positive solutions of the three point boundary value problem for second order differential equations with an advanced argument abstract in this paper by using the fixed point index method we establish the existence of at least one or at least two positive solutions to the three point boundary value problem for a second order differential equation with an advanced argument u t a t f u h t 0 t 0 1 u 0 0 u u 1 where 0 1 0 and 1 0 as an application we also give an example to demonstrate our result

positive solutions for a three point boundary value problem the second order three point boundary value problem x t 2x t h t f t x t t 0 1 x 0 0 x x 1 is considered under some conditions concerning the first eigenvalue of the relevant linear operator where 0 1 is a constant h t is allowed to be singular at t 0 and t 1 the existence of positive solutions is studied by means of fixed point index theory

multiple positive solutions of dirichlet boundary value problems for second order impulsive differential equations abstract this paper is devoted to study the existence of multiple positive solutions for the second order dirichlet boundary value problem with impulse effects the main results here is the generalization of liu and li l liu f y li multiple positive solution of nonlinear two point boundary value problems j math anal appl 203 1996 610 625 for ordinary differential equations existence is established via the theory of fixed point index in cones

positive solutions of three point boundary value problems for second order impulsive differential equations with advanced arguments in this paper we discuss three point boundary value problems for second order impulsive differential equations with advanced arguments we establish sufficient conditions under which such problems have positive solutions to obtain the results we use the fixed point index

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

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 problems for the second order functional differential equations the novelty is that we introduce a new concept for 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

multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations we study the existence behavior of positive solutions to a singular two point boundary value problem of second order impulsive equation with fixed moments proofs are based on combining a method of upper and lower solutions with fixed point index theorems on a cone

empirical measure of multiclass generalization performance the k winner machine case combining the k winner machine kwm model with empirical measurements of a classifier s vapnik chervonenkis vc dimension gives two major results first analytical derivations refine the theory that characterizes the generalization performances of binary classifiers second a straightforward extension of the theoretical framework yields bounds to the generalization error for multiclass problems

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

positive solutions for fourth order differential equations with deviating arguments and integral boundary conditions abstract in this paper we investigate integral boundary value problems for fourth order differential equations with deviating arguments we discuss our problem both for advanced or delayed arguments we establish sufficient conditions under which such problems have positive solutions to obtain the existence of multiple at least three positive solutions we use a fixed point theorem due to avery and peterson an example is also included to illustrate that corresponding assumptions are satisfied the results are new

multiplicity of positive solutions for second order three point boundary value problems we study the multiplicity of positive solutions for the second order three point boundary value problem u h t f u 0 t 0 1 u 0 0 u u 1 where 0 1 0 1 the methods employed are fixed point index theorems and leray schauder degree and upper and lower solutions

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

positive solutions to second order four point boundary value problems for impulsive differential equations abstract in this paper by using the leggett williams theorem we present sufficient conditions which guarantee the existence of three positive solutions to second order four point boundary value problems for impulsive differential equations

an acoustic boundary element method based on energy and intensity variables for prediction of high frequency broadband sound fields a boundary element method is formulated in terms of time averaged energy and intensity variables the approach is applicable to high modal density fields but is not restricted to the usual low absorption diffuse and quasiuniform assumptions a broadband acoustic energy intensity source is the basic building block for the method a directivity pattern for the source is derived to account for local spatial correlation effects and to model specular reflections approximately a distribution of infinitesimal uncorrelated directional sources is used to model the boundaries of an enclosure these sources are discretized in terms of boundary elements a system of equations results from applying boundary conditions in terms of incident reflected and absorbed intensity the unknown source power for each element is determined from this system of equations a two dimensional model problem is used to demonstrate and verify the method exact numerical solutions were also obtained for this model problem the results show that spatially varying mean square pressure levels are accurately predicted at very low computational cost

existence of solutions for second order impulsive differential equations with deviating arguments abstract this paper deals with impulsive second order differential equations with deviating arguments we investigate the existence of solutions of such problems with nonlinear boundary conditions to obtain corresponding results we discuss also second order impulsive differential inequalities with deviating arguments

existence of positive solutions to second order four point impulsive differential problems with deviating arguments in this paper we discuss four point boundary value problems for impulsive second order differential equations with deviating arguments we investigate separately cases when arguments are of delayed or advanced types we formulate sufficient conditions under which our problems have at least one or two positive solutions to obtain our results we apply the fixed point index

existence of positive periodic solutions of impulsive functional differential equations with two parameters in this paper we employ a well known fixed point index theorem to study the existence and non existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters several existence and non existence results are established

on the approximation of the boundary layers for the controllability problem of nonlinear singularly perturbed systems abstract a new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the boundary layers is proposed for example problems with feedback control such as the steady states of the thermostats where the controllers add or remove heat depending upon the temperature registered in another place of the heated bar can be interpreted with a second order ordinary differential equation subject to a nonlocal three point boundary condition the o accurate approximation of behavior of these nonlinear systems in terms of the exponentially small boundary layer functions is given at the end of this paper we formulate the unsolved controllability problem for nonlinear systems

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

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results