positive solutions for a class of multiparameter ordinary elliptic systems abstract using a fixed point theorem due to m a krasnosel skii the upper lower solutions method and fixed point index theory we study existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations we give a new notion of superlinearity for nonlinearities observe that the nonlinearities may even be in some sense singular as an application we show multiplicity results for a class of semilinear elliptic systems in both bounded annular domains and exterior domains in addition we apply our results to fourth order boundary value problems

on periodic boundary conditions and ergodicity in computational homogenization of heterogeneous materials with random microstructure abstract due to high computational costs associated with stochastic computational homogenization a highly complex random material microstructure is often replaced by simplified parametric ergodic and sometimes periodic models this replacement is often criticized in the literature due to unclear error resulting from the periodicity and ergodicity assumptions in the current contribution we perform a validation of both assumptions through various numerical examples to this end we compare large scale non simplified and non ergodic models with simplified ergodic and periodic solutions in addition we analyze the hill mandel condition for stochastic homogenization problems and demonstrate that for a stochastic problem there are more than three classical types of boundary conditions as an example we propose two novel stochastic periodic boundary conditions which possess a clear physical meaning the effect of these novel periodic boundary conditions is also analyzed by comparing with non ergodic simulation results

existence of positive solutions for 2m order nonlinear differential systems abstract the existence of positive solutions for dirichlet boundary value problem of some nonlinear differential systems is discussed

fast frequency response computation for rayleigh damping we present a model reduction lanczos method for the computation of frequency response functions of rayleigh damping problems the connection with modal extraction and modal superposition is made the usual model reduction methods require complex arithmetic with the proposed method complex arithmetic is only used for the reduced problem a numerical example from structural damping is given copyright 2007 john wiley sons ltd

local superlinearity for elliptic systems involving parameters abstract we study the existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations using the fixed point theorem of cone expansion compression type the upper lower solutions method and degree arguments we apply our abstract results to study semilinear elliptic systems in bounded annular domains with non homogeneous boundary conditions here the nonlinearities satisfy local superlinear assumptions

multiple positive solutions of singularly perturbed differential systems with different orders in this paper we consider the multiplicity of positive solutions for a class of singular higher order perturbed differential systems with different orders by employing a well known fixed point theorem some new existence results are given under the case where nonlinearity can be sign changing

positive solutions for a second order differential system this paper investigates the existence of positive solutions for a second order differential system by using the fixed point theorem of cone expansion and compression

superlinear systems of second order ode s abstract we discuss the existence of positive solutions of the system u f t u v u v in 0 1 v g t u v u v in 0 1 u 0 u 1 v 0 v 1 0 where the nonlinearities f and g satisfy a superlinearity condition at both 0 and our main result is the proof of a priori bounds for the eventual solutions as an application we consider the dirichlet problem in an annulus for systems of semilinear elliptic equations with nonlinearities depending on the gradient as well as a second application we consider fourth order elastic beam equations with dependence also on the derivatives u u u

existence and multiplicity of positive solutions for multi parameter three point differential equations system abstract in this paper we study the existence and multiplicity of positive solutions for the differential equations system x a 1 t f 1 x t y t 0 0 t 1 y a 2 t f 2 x t y t 0 0 t 1 x 0 0 x 1 1 x 1 y 0 0 y 1 2 y 2 where 0 are parameters 0 2 1 1 1 2 0 1 a 1 c 0 1 0 and f 2 c 0 0 0 the system is a semi positone problem since the nonlinear term f 1 is allowed to take negative values and a 2 t may change sign on 0 1 the results are established via fixed point index theory

positive solution of singular dirichlet boundary value problems for second order differential equation system this paper investigates the existence of positive solutions of singular dirichlet boundary value problems for second order differential system a necessary and sufficient condition for the existence of c 0 1 c 0 1 positive solutions as well as c1 0 1 c1 0 1 positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems our nonlinearity fi t x1 x2 may be singular at x1 0 x2 0 t 0 and or t 1 i 1 2

necessary and sufficient condition for the existence of positive solutions of a coupled system for elastic beam equations in this work by using fixed point theorem and monotone iterative technique the author establishes a necessary and sufficient condition of the existence of positive solutions for a class of nonlinear singular elastic beam differential system under reasonable conditions moreover some uniqueness results of positive solution and the estimate of convergent rate of the iterative sequence of solution are obtained

positive periodic solutions of higher dimensional functional difference equations with a parameter by using krasnoselskii s fixed point theorem and upper and lower solutions method we find some sets of positive values determining that there exist positive t periodic solutions to the higher dimensional functional difference equations of the form x n 1 a n x n h n fxn n n z where a n diag a1 n a2 n am n h n diag h1 n h2 n hm n aj hj z r z z are t periodic j 1 2 m t 1 0 x z rm f r m r m where r m x1 xm t rm xj 0 j 1 2 m r x r x 0

positive solutions of two point boundary value problems for systems of nonlinear second order singular and impulsive differential equations abstract this paper is devoted to the study of multiple and single positive solutions of two point boundary value problems for nonlinear second order singular and impulsive differential systems by constructing a cone k 1 k 2 which is the cartesian product of two cones in the space c 0 1 and computing the fixed point index in the k 1 k 2 we establish the conditions for the existence of at least one or at least two positive solutions to two point boundary value problems for systems of nonlinear second order singular and impulsive differential equations

positive solutions of systems of singular hammerstein integral equations with applications to semilinear elliptic equations in annuli abstract the existence of multiple positive solutions of systems of singular hammerstein integral equations is studied where the nonlinearities involved are allowed to have singularities in their second variables and satisfy weaker conditions involving the first eigenvalues of the corresponding linear hammerstein integral operators such systems contain some mathematical models arising in science and engineering applications are given to the existence of multiple positive radial solutions of systems of semilinear singular elliptic equations in annuli on which to the best of our knowledge there has been little study

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system abstract in this paper the existence of positive doubly periodic solutions for nonlinear telegraph system is discussed using the method of upper and lower solutions

positive solutions for 2p order and 2q order nonlinear ordinary differential systems abstract in this paper by using krasnosel skii fixed point theorem and under suitable conditions we present the existence of single and multiple positive solutions to the following systems 1 p u 2 p a t f u t v t t 0 1 1 q v 2 q b t g u t v t t 0 1 u 2 i 0 u 2 i 1 0 0 i p 1 v 2 j 0 v 2 j 1 0 0 j q 1 where 0 0 p q n we derive two explicit intervals of and such that for any and in the two intervals respectively the existence of at least one solution to the systems is guaranteed and the existence of at least two solutions for and in appropriate intervals is also discussed

positive solutions of second order two delay differential systems with twin parameter abstract the paper is concerned with the existence of positive solutions for a second order two delay differential systems with twin parameter firstly we present some sufficient conditions with the twin parameter belonging to an open rectangular region eigenvalue region to ensure the existence of positive solutions for the differential systems with singularity secondly we deal with the superlinear semipositone problem of the differential systems and establish the existence of positive solutions for the systems the proofs are based on a fixed point theorem in cones

existence of positive solutions for a second order ordinary differential system abstract in this paper we consider the existence of positive solutions for a second order ordinary differential system where the nonlinear term is superlinear in one equation and sublinear in the other equation by constructing a cone k 1 k 2 which is the cartesian product of two cones in space c 0 1 and computing the fixed point index in k 1 k 2 we establish the existence of positive solutions for the system we remark that differently from the literature we deal with our problem on the cartesian product of two cones in which the feature of two equations can be exploited better

positive solutions of singular sub linear boundary value problems for fourth order and second order differential equation systems abstract this paper investigates the existence of positive solutions of singular sub linear boundary value problems for fourth order and second order differential equation systems first of all we establish some important lemmas then we define a partial ordering in c 2 a b c 4 a b c a b c 2 a b and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c 2 0 1 c 0 1 positive solutions as well as c 3 0 1 c 1 0 1 positive solutions our nonlinearity f t x 1 x 2 x 3 g t x 1 x 2 may be singular at x 1 0 x 2 0 x 3 0 t 0 and or t 1

positive solutions and eigenvalue regions of two delay singular systems with a twin parameter abstract the paper is concerned with a two delay singular differential system with a twin parameter applying fixed point index theory we show the relationship between the asymptotic behaviors of nonlinearities at zero and infinity and the open regions eigenvalue regions of parameters which are correlated with delays such that the system has zero one and two positive solution s

necessary and sufficient condition for the existence of positive solutions of a coupled system for reaction diffusion equations abstract in this article by using fixed point theorem and monotone iterative technique the author presents necessary and sufficient conditions of the existence of positive solutions for a class of nonlinear singular reaction diffusion system of differential equations under reasonable conditions moreover some uniqueness results of positive solution and estimate of convergent rate of iterative sequence of solution are obtained

positive periodic solutions of nonlinear functional difference equations depending on a parameter in this paper we use the upper and lower solutions method to show that there existsa l such that the nonlinear functional difference equation of the form g n 1 a n g n lh n g n t n n e z has at least one positive t periodic solutions for l e 0 l and does not have any positive t periodic solutions for l l where a n h n and t n are t periodic functions

positive periodic solutions of infinite delay functional differential equations depending on a parameter in this paper we employ the upper and lower solutions method to study the existence of positive periodic solutions to a system of infinite delay equations with a email protected t a t x t email protected t x t

positive periodic solutions of a class of functional differential systems with feedback controls abstract in this paper by using the upper and lower solutions method we investigate the existence and nonexistence of positive periodic solutions of infinite delay functional differential system with a parameter and feedback controls x t a t x t f t x t x g t x t u t x t u t b t u t e t x t x h t x t

a multiplicity result for generalized laplacian systems with multiparameters abstract in this paper we consider the existence nonexistence and multiplicity of a positive solution for a gelfand type generalized laplacian system with a singular indefinite weight and a vector parameter by using the upper and lower solution method and fixed point index theory we obtain a global multiplicity result with respect to the parameter