contraction and approximate contraction with an application to multi point boundary value problems abstract the paper deals with some general iterative methods in n metric spaces the obtained results are more explicit than those known in the literature and provides error estimates when the sequence obtained on a floating point system starts oscillating a stopping criteria and error estimates at that stage are provided an application to multi point boundary value problems is also given

positive solutions of nth order impulsive boundary value problems with integral boundary conditions in banach spaces abstract by using the fixed point theory for strict set contraction operator this paper investigates the existence of positive solutions for a class of n th order impulsive boundary value problems with integral boundary conditions in banach spaces moreover we offer some interesting discussion of the associated boundary value problems since the technique to deal with n th order bvp is completely different from that of previous papers the expression of the associated integral equation is simpler than that of relevant papers and upper and lower bounds for these positive solutions also are given our work is new

iterative methods for a fourth order boundary value problem abstract we consider a fourth order nonlinear ordinary differential equation together with two point boundary conditions and provide a priori error estimates on the length of the interval b a so that the picard s iterative method the approximate picard s iterative method and the quasilinear iterative method convergence to the solution of the problem

monotone convergence of iterative methods for right focal point boundary value problems abstract we provide sufficient conditions so that the picard iterative scheme for the right focal point boundary value problems converges monotonically an example which dwells upon the usefulness of this technique is also included

boundary value problems for nth order lipschitz equations on considere l unicite des solutions de problemes aux valeurs limites pour une equation scalaire d ordre n y n f t y y y n 1 ou f est continue sur a b r n et satisfait une condition de lipschitz

initial value methods for discrete boundary value problems motivated by the work of angel and kalaba s and golberg 8 on twopoint boundary value problems for difference equations in this paper we shall study several initial value methods for multipoint boundary value problems for linear and nonlinear difference systems we generalize method of adjoints goodman and lance 9 method of complementary functions tifford 17 d an method of particular solutions miele 111 proposed for two point continuous problems to linear multipoint problems for difference equations next we show that method of adjoint and method of complementary functions can be used in an iterative way to solve nonlinear problems to justify the results obtained here several examples are also given the methods discussed here are similar to our earlier work l 3 on continuous problems we will take up the initial adjusting method of ojika kasue and welsh 12 15 18 for the discrete case later throughout the paper we shall assume the existence uniqueness and stability properties of solutions of the problems discussed and refer to 4 for some of these questions

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

existence of solutions for third order boundary value problems on a time scale abstract let t be a closed subset of r with inf t and sup t for the third order nonlinear equation u 3 f t u u u t t where f t r3 r is continous we assume solutions of initial value problems are unique and extend to t we consider questions of the uniqueness of solutions implying the existence of solutions for conjugate boundary problems on t

maximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic direction abstract for second order linear equations and inequalities which are degenerate elliptic but which possess a uniformly elliptic direction we formulate and prove weak maximum principles which are compatible with a solvability theory in suitably weighted versions of l 2 based sobolev spaces the operators are not necessarily in divergence form have terms of lower order and have low regularity assumptions on the coefficients the needed weighted sobolev spaces are in general anisotropic spaces defined by a non negative continuous matrix weight as preparation we prove a poincare inequality with respect to such matrix weights and analyze the elementary properties of the weighted spaces comparisons to known results and examples of operators which are elliptic away from a hyperplane of arbitrary codimension are given finally in the important special case of operators whose principal part is of grushin type we apply these results to obtain some spectral theory results such as the existence of a principal eigenvalue

iterative methods for solving right focal point boundary value problems abstract we provide necessary and sufficient conditions for the existence of a solution of n th order differential equation satisfying right focal point boundary conditions for the linear problems we propose forward forward and backward backward one pass practical shooting methods which convert the boundary value problems to its equivalent initial value problems for the nonlinear problems iterative methods are discussed and a priori conditions for the convergence are obtained several examples are also illustrated

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

a new perturbation analysis for signal enumeration in rotational invariance techniques the esprit algorithm is a subspace based high resolution method used in source localization and spectral analysis which provides very accurate estimates of the signal parameters however the underlying theory assumes a known model order which is usually not the case in many applications in particular it is well known that underevaluating the model order biases the estimation in this paper we analyze the perturbation induced by an erroneous model order and we present an error bound for the estimated parameters based on this theoretical framework we propose a new method for selecting an appropriate modeling order which consists in minimizing the error bound this approach is applied to both synthetic and musical signals and its performance is compared to that of existing methods such as the information theoretic criteria

optimality for boundary value problems for lipschitz equations on considere les solutions de problemes aux valeurs limites pour une equation scalaire d ordre n x n f t x x x n 1 ou f est continue sur a b r n et satisfait une condition de lipschitz on determine les sous intervalles de longueur optimale de a b en fonctions des coefficients de lipschitz sur lesquels des solutions sont uniques

multiple solutions and eigenvalues for third order right focal boundary value problems abstract we are concerned with the right focal boundary value problem x t f t x t t 1 t t 3 x t 1 x t 2 x t 3 0 and the associated eigenvalue problem x t a t f x t with the same boundary conditions under various assumptions on f a and we establish intervals of the parameter which yield the existence of a positive solution of the eigenvalue problem by placing certain restrictions on the nonlinearity we prove the existence of at least one at least two at least three and infinitely many positive solutions of the boundary value problem by applying some known fixed point theorems as well as some recent generalizations of these fixed point theorems

a new reproducing kernel method for linear nonlocal boundary value problems in the previous works the authors developed the reproducing kernel method rkm for nonlocal boundary value problems a key of the method is the construction of the reproducing kernel rk satisfying the homogenous boundary conditions bcs of the considered problems however it is very difficult to obtain the rk of a reproducing kernel space satisfying nonlocal bcs or nonlinear bcs even if the rk is found its representation is also very complicated compared with the rk without any bcs in this paper we will present a new rkm for linear nonlocal boundary value problems the method can avoid reducing the inhomogeneous bcs to homogeneous bcs and constructing rk satisfying homogeneous nonlocal linear bcs numerical examples are provided to show the effectiveness of the new method

a generalized approach to direction finding with reference to the recently developed estimation of signal parameters using a rotational invariance techniques esprit it is pointed out that other operators can be used to generate the matrix pencil by way of example the moving window operator is discussed

existence uniqueness and iterative methods for third order boundary value problems abstract in this paper we shall provide necessary and sufficient conditions for the existence and uniqueness of solutions of third order nonlinear differential equations satisfying three point boundary conditions for the linear case we propose a constructive method which is a variation of the method of chasing for the nonlinear problems sufficient conditions are provided to ensure the convergence of a general class of iterative methods several examples are also included

uniqueness and existence for bounded boundary value problems the existence and uniqueness of solutions for the boundary value problems with general linear point evaluation boundary conditions is established we assume that f is bounded and that there is uniqueness on a homogeneous problem and on the linear variational problems

mode count and modal density of structural systems relationships with boundary conditions the effects of boundary conditions on the mode count and modal density of one and two dimensional structural systems beams and plates respectively are investigated by using the wavenumber integration method bending vibrations are examined first for a single beam in this case it is demonstrated that the average mode count is reduced by between 0 and 1 for each boundary constraint depending on the type of boundary conditions for more generalised mass and stiffness constraints a frequency dependent coefficient which need not lie between 0 and 1 is obtained the effects of line constraints on the mode count of two dimensional systems are similar to the equivalent one dimensional constraints but they are always frequency dependent then the mode count of systems of multiple collinear beams and coplanar plates is studied it is found that an intermediate constraint has the same effect on the average mode count as the same type of constraint applied at an end of the system the modal density is largely independent of boundary conditions for one dimensional systems although there are exceptions while it is dependent on boundary conditions for two dimensional systems the results are compared with those from previously published formulae for natural frequencies and with results from finite element method fem analysis inclusion of the effect of the boundary conditions in statistical energy analysis sea estimations will result in improved agreements with both analytical and numerical results

boundary value problems for higher order integro differential equations where r t x t x t x j t and a is a continuous operator map c l al a c ar a the function f is continuous in all of its arguments the problem l l 1 2 includes several particular cases for example the boundary value problems for the differential equations if a 0 considered in 7 8 and the references therein for the integro differential equations of the volterra type if

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

boundary value problems for second order differential equations of sobolev type abstract in this paper we provide necessary and sufficient conditions for the existence and uniqueness of solutions of second order differential equations of sobolev type satisfying some boundary conditions we also give sufficient conditions so that the picard and approximate picard method converge to the unique solution of these boundary value problems

macro parameters describing the mechanical behavior of classical guitars since the 1960s and 1970s researchers have proposed simplified models using only a few parameters to describe the vibro acoustical behavior of string instruments in the low frequency range this paper presents a method for deriving and estimating a few important parameters or features describing the mechanical behavior of classical guitars over a broader frequency range these features are selected under the constraint that the measurements may readily be made in the workshop of an instrument maker the computations of these features use estimates of the modal parameters over a large frequency range made with the high resolution subspace esprit algorithm estimation of signal parameters via rotational invariant techniques and the signal enumeration technique ester estimation of error the methods are applied to experiments on real metal and wood plates and numerical simulations of them the results on guitars show a nearly constant mode density in the mid and high frequency ranges as it is found for a flat panel four features are chosen as characteristic parameters of this equivalent plate mass rigidity characteristic admittance and the mobility deviation application to a set of 12 guitars indicates that these features are good candidates to discriminate different classes of classical guitars

existence and uniqueness of solutions for nth order nonlinear two point boundary value problems in this paper we present some general results of existence and uniqueness of solutions for nth order nonlinear two point boundary value problems by using shooting method together with maximum principle and kneser hukahara continuum theorem as applications we give certain concrete sufficient conditions for the existence and uniqueness of solutions of nonlinear two point boundary value problems of nth order lipschitz equations

quasilinearization and approximate quasilinearization for multipoint boundary value problems quasilinearization technique has been applied to a general nonlinear lidstone boundary value problem for the construction of a sequence of its approximate solutions xn t sufficient conditions

the use of the matrix pencil method for the spectrum analysis of musical signals in the context of spectrum analysis high resolution estimation methods present interesting alternatives to classical fourier transform these methods are based on the assumption that the analyzed signal is composed of damped sinusoids and yield estimates of their parameters frequencies damping factors original amplitudes and phases this paper investigates the use of a specific high resolution estimation method the matrix pencil method for the spectrum analysis of musical signals in spite of its computational cost this technique is shown to achieve extremely good results in the case of highly damped signals short data records or close frequencies

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

hardy type inequalities and pohozaev type identities for a class of p degenerate subelliptic operators and applications abstract the purpose of this paper is to consider a class of p degenerate subelliptic operators l p constructed by generalizing greiner s vector fields their fundamental solutions at the origin are established with the aid of the properties of radial functions a picone type identity and a hardy type inequality with respect to vector fields are proved some pohozaev type identities and applications to nonlinear equations are given finally a carleman type estimate and uniqueness of the operator l 2 are discussed

disconjugacy disfocality and differentiation with respect to boundary conditions in particular under certain assumptions concerning the disconjugacy or disfocality of 1 we will consider the differentiability of solutions of 1 with respect to boundary conditions both boundary values and boundary points in so doing we will prove an analogue of a theorem of peano s which appears in hartman s text 1 theorem 3 1 p 951 with the consideration therein being with the differentiation of solutions of 1 with respect to initial conditions in this setting given a solution y x of 1 we are also interested in solutions of the linear nth order differential equation

a second order nonlinear difference equation oscillation and asymptotic behavior discrete analogues are investigated for well known results on oscillation growth and asymptotic behavior of solutions of y q t y 0 for q t 0 and for q t 0 the analogue of atkinson s oscillation criterion is shown to be true for 2yn 1 qn yn 0 but the analogue for atkinson s nonoscillation criterion is shown to be false

liapunov type inequalities for third order half linear equations and applications to boundary value problems abstract we derive liapunov type inequalities for third order half linear differential equations these inequalities utilize integrals of both q t and q t rather than those of q t as in most papers in the literature for higher order liapunov type inequalities furthermore by combining these inequalities with the uniqueness implies existence theorems by several authors we establish the uniqueness and hence existence uniqueness for several classes of boundary value problems for third order linear equations we believe that this is the first time for liapunov type inequalities to be used to deal with boundary value problems and expect that this approach can be further applied to study general higher order boundary value problems

existence of solutions of right focal point boundary value problems for ordinary differential equations y f x y y y 1 1 with respect to l two conditions which we will assume are a f x y 7 yz y is continuous on a b x r b solutions of initial value problems for 1 are unique motivated by the idea of right disfocality of a linear nth order differential operator given by muldowney 11 we shall be concerned with uniqueness of solutions of 1 which satisfy boundary conditions of the form y l x yi 1 i n where x1 x q a x for related results in the linear case where x1 x x x see for example nehari 2 peterson 3 and elias 4 5 1 to be more definite we define what is meant by a right m 1 m focal point boundary value problem for 1 on an interval i

existence and uniqueness of solutions of k 2 point nonlocal boundary value problems for ordinary differential equations abstract sufficient conditions are given under which the existence of solutions of 4 point nonlocal boundary value problems for n th order nonlinear ordinary differential equations yields the existence of unique solutions of k 2 point boundary value problems for 1 k n 1 the results are motivated by a henderson and jackson paper involving relationships between 2 point and n point conjugate boundary value problems

optimal interval lengths for nonlocal boundary value problems associated with third order lipschitz equations abstract for the third order differential equation y f x y y y where f x y 1 y 2 y 3 is lipschitz continuous in terms of y i i 1 2 3 we obtain optimal bounds on the length of intervals on which there exist unique solutions of certain nonlocal three and four point boundary value problems these bounds are obtained through an application of the pontryagin maximum principle from the theory of optimal control

regularity estimates for the solution and the free boundary of the obstacle problem for the fractional laplacian we use a characterization of the fractional laplacian as a dirichlet to neumann operator for an appropriate differential equation to study its obstacle problem we write an equivalent characterization as a thin obstacle problem in this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary

on svd for estimating generalized eigenvalues of singular matrix pencil in noise several algorithms for estimating generalized eigenvalues ges of singular matrix pencils perturbed by noise are reviewed the singular value decomposition svd is explored as the common structure in the three basic algorithms direct matrix pencil algorithm pro esprit and tls esprit it is shown that several svd based steps inherent in the algorithms are equivalent to the first order approximation in particular the pro esprit and its variant tls pro esprit are shown to be equivalent and the tls esprit and its earlier version ls esprit are shown to be asymptotically equivalent to the first order approximation for the problem of estimating superimposed complex exponential signals the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first order approximation the second order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal an improved state space algorithm is found to be the most robust to noise

differentiation of solutions of boundary value problems with respect to nonlinear boundary conditions we consider solutions of boundary value problems for the ordinary differential equation y n x y y y n 1 which satisfy gi y xi yi 1 i n where x1 xn and yi r 1 i n the implicit function theorem is used to establish results in which solutions of the boundary value problems are differentiated with respect to the boundary conditions

uniqueness implies existence on time scales abstract the uniqueness of solutions of initial value boundary value problems along with some uniqueness conditions on two point boundary value problems imply the existence of solutions for the same boundary value problems for the second order nonlinear dynamic equation y f t y y on a time scale this existence is established using shooting methods

eigenvalue problems for second order nonlinear dynamic equations on time scales abstract this paper is concerned with the existence and nonexistence of positive solutions of the second order nonlinear dynamic equation u t a t f u t 0 t 0 1 satisfying either the conjugate boundary conditions u 0 u 1 0 or the right focal boundary conditions u 0 u 1 0 where a and f are positive we show that there exists a 0 such that the above boundary value problem has at least two one and no positive solutions for 0 and respectively furthermore by using the semiorder method on cones of the banach space we establish an existence and uniqueness criterion for positive solution of the problem in particular such a positive solution u t of the problem depends continuously on the parameter i e u t is nondecreasing in lim 0 u 0 and lim u

discrete polynomial interpolation green s functions maximum principles error bounds and boundary value problems abstract we construct discrete interpolating polynomials provide explicit representations of discrete green s functions give several identities and inequalities for these green s functions use the explicit forms of the interpolating polynomials and that of green s functions to establish several maximum principles further we obtain error bounds in discrete polynomial interpolation and use them to study existence and uniqueness of the discrete boundary value problems these bounds are also used to provide sufficient conditions for the convergence of the picard s method the approximate picard s method quasilinearization and the approximate quasilinearization the monotone convergence of the picard s iterative method is also analysed

perturbation analysis of tk method for harmonic retrieval problems the authors present a first order perturbation analysis of the tufts kumaresan tk 1980 method used to estimate frequencies of complex sinusoids in small additive noise several fundamental properties are presented and proved further illustrations are provided through numerical examples

on the right focal point boundary value problems for integro differential equations abstract for the nth order nonlinear integro differential equations subject to right focal point boundary conditions we provide necessary and sufficient conditions for the existence uniqueness and convergence of an approximate iterative method

riccati type transformations for second order linear difference equations abstract oscillation and comparison theorems for a linear homogeneous second order difference equation are proved by employing various equivalent non linear equations obtained by means of transformations analogous to the riccati transformation for ordinary differential equations

from refined estimates for spherical harmonics to a sharp multiplier theorem on the grushin sphere abstract we prove a sharp multiplier theorem of mihlin hormander type for the grushin operator on the unit sphere in r 3 and a corresponding boundedness result for the associated bochner riesz means the proof hinges on precise pointwise bounds for spherical harmonics

existence and uniqueness of solutions of k point boundary value problems for ordinary differential equations for boundary value problems for linear differential equations in which the boundary conditions are linear the uniqueness of solutions implies the existence of solutions this is not the case in general for nonlinear differential equations but in the past several years a number of results of the uniqueness implies existence type for boundary value problems for nonlinear equations have been proven for example 1 2 4 5 9 111 in this paper we prove some additional results of this type we will be concerned with boundary value problems

criteria for right disfocality of linear difference equations abstract right disfocality and criteria for right disfocality of linear difference equations are considered the criteria require the positivity of appropriate minors of a wronskian determinant and are analogues to criteria for the disconjugacy of linear ordinary differential equations and linear difference equations

uniqueness of solutions of right focal problems for third order differential equations on considere l unicite des solutions quand elles existent de certains problemes aux valeurs limites pour l equation differentielle d ordre 3 y f x y y y on suppose que f a b r 3 r est continue

boundary data smoothness for solutions of nonlocal boundary value problems for second order differential equations abstract under certain conditions solutions of the boundary value problem y f x y y y x 1 y 1 and y x 2 i 1 m r i y i y 2 are differentiated with respect to boundary conditions where a x 1 1 m x 2 b r 1 r m r and y 1 y 2 r

total least squares approach for frequency estimation using linear prediction the resolution of the estimated closely spaced frequencies of the multiple sinusoids degrades as the signal to noise ratio snr of the received signal becomes low this resolution can be improved by using the total least squares tls method in solving the linear prediction lp equation this approach makes use of the singular value decomposition svd of the augmented matrix for low rank approximation to reduce the noise effect from both the observation vector and the lp data matrix simultaneously comparison is made to the principle eigenvector pe method of tufts and kumaresan both on theoretical and experimental grounds the tls algorithm exhibits superior performance over the pe method where low rank approximation is applied to the data matrix only

a classification of the solutions of a difference equation according to their behavior at infinity on considere l equation aux differences lineaires d ordre n ly t p t y t 0 ou p t est de signe defini sur a a a 1 a est un entier

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

uniqueness existence and optimality for fourth order lipschitz equations for each t y y y y4 t zi z2 z3 z e a 6 x r4 in particular we will characterize optimal length subintervals of a b in terms of the lipschitz coefficients k i 1 2 3 4 on which certain two three and four point boundary value problems for 1 have unique solutions the techniques we employ here involve applications of the pontryagin maximum principle 14 p 3141 in conjunction with uniqueness implies existence results for solutions of boundary value problems for 1 these techniques are motivated by works of melentsova 15 and melentsova and mil shtein 16 171 and most notably by the two papers by jackson ll 121 furthermore the results contained herein can be considered as extensions of a recent paper by henderson 6 dealing with boundary value problems for third order equations in relating the results of this paper to previous works we will formulate the boundary value problems in terms of the nth order differential equation

focal boundary value problems for nonlinear difference equations ii on considere l unicite des solutions impliquant l existence des solutions de problemes aux valeurs limites de type focal pour l equation aux differences non lineaire d ordre n u t n f t u t u t n 1 ou f a r n r est continue et l equation u n 1 f t u 1 u n peut etre resolue pour u 1 comme fonction continue des variables t u 2 u u 1

information criteria and selection of vibration models this paper presents a method of determining an appropriate equation of motion of two dimensional plane structures like membranes and plates from vibration response measurements the local steady state vibration field is used as input for the inverse problem that approximately determines the dispersion curve of the structure this dispersion curve is then statistically treated with akaike information criterion aic which compares the experimentally measured curve to several candidate models equations of motion the model with the lowest aic value is then chosen and the utility of other models can also be assessed this method is applied to three experimental case studies a red cedar wood plate for musical instruments a thick paper subjected to unknown membrane tension and a thick composite sandwich panel these three cases give three different situations of a model selection

the iterative solutions of 2nth order nonlinear multi point boundary value problems abstract the aim of this paper is to investigate the existence of iterative solutions for a class of 2 n th order nonlinear multi point boundary value problems the multi point boundary condition under consideration includes various commonly discussed boundary conditions such as three or four point boundary condition n 2 point boundary condition and 2 n m point boundary condition the existence problem is based on the method of upper and lower solutions and its associated monotone iterative technique a monotone iteration is developed so that the iterative sequence converges monotonically to a maximal solution or a minimal solution depending on whether the initial iteration is an upper solution or a lower solution two examples are presented to illustrate the results

boundary value problems occurring in plate deflection theory abstract the paper deals with several iterative methods for solving some boundary value problems occurring in plate deflection theory making it possible to avoid the lengthy problem preparation which is required to solve these problems by finite difference methods

uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for nth order differential equations abstract for the nth order differential equation y n f x y y y n 1 we consider uniqueness implies existence results for solutions satisfying certain nonlocal k 2 point boundary conditions 1 k n 1 uniqueness of solutions when k n 1 is intimately related to uniqueness of solutions when 1 k n 2 these relationships are investigated as well

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

method of chasing for multipoint boundary value problems the method of chasing developed by gel fand and lokutsiyevskii is completely formulated here for nth order ordinary linear differential equations subject to separated multipoint boundary conditions

on nonlinear discrete boundary value problems mo x 1 x n 0 1 4 where n is a fixed positive integer 8 represent n by n constant matrices a t is an n by n matrix for each te 0 l h t belongs to ir for each nonnegative integer t u is in r 1 is a real parameter f and g are continuously differentiable f r i ir and g r i r for systems 1 1 1 2 we prove that if the linear system x t l a l x t h t 1 5 subject to

right focal point boundary value problems for ordinary differential equations and variational equations where x g x such problems are called right focal point boundary value problems in the last few years a number of papers have appeared dealing with such boundary value problems most notable in the case when 1 is linear are papers by elias 11 muldowney 7 8 and peterson 19 io and for nonlinear considerations the papers by henderson 3 4 jackson 5 and peterson 11 121 in those papers several analogues of known results for conjugate type boundary value problems are considered for eq l we will have need of the hypotheses