factorization of wiener hopf kernels of khrapkov type there are a great many problems in mathematical physics and engineering which when modelled mathematically are reduced to wiener hopf functional equations defined in some region of a complex plane in simple models this equation is scalar but in more complicated situations inherent coupling etc can often give rise to coupled systems of equations and so the resulting wiener hopf kernels are of matrix form the crucial step in the solution of any wiener hopf equation is to decompose the kernel which can be a quite general function of the complex transform variable into a product of two factors which are regular in overlapping half planes this can be accomplished explicitly for scalar kernels and may be generalized to a particular class of matrix kernels namely those which permit a commutative decomposition although this class is wide and therefore contains some valuable physical problems it is found that many such kernels yield factorization elements with exponentially large behaviour at infinity in their half planes of analyticity this prevents a later step in the wiener hopf procedure being carried through and therefore introduces a serious limitation to the usefulness of khrapkov s approach previous researchers have offered schemes to eliminate the exponential behaviour of the khrapkov factors but for reasons discussed herein these have problems in their successful implementation this article offers a new procedure for quenching the exponential growth which is based on a method proposed recently by the author for fully coupled kernels which do not have commutative factors the approach is two step first a commutative factorization is obtained which is algebraic at infinity as required but which has spurious branch cuts in the regions of intended analyticity second an approximate procedure is used to eliminate the offending branch points by introduction of pade approximants for a certain scalar function and by inclusion of a regularizing meromorphic matrix for one particular example kernel in which an exact factorization happens to be known the explicit approximate kernel factors thus derived are shown to yield very close agreement to the exact factors the application of this work to problems in the area of fluid structural interaction is discussed

existence of solutions for quasilinear elliptic obstacle problems two existence results for a class of obstacle problems are obtained by using a result developed in this paper

separating multipaths by global optimization of a multidimensional matched filter a transmitted signal can arrive at a receiver via several refracted fermat paths if the paths are independent in the fresnel sense then the received signal can be modeled as the sum of amplitude scaled and time shifted copies of a predetermined replica plus white noise we present an algorithm that uses the replica to determine the time shifts and amplitudes for each path it is referred to as an n dimensional matched filter algorithm by analogy with the well known matched filter algorithm the cross correlation between the received signal and the replica oscillates near the center frequency of the transmitted signal this causes the n dimensional matched filter output to have many local maxima that are not globally optimal the time shifts and amplitude scalings for the fermat paths are determined by maximizing the output of the n dimensional matched filter the algorithm is more robust and efficient than others currently available simulated realizations of received signals were generated with multipath and noise characteristics similar to an ocean acoustic transmission case these realizations were then separated into arrival times and corresponding amplitudes by the algorithm the results of these tests and the general limitations of the algorithm are discussed

multiple solutions for elliptic systems with nonlinearities of arbitrary growth abstract we prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of arbitrary growth moreover if the symmetry of the problem is broken by a small enough perturbation term we find at least three solutions the proofs utilise a variational setting given by de figueiredo and ruf in order to prove an existence s result and the algebraic approach based on the pohozaev s fibering method

separation of superimposed signals by a cross correlation method an approach is presented for separating a superposition of delayed finite duration signals with unknown gains and delays which overlap both in the time and frequency domains the method is partly based on the cross correlations among the signals and some of their derivatives given the data an initial detection scheme formulates hypotheses on signals which may be present in the mixture and provides estimates of the signal positions for each hypothesis in the second stage the most likely hypotheses are selected and accurate values of the signal amplitudes and their time positions are determined by a nonlinear least squares approach the method is illustrated by a simulation with myoelectric emg signals

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

resonance problems for the p laplacian with a nonlinear boundary condition abstract consider resonance problems at an arbitrary eigenvalue of the elliptic equations p u u p 2 u g 1 u h 1 x in u p 2 u u p 2 u g 2 u h 2 x on some existence theorems are obtained under the landesman lazer type conditions by using variational method

superlinear problems without ambrosetti and rabinowitz growth condition superlinear elliptic boundary value problems without ambrosetti and rabinowitz growth condition are considered existence of nontrivial solution result is established by combining some arguments used by struwe and tarantello and schechter and zou also by wang and wei firstly by using the mountain pass theorem due to ambrosetti and rabinowitz is constructed a solution for almost every parameter by varying the parameter then it is considered the continuation of the solutions

scattering by a semi infinite sandwich panel perforated on one side the scattering of sound waves by the edge of a sandwich panel which consists of two thin elastic plates containing a light interior cellular structure is analysed the wiener hopf method is used to examine the interaction effects of a semi infinite panel clamped to a semi infinite rigid screen one major difficulty is that the presence of two different velocity potentials on either side of the plane y 0 results in a matrix wiener hopf equation an approximate solution is given in the asymptotic limit of small values of a parameter tau which accounts for the perforations

nonuniformly nonlinear elliptic equations of p biharmonic type this paper deals with the existence and multiplicity of weak solutions to nonlinear differential equations involving a general p biharmonic operator in particular p biharmonic operator under dirichlet boundary conditions or navier boundary conditions our method is mainly based on variational arguments

estimation of the parameters of a multipath channel using set theoretic deconvolution a method for the estimation of the parameters of multipath communication channels is developed the method makes use of matched filtering set theoretic deconvolution and autoregressive modeling pulse compression waveforms are used as channel probing signals the results of a feasibility study in which the proposed method is applied to specular multipath channels to estimate the multipath parameters at a number of different signal to noise ratios snr are presented

bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity this paper deals with existence results for the following nonlinear problem with the dirichlet p laplacian p in a bounded domain rn pu u p 2u h x u in u 0on here pu defdiv u p 2 u where p 1 is a fixed number h h x s is a given function from r into r and r stands for a spectral parameter we focus on close to 1 including the resonant case 1 the nonlinearity h is assumed to be of landesman lazer type but we can deal with vanishing nonlinearities as well our asymptotic method substitutes the lyapunov schmidt method in some sense unlike in the semilinear case p 2 our method can treat more general nonlinearities if p 2 vanishing nonlinearities with very fast decay

the effective boundary conditions for a perforated elastic sandwich panel in a compressible fluid the transmission of sound through a sandwich panel consisting of a honeycomb cellular structure bounded by two thin elastic plates is considerably reduced at a certain frequency if one or both of the plates is perforated so as to link a significant number of the cells to the exterior fluid this effect occurs at or near the helmholtz resonance frequency for the cells with the acoustic wavelength large compared with the cell dimensions an analysis is given for the problem of plane waves incident upon a plane sandwich plate of infinite extent using matched expansions for the cases of acoustically hard or acoustically transparent cell walls the compound panel is shown to be acoustically equivalent to that of a hypothetical surface with different normal velocities on either side and effective boundary conditions are derived with generalizations to deal with more complicated structures finite plates and more general incident fields

deconvolution in the presence of doppler with application to specular multipath parameter estimation high resolution multipath parameter estimates can be obtained through various deconvolution procedures all of which in the limit rely on some form of inverse filtering although deconvolution in a multipath environment free from doppler is well understood and well documented this is not true for the case when motion of the multipath components relative to the receiver imposes a doppler shift on the transmitted probing signal this paper describes the effect of doppler on a broad class of deconvolution methods by studying the effect of doppler on the output of an inverse filter it is shown that in the presence of doppler the deconvolution outputs are comprised chiefly of two signal related functions one of which may be designed in such a way as to be free from the range doppler coupling effects inherent in correlation processing knowledge of these two functions provides insight into the signal design issues relevant to deconvolution based multipath parameter estimation systems and is useful in designing appropriate constraints and post processing algorithms that may lead to an accurate extraction of the doppler and delay parameters of the multipath channel these results are applied to two known deconvolution methods the method of projection onto convex sets pocs and the method of least squares ls

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

convergence analysis of the least squares constant modulus algorithm in interference cancellation applications the convergence behavior of the least squares constant modulus cm algorithm in an adaptive beamforming application is examined it is assumed that the desired signal and the interference are uncorrelated the improvement in output signal to interference ratio sir with each iteration of the algorithm is predicted for several different signal environments deterministic results are presented for an environment containing two complete sinusoids probabilistic results are presented for a cm desired signal with a cm interferer and with a gaussian interferer the asymptotic improvement in output sir as the output sir becomes high is also derived the results of monte carlo simulations using sinusoidal frequency modulation and quadrature phase shift keying signals are included to support the derivations

nontrivial solutions of superlinear p laplacian equations we consider p laplacian equations on a bounded domain where the nonlinearity is superlinear but dose not satisfy the usual ambrosetti rabinowitz condition near infinity or its dual version near zero nontrivial solutions are obtained by computing the critical groups and morse theory

resonance problems for the p laplacian abstract we consider resonance problems at an arbitrary eigenvalue of the p laplacian and prove the existence of weak solutions assuming a standard landesman lazer condition we use variational arguments to characterize certain eigenvalues and then to establish the solvability of the given boundary value problem

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

existence of solutions for a class of noncooperative elliptic systems we establish the existence of a nontrivial solution for a class of noncooperative elliptic systems with nonlinearities of superlinear growth moreover if there is resonance we also find at least a solution all results are obtained by the minimax methods in critical point theory

adaptive image restoration with artifact suppression using the theory of convex projections the authors develop an iterative adaptive space variant restoration incorporating both regularization and artifact suppression constraints the algorithm is formulated using the method of projections onto convex sets pocs they introduce a closed convex regularization constraint set called the partial wiener solution set projection onto this set forces the solution to be equal to the wiener solution over a predetermined set of frequencies that lie outside the neighborhoods of the zeros of the degradation transfer function in the neighborhoods of the zeros the wiener solution contains significant errors that contribute to artifacts hence in these neighborhoods the wiener solution is discarded and the missing frequency components are determined so that the entire solution is consistent with the artifact suppression constraints and other a priori information the proposed artifact suppression constraints bound the norm of the variation of the image from its local mean using regionally adaptive bounds the high quality of the resulting restorations is noteworthy

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

quasilinear elliptic problems under strong resonance conditions abstract in this paper we establish the existence and multiplicity of solutions for a quasilinear elliptic problem under strong resonance conditions at infinity in order to control the resonance we consider a new hypothesis on the nonlinear term in all results we use variational methods critical groups and the morse theory

the behavior of the best sobolev trace constant and extremals in thin domains in this paper we study the asymptotic behavior of the best sobolev trace constant and extremals for the immersion w 1 p o l q o in a bounded smooth domain when it is contracted in one direction we find that the limit problem when rescaled in a suitable way is a sobolev type immersion in weighted spaces over a projection of o w 1 p p o a l q p o b for the special case p q this problem leads to an eigenvalue problem with a nonlinear boundary condition we also study the convergence of the eigenvalues and eigenvectors in this case