on nonlinear two point boundary value problems for impulsive differential algebraic problems in this paper we investigate boundary value problems for first order impulsive differential algebraic problems with causal operators note that a corresponding boundary condition is given by a nonlinear function using a monotone iterative method we formulate general sufficient conditions under which such problems have solutions extremal or a unique an example shows that corresponding assumptions are satisfied the results are new

monotone method for first order functional differential equations we study periodic boundary value problems relative to a general class of first order functional differential equations for this class of problems we develop the monotone iterative technique our formulation is very general including delay differential equations functional differential equations with maxima and integro differential equations but the case where the operator defining the functional dependence is not necessarily lipschitzian is also considered

monotone iterative technique for periodic boundary value problems with causal operators abstract in this paper we develop the monotone iterative technique for periodic boundary value problems with causal operators

differential equations with causal operators in a banach space abstract in this paper differential equations with causal operators in the framework of an arbitrary banach space are studied basic results such as existence uniqueness and global existence are proved the theory of cones is employed to investigate the extremal solutions of such equations

solvability of three point boundary value problems for second order differential equations with deviating arguments the monotone iterative technique is used to boundary problems for second order ordinary differential equations with deviating arguments corresponding results are formulated when the problem has extremal solutions or weakly coupled extremal quasi solutions

boundary value problems with causal operators abstract in this paper we apply the monotone iterative method for nonlinear two point boundary value problems with causal operators we formulate sufficient conditions under which such problems have extremal or quasisolutions in a corresponding sector we also investigate differential inequalities

first order impulsive ordinary differential equations with advanced arguments this paper deals with impulsive advanced ordinary differential equations with boundary conditions we investigate the existence of solutions and quasisolutions for advanced impulsive differential equations to obtain such results we apply schauder s fixed point theorem corresponding results are also formulated for differential inequalities

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problem for second order functional differential equations by using the method of lower and upper solutions coupled with monotone iterative technique

nonhomogeneous boundary value problem for first order impulsive differential equations with delay the authors employ the method of upper and lower solution coupled with the monotone iterative technique to obtain results of existence and uniqueness for a nonhomogeneous boundary value problem of impulsive differential equations with delay

periodic boundary value problem for first order impulsive functional differential equations in this paper by means of the method of upper and lower solutions and the monotone iterative technique the existence of minimal and maximal solutions of the periodic boundary value problem for first order impulsive functional differential equations is considered

a uniqueness theorem for the singly periodic genus one helicoid the singly periodic genus one helicoid was in the origin of the discovery of the first example of a complete minimal surface with finite topology but infinite total curvature the celebrated hoffman karcher wei s genus one helicoid the objective of this paper is to give a uniqueness theorem for the singly periodic genus one helicoid provided the existence of one symmetry

inequalities for the constants of landau and lebesgue the constants of landau and lebesgue are defined for all integers n 0 by gn k 0n1 16k 2 and ln 12 sin n t sin t dt respectively we establish sharp inequalities for gn and ln 2 in terms of the logarithmic derivative of the gamma function further we prove that the sequence gn is completely monotonic we provide best possible upper and lower bounds for the ratios gn 1 gn 1 gn and l n 1 2 l n 1 2 ln 2 and we present sharp bounds for ln 2 gn and ln 2 gn

on the convergence of iterative methods for general differential algebraic systems in this paper the existence and uniqueness of solutions to quite general classes of integro algebraic systems and differential algebraic systems are investigated the convergence of different iterative processes of solving such systems including waveform relaxation methods is also investigated there are given constructive sufficient conditions under which the solutions exist and are unique and the considered iterative processes are convergent

nonlinear boundary value problem of first order impulsive functional differential equations this paper discusses nonlinear boundary value problem for first order impulsive functional differential equations we establish several existence results by using the lower and upper solutions and monotone iterative techniques two examples are discussed to illustrate the efficiency of the obtained results

periodic boundary value problem for non lipschitzian impulsive functional differential equations we consider a class of first order impulsive functional differential equations where the functional dependence is not necessarily a lipschitzian function the new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented we give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution

nonlinear boundary value problems for second order differential equations with causal operators in this paper we deal with second order differential equations with causal operators to obtain sufficient conditions for existence of solutions we use a monotone iterative method we investigate both differential equations and differential inequalities an example illustrates the results obtained

inequalities and asymptotic expansions for the constants of landau and lebesgue the constants of landau and lebesgue are defined for all integers n 0 in order by g n k 0 n 1 16 k 2 k k 2 and l n 1 2 sin n 1 2 t sin 1 2 t d t which play important roles in the theories of complex analysis and fourier series respectively diverse inequalities and approximations for these constants have been investigated and developed by many authors here in this paper we establish new asymptotic expansions for the constants g n and l n 2 of landau and lebesgue respectively in terms of the digamma and polygamma functions based on our expansion for the landau constants g n we present new bounds for the landau constants g n in terms of the digamma and polygamma functions we also establish inequalities for the lebesgue constants l n 2 which are applied to derive an asymptotic expansion for l n 2 in terms of 1 n 1 furthermore by giving numerical calculations to be compared among several developed asymptotic expansions for the constants g n and l n 2 it is shown that our expansions presented here would be best ones

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

boundary value problems for first order impulsive delay differential equations with a parameter in this paper by means of the method of upper and lower solutions and monotone iterative technique the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established

boundary value problems for first order differential equations of mixed type abstract we apply the monotone iterative method to formulate existence results for integro differential equations with nonlinear boundary conditions some results for integro differential inequalities are also given examples illustrate obtained results

on differential algebraic problems in this paper the existence of extremal or quasi solutions for differential algebraic problems with causal operators is investigated the case when such problems have a unique solution is also discussed to obtain existence results a monotone iterative technique is applied

advanced differential equations with nonlinear boundary conditions we investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions sufficient conditions when the problem has extremal solutions or a unique solution are formulated linear advanced differential inequalities are also discussed

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

some sharp estimates of the constants of landau and lebesgue we establish several sharp two sided inequalities involving the constants of landau and lebesgue which occur and play important roles in two related extremal problems in complex analysis and in fourier analysis respectively the main results improves essentially the watson asymptotic expansion formulas for these constants

periodic boundary value problems for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results

periodic boundary value problem for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problem for a class of first order impulsive functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results