oscillation theorems for differential equations with a nonlinear damping term in this paper we are concerned with a class of nonlinear second order differential equations with a nonlinear damping term passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity and as a consequence our results apply to wider classes of nonlinear differential equations two illustrative examples are considered

on oscillation of nonlinear second order differential equation with damping term we present new oscillation criteria for the second order nonlinear differential equation with damping our theorems are stated in general form they complement and extend related results known in the literature the relevance of our results is illustrated with a number of examples to facilitate computations in these examples we use mathematica r a symbolic computer language

positive periodic solutions for a neutral delay lotka volterra system abstract applying a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions for a class of neutral delay lotka volterra systems x i t x i t r i t j 1 n a i j t x j t j 1 n b i j t x j t i j t j 1 n c i j t x j t i j t i 1 2 n compared to known results our main generalization is that delays of the derivatives are not assumed to be constants and our results are more easily verifiable

a third order modification of newton s method for multiple roots in this paper we present a new third order modification of newton s method for multiple roots which is based on existing third order multiple root finding methods numerical examples show that the new method is competitive to other methods for multiple roots

on the existence of periodic solutions of a neutral delay model of single species population growth abstract in this paper we employ some new techniques to study the existence of positive periodic solutions of the neutral delay model n t n t a t t n t b t n t t c t n t t our result gives a correct answer to the open problem 9 2 due to y kuang 1993 delay differential equations with applications in population dynamics academic press new york

existence of positive periodic solutions for neutral functional differential equations abstract applying a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions of the following neutral functional differential equation x t x t a t f t x t x t 1 t x t n t x t 1 t x t m t

oscillation criteria for certain nonlinear differential equations we present new oscillation criteria for certain classes of second order nonlinear differential equations and delay differential equations obtained by using an integral averaging technique our theorems complement a number of existing results and handle the cases which are not covered by known criteria

a composite third order newton steffensen method for solving nonlinear equations in this paper we suggest a third order method formed by the composition of newton and steffensen methods for finding simple and real roots of a nonlinear equation in single variable per iteration the formula requires two evaluations of the function and single evaluation of the derivative experiments show that the method is suitable in the cases where newton and steffensen methods fail

oscillation behavior of second order nonlinear neutral differential equations with deviating arguments oscillation criteria are established for second order nonlinear neutral differential equations with deviating arguments of the form r t z t a 1z t f t x s t 0 t t 0 where a 0 and z t x t p t x t t our results improve and extend some known results in the literature some illustrating examples are also provided to show the importance of our results

an easy method to accelerate an iterative algebraic equation solver this article proposes to add a single function calls to an iterative algebraic equation solver with an order n convergence rate and to raise for n 1n 1 the order of convergence to 2n 12n 1

differentiability of solutions with respect to parameters in neutral differential equations with state dependent delays in this paper we consider a class of nonlinear neutral differential equations with state dependent delays in both the neutral and the retarded terms we study well posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the c norm

oscillation criteria for nonlinear differential equations with damping oscillation criteria are established for the nonlinear second order damped differential equation rx px qf x 0 which are different from most known results

oscillation criteria for second order quasi linear neutral delay differential equations abstract in this paper some new oscillation criteria for second order neutral nonlinear differential equation r t x t p t x t m 1 x t p t x t q t f x t 0 are established new oscillation criteria are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel

oscillation of certain second order nonlinear differential equations abstract in this paper we consider the second order nonlinear differential equation formula where 0 is any quotient of odd integers a c 1 r 0 q c r r f c r r xf x 0 f x 0 for x 0 some new sufficient conditions for the oscillation of all solutions of are obtained several examples that dwell upon the importance of our results are also included

iterative methods improving newton s method by the decomposition method in this paper we present a sequence of iterative methods improving newton s method for solving nonlinear equations the adomian decomposition method is applied to an equivalent coupled system to construct the sequence of the methods whose order of convergence increases as it progresses the orders of convergence are derived analytically and then rederived by applying symbolic computation of maple some numerical illustrations are given

new kamenev type oscillation criteria for second order nonlinear differential equations with damping abstract some new oscillation criteria are established for the nonlinear damped differential equation r t y p t y q t f y 0 that are different from most known ones in the sense that they are based on a class of new functions t s r defined in the sequel our results are sharper than some previous results which can be seen by the examples at the end of this paper

note on the paper of džurina and stavroulakis abstract in this paper we will establish some new oscillation criteria for the second order retarded differential equation of the form r t u t 1 u t p t u t 1 u t 0 the results obtained essentially improve and extend those of d urina and stavroulakis oscillation criteria for second order delay differential equations appl math comput 140 2003 445 453 an open problem is proposed at the end of this paper

on newton type methods with cubic convergence recently there has been some progress on newton type methods with cubic convergence that do not require the computation of second derivatives weerakoon and fernando appl math lett 13 2000 87 derived the newton method and a cubically convergent variant by rectangular and trapezoidal approximations to newton s theorem while frontini and sormani j comput appl math 156 2003 345 140 2003 419 derived further cubically convergent variants by using different approximations to newton s theorem homeier j comput appl math 157 2003 227 169 2004 161 independently derived one of the latter variants and extended it to the multivariate case here we show that one can modify the werrakoon fernando approach by using newton s theorem for the inverse function and derive a new class of cubically convergent newton type methods

periodic solutions for general nonlinear state dependent delay logistic equations abstract in this paper by using the continuation theorem of coincidence degree theory we investigate the existence of periodic solutions for more general state dependent delay logistic equations several sufficient conditions are given and the obtained conditions possess important significance in both theories and applications

some new oscillation criteria for second order quasi linear neutral delay differential equations in this paper we will establish some new oscillation criteria for second order quasi linear neutral delay differential equations of the form r t x t p t x email protected a 1 x t p t x email protected q t f x s t 0 the results obtained essentially improve and extend those of dzurina and stavroulakis j dzurina i p stavroulakis oscillation criteria for second order delay differential equations appl math comput 140 2003 445 453 sun and meng y g sun f w meng note on the paper of dzurina and stavroulakis appl math comput 174 2006 1634 1641

oscillation theorems for second order neutral functional differential equations some new oscillation criteria are given for second order neutral functional differential equations of the form d 2dt 2 x t lx t t mx t s qx t a px t b 0 where l t m s p and q are real numbers and a and b are real positive constants

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

new oscillation criteria for second order nonlinear neutral delay differential equations in this paper several new oscillation criteria for the second order nonlinear neutral delay differential equation r t x t p t x s t m 1 x t p t x s t q t f x t t 0 t t 0 are established these oscillation criteria extend and improve some known results an interesting example illustrating the importance of our results is also provided

existence of periodic solutions in neutral state dependent delays equations and models sufficient conditions are obtained for the existence of positive periodic solutions of neutral equations with state dependent delays the proof is based on the theory of coincidence degree the existence results are applied to equations of population dynamics

boundedness of solutions of a nonlinear nonautonomous neutral delay equation abstract sufficient conditions are obtained for the boundedness of solutions of the non linear nonautonomous neutral equation x t r t x t a t x t 1 c t x t 1 which arise in a food limited population model this partially answers a recent open question proposed by k gopalsamy and b g zhang

improving the order of convergence of iteration functions abstract improving methods for the order of convergence of iteration functions are give using these methods new third or fourth order root finding methods for a single equation with a multiple root are derived numerical examples are given

oscillation theorems for nonlinear differential equations of second order abstract in this paper we present some new criteria for the oscillation of the differential equation a t x t x t p t x t q t f x t 0 the obtained results extend improve and correlate a number of existing criteria

periodic solution of a periodic neutral delay equation abstract sufficient conditions are obtained for the existence of a positive periodic solution of the periodic neutral delay equation t n t a t n j 1 b j t n t j j 1 n c j t t j which arise in a food limited population model

some third order families of iterative methods for solving nonlinear equations abstract in this paper we present a convenient third order iteration formula improving newton s method for solving nonlinear equations with any two iteration functions of order two the formula provides one parameter third order family of methods each family member is free from second derivatives and per iteration it requires three evaluations of the given function and its derivative several numerical examples are given to illustrate the efficiency and performance of some of the presented methods

some variant of newton s method with third order convergence we present a new modification of the newton s method which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given and the best efficiency in term of function evaluations of two of this new methods is provided

oscillation for a second order neutral differential equation with impulses we consider a certain type of second order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations called impulses as a matter of fact some particular non impulsive cases of the system are oscillatory already thus we are interested in finding adequate impulse controls under which our system remains oscillatory

construction of newton like iteration methods for solving nonlinear equations in this paper we present a simple and yet powerful and easily applicable scheme in constructing the newton like iteration formulae for the computation of the solutions of nonlinear equations the new scheme is based on the homotopy analysis method applied to equations in general form equivalent to the nonlinear equations it provides a tool to develop new newton like iteration methods or to improve the existing iteration methods which contains the well known newton iteration formula in logic those all improve the newton method the orders of convergence and corresponding error equations of the obtained iteration formulae are derived analytically or with the help of maple some numerical tests are given to support the theory developed in this paper

oscillation criteria for second order nonlinear perturbed differential equations abstract we present new oscillation criteria for the second order nonlinear perturbed differential equations these criteria are of a high degree of generality and they extend and unify a number of existing results

oscillation theorems for second order nonlinear neutral differential equations the purpose of this paper is to study the oscillation of the second order neutral differential equations of the form a t z t c q t x b s t 0 where z t x t p t x t t we explore properties of given equations by examining those of associated first order delay equations new comparison theorems essentially simplify the examination of the equations studied as they allow us to deduce the oscillation of the second order delay differential equation by applying the oscillation criteria obtained to the first order delay equations the results obtained are easy to verify

letter to the editor third order modification of newton s method in this paper we present a new modification of newton s method for solving non linear equations analysis of convergence shows that the new method is cubically convergent numerical examples show that the new method can compete with the classical newton s method

oscillation criteria for second order nonlinear differential equations with damping abstract for a second order nonlinear differential equation with a damping term we obtain new oscillation criteria without an assumption that has been required for related results reported in the literature over the last two decades two approaches refining the standard integral averaging technique suggested in the paper can be used to derive a variety of simpler oscillation theorems for different classes of nonlinear differential equations and both sets of oscillation criteria established in the paper are of independent interest several examples are provided to illustrate the relevance of the new theorems

oscillation criteria for second order neutral delay difference equations abstract in this paper we establish some oscillation criteria of the second order delay difference equation a n 1 x n 1 p n 1 x n 1 q n f x n 0 where and are nonnegative constants an and pn qn are nonnegative sequences and f c

oscillation theorems for certain neutral functional differential equations in this paper we shall offer sufficient conditions for the oscillation of all solutions to neutral functional differential equations of mixed type of the form dndtn x t ax t bx t q t x t g p t x t h 0 1 here p and q are periodic functions

oscillation and asymptotic analysis on a new generalized emden fowler equation abstract in this work we analyze the new generalized emden fowler equation with neutral type delays r t z t 1 z t q t x t 1 x t 0 where z t x t p t x t 0 by use of averaging technique and specific analytical skills some easily accessible oscillation and asymptotic criteria are established which have extended the results in the cited literature

linearized stability for a class of neutral functional differential equations with state dependent delays abstract in this paper we formulate a stability theorem by means of linearization around a trivial solution in the case of autonomous neutral functional differential equations with state dependent delays we prove that if the trivial solution of the linearized equation is exponentially stable then the trivial solution of the nonlinear equation is exponentially stable as well as an application of the main result explicit stability conditions are given

sufficient conditions for the existence of positive periodic solutions of a class of neutral delay models by using the theory of coincidence degree the existence of positive periodic solutions is studied for the neutral model with periodic delaysn t n t a t email protected t n t email protected i 1 nb i t n email protected i t email protected i 1 nc i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

non oscillatory solutions for a nonlinear neutral delay differential equation abstract we study the existence of non oscillatory bounded solutions for a second order nonlinear neutral delay differential equation some sufficient conditions for the existence of non oscillatory bounded solutions with positive lower bound or negative upper bound are established and the non oscillatory solutions with decay as t are discussed

oscillation theorems for second order neutral differential equations the aim of this paper is to study the oscillation of the second order neutral differential equations e r t x t p t x t t q t x s t 0 the obtained results are based on the new comparison theorems that enable us to reduce the problem of the oscillation of the second order equation to the oscillation of the first order equation the obtained comparison principles essentially simplify the examination of the studied equations

a simply constructed third order modifications of newton s method in this paper we present a simple and easily applicable approach to construct some third order modifications of newton s method for solving nonlinear equations it is shown by way of illustration that existing third order methods can be employed to construct new third order iterative methods the proposed approach is applied to the classical chebyshev halley methods to derive their second derivative free variants numerical examples are given to support that the methods thus obtained can compete with known third order methods

existence results for an impulsive abstract partial differential equation with state dependent delay in this paper we establish the existence of mild solutions for a class of impulsive abstract partial functional differential equation with state dependent delay

integral averaging techniques for the oscillation of second order nonlinear differential equations abstract in this paper we enlist some known and establish some new oscillation criteria for the second order nonlinear differential equations of the form if a t x t t su p t t q t f x t 0 where the coefficients p t and q t are not assumed to be nonnegative for all large values of t these criteria are obtained by using integral averaging techniques and can be applied to some special cases where other classical oscillation results are not applicable a systematic study is attempted to extend improve and correlate a number of existing results

periodic solutions of the higher dimensional non autonomous systems in this paper the new existence theorem unique theorem of periodic solution of the periodic system x a t x x g t x and new stationary oscillation theorem of the periodic system x f t x g t x are derived by using functional analysis method algebraic method and the new estimated formulas of solution of the homogenous linear system our results extend and improve some main results related to references in addition these criteria are of great interest in many applications such as computation

oscillation criteria for second order delay differential equations the aim of this paper is to establish some new oscillation criteria for the second order retarded differential equation r t u t a 1u t p t u t t a 1u t t 0 the results obtained essentially improve known results in the literature

positive periodic solutions of neutral lotka volterra system with periodic delays in this paper several sufficient conditions are investigated for the existence of positive periodic solutions of a general neutral lotka volterra system with unbounded delays by using the theory of coincidence degree our results extend and improve existing results and have further applications in population dynamics

a modification of newton method with third order convergence in this paper we present a new modification of newton method for solving non linear equations analysis of convergence shows that the new method is cubically convergent per iteration the new method requires two evaluations of the function and one evaluation of its first derivative thus the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself its practical utility is demonstrated by numerical examples

an acceleration of newton s method super halley method from a study of the convexity we give an acceleration for newton s method and obtain a new third order method then we use this method for solving non linear equations in banach spaces establishing conditions on convergence existence and uniqueness of solution as well as error estimates

some fourth order modifications of newton s method abstract in this paper we construct some fourth order modifications of newton s method for solving nonlinear equations any two existing fourth order methods can be effectively used to give rise to new fourth order methods per iteration the new methods require two evaluations of the function and one of its first derivative numerical examples are given to show the performance of the presented methods

oscillation criteria for second order nonlinear neutral differential equations by refining the standard integral averaging technique we obtain new oscillation criteria for a class of second order nonlinear neutral differential equations of the form r t x t p t x email protected q t f x t x s t 0 assumptions in our theorems are less restrictive whereas the proofs are significantly simpler compared to those in the recent paper by shi and wang 18 and related contributions to the subject examples are provided to illustrate the relevance of new theorems

periodic solutions of periodic delay lotka volterra equations and systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic lotka volterra equations and systems with distributed or state dependent delays our results substantially extend and improve existing results

on kamenev type oscillation theorems for second order differential equations with damping abstract oscillation criteria for the nonlinear second order ordinary differential equation with damping x p t x f x 0 are given the results are extensions of integral averaging technique of kamenev and include earlier results of yeh yan and chen