on the existence and multiplicity of positive periodic solutions for first order vector differential equation abstract in this paper we consider the existence and multiplicity of positive periodic solutions for first order vector differential equation x t f t x t 0 a e t 0 under the periodic boundary value condition x 0 x here is a positive constant and f 0 r n r n is a caratheodory function some existence and multiplicity results of positive periodic solutions are derived by using a fixed point theorem in cones

remarks on the periodic boundary value problems for first order differential equations this paper is concerned with the existence of solutions and the monotone method of first order periodic boundary value problems when the lower and upper solutions and violate the boundary conditions 0 2 and 0 2 using the topological degree theory two existence theorems are established under weaker conditions than the one side lipschitz conditions an example is given which illustrates that pbvp may not have solutions between and without further restrictions to f t u the monotone method is also discussed with some new results

remarks on first and second order periodic boundary value problems on etudie les problemes aux valeurs limites periodiques d ordre 1 et 2 suivants u f t u u 0 u 2 et u f t u u 0 u 2 u 0 u 2 on obtient l existence de solutions extremales comme limites d iterees monotones

the method of upper lower solutions and hyperbolic partial differential equations on presente l etude de la methode des solutions superieures et inferieures pour des equations differentielles hyperboliques on considere la theorie des inegalites differentielles hyperboliques d une facon generale et on demontre un resultat d existence

the method of lower and upper solutions for systems of boundary value problems the method of lower and upper solutions for second order differential system x f t x with dirichlet boundary condition x 0 x 1 0 is used to give sufficient conditions for the existence of at least one solution

ordinary differential equations with nonlinear boundary conditions of antiperiodic type abstract the quasilinearization method is successfully applied to differential problems with nonlinear boundary conditions of antiperiodic type given are sufficient conditions under which the monotone iterations converge quadratically to a unique solution of our problem the advantage of this approach lies in the fact that the approximate solutions are obtained iteratively as solutions of the above mentioned iterations

positive solution for system of nonlinear first order pbvps on time scales abstract in this paper we are concerned with the following system of nonlinear first order periodic boundary value problems on time scale t x i t f i t x 1 t x 2 t x n t 0 t 0 t x i 0 x i t i 1 2 n where f i 0 t 0 n r is continuous and there exists a constant m i 0 such that m i x i f i t x 1 x 2 x n 0 for x 1 x 2 x n 0 n t 0 t some existence criteria of positive solution are established by using a fixed point theorem for operators on cone

linecast line based distributed coding and transmission for broadcasting satellite images in this paper we propose a novel coding and transmission scheme called linecast for broadcasting satellite images to a large number of receivers the proposed linecast matches perfectly with the line scanning cameras that are widely adopted in orbit satellites to capture high resolution images on the sender side each captured line is immediately compressed by a transform domain scalar modulo quantization without syndrome coding the transmission power is directly allocated to quantized coefficients by scaling the coefficients according to their distributions finally the scaled coefficients are transmitted over a dense constellation this line based distributed scheme features low delay low memory cost and low complexity on the receiver side our proposed line based prediction is used to generate side information from previously decoded lines which fully utilizes the correlation among lines the quantized coefficients are decoded by the linear least square estimator from the received data the image line is then reconstructed by the scalar modulo dequantization using the generated side information since there is neither syndrome coding nor channel coding the proposed linecast can make a large number of receivers reach the qualities matching their channel conditions our theoretical analysis shows that the proposed linecast can achieve shannon s optimum performance by using a high dimensional modulo lattice quantization experiments on satellite images demonstrate that it achieves up to 1 9 db gain over the state of the art 2d broadcasting scheme and a gain of more than 5 db over jpeg 2000 with forward error correction

a generalized upper and lower solutions method and multiplicity results for nonlinear first order ordinary differential equations abstract we introduce a generalized upper and lower solutions method for the solvability of first order ordinary differential equations u t t u t u 0 u 1 in order to cover the case when the function satisfies caratheodory conditions this method is then applied to get multiplicity results when the nonlinearity interacts with the real eigenvalue of the linearized problem our proofs are based on differential inequalities and classical leray schauder degree

renormalizing upper and lower bounds for integrated risk in the white noise model where wt is brownian motion many results which might be difficult to prove in the density estimation or nonparametric regression context take on a more transparent form in this white noise model a sample size of n in the density estimation and nonparametric regression problems corresponds to o 0 o xn in 1 when ois suitably chosen in particular the tools of rescaling developed in low 1992 and donoho and low 1992 and the hardest one dimensional subfamily arguments of donoho and liu 1987 1991 have yielded a fairly complete picture of how to estimate both bounded and unbounded linear functionals on the basis of observations generated by 1 a separate literature is developing to show how to replace density estimation and regression problems by the corresponding white noise problems see for example low 1992 brown and low 1990 and donoho and low 1990 in this paper we focus attention on estimating the entire function f on the basis of the observation scheme given by 1 using integrated squared error as a measure of loss in particular we shall let r f o denote the minimax risk under this loss function that is

nonlinear second order periodic boundary value problems abstract in this paper we study a periodic boundary value problem pbvp for brevity of second order it is well known that if and are upper and lower solutions respectively with then there exists a solution u such that u when nothing was known the main purpose of this paper is to consider this last case also we study the structure of the set of solutions of the pbvp in the sector when and we apply the results to the case

quadratic approximation of solutions for differential equations with nonlinear boundary conditions the quasilinearization method is used for nonlinear ordinary differential equations with nonlinear boundary conditions given are sufficient conditions when corresponding monotone sequences converge to the unique solution and this convergence is quadratic

the monotone method for first order problems with linear and nonlinear boundary conditions in this paper we develop the monotone method for the first order problem u t f t u t for a e t a b when f is a caratheodory function and u w 1 1 a b we consider the nonlinear boundary conditions l u a u b 0 with l c r 2 r nondecreasing in x or nonincreasing in y and the linear boundary conditions a 0u 0 b 0u t l 0 with a 0 b 0 and l 0 r we prove the existence of solutions and the validity of the monotone method if there exists a lower solution a and an upper solution b with either a b for the linear conditions we obtain eight new concepts of lower and upper solutions which generalize previous known cases

iterative approximation of limit cycles for a class of abel equations this article considers the analytical approximation of limit cycles that may appear in abel equations written in the normal form the procedure uses an iterative approach that takes advantage of the contraction mapping theorem thus the obtained sequence exhibits uniform convergence to the target periodic solution the effectiveness of the technique is illustrated through the approximation of an unstable limit cycle that appears in an abel equation arising in a tracking control problem that affects an elementary second order bilinear power converter

monotone iterative techniques of v lakshmikantham for a boundary value problem for systems of impulsive differential difference equations by means of the monotone iterative techniques of v lakshmikantham a couple of minimal and maximal quasisolutions of a two point boundary value problem for a system of impulsive differential difference equations are constructed

a monotone method for the equation uxyz f comparison theorems for the nonlinear boundary value problem u x y z f x y z u u x u y u z u x y u y z u z x with the boundary conditions u o y z a y z u x 0 z b z x u x y 0 c x y a y 0 c 0 y a 0 z b z 0 b 0 x c x 0 are established under certain conditions then it is shown that there exist sequences of lower and upper solutions which converge uniformly and monotonically to minimal and maximal solutions respectively

periodic solutions of nonlinear boundary value problems one of the well known techniques in the theory of nonlinear boundary value problems bvp is the method of differential inequalities or the method of upper and lower solutions the method of alternative problems a global variant of the lyapunov schmidt method has been used in the study of problems at resonance the investigation of periodic bvp s forms an important subclass of problems at resonance our aim is to combine the two approaches to discuss nonlinear problems at resonance we restrict ourselves in this paper to the discussion of periodic boundary value problems in section 1 we shall indicate the method of upper and lower solutions the results for systems are given in a general way so as to include known results and also offer new directions section 2 deals with the abstract existence results at resonance in the desired framework in section 3 we consider the scalar periodic bvp s by combining the two techniques namely alternative methods and the method of differential inequalities

existence of periodic solutions for fully nonlinear first order differential equations in this paper we establish some existence results for periodic solutions of fully nonlinear first order scalar differential equation f t x x 0 the approach here uses the viscosity solutions method developed in recent decades and the classical upper lower solutions method

approximation of solutions for nonlinear periodic boundary value problems with discontinuous upper and lower solutions we prove that it is possible to approximate the solutions of a nonlinear periodic boundary value problem via monotone sequences starting at piecewise continuous upper and lower solutions in fact we present here two different iterative methods explicit expression of each iteration is obtained by solving some linear initial value problems