three fixed sign solutions of system model with sturm liouville type conditions abstract we consider the following system of differential equations u i m i t p i t u 1 t u 2 t u n t 0 t 0 1 1 i n together with sturm liouville boundary conditions u i j 0 0 0 j m i 3 u i m i 2 0 u i m i 1 0 0 u i m i 2 1 u i m i 1 1 0 1 i n where m i 2 for each 1 i n 0 0 0 0 and 0 by using two different fixed point theorems we offer criteria for the existence of three solutions of the system which are of fixed signs on the interval 0 1 examples are also included to illustrate the results obtained

positive solutions of difference equations with two point right focal boundary conditions abstract we consider the following boundary value problem formula formula where 1 p n 1 is fixed using a fixed point theorem for operators on a cone we develop criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are established for special cases we also include several examples to dwell upon the importance of the results obtained

multiple solutions for 2mth order sturm liouville boundary value problems growth conditions are imposed on f such that the following boundary value problem 1 my 2m f t y i 1y 2i 0 i 1y 2i 1 0 i 1y 2i 1 i 1y 2i 1 1 0 0 i m 1 has an arbitrary number of positive solutions

the three dimensional ising model revisited numerically several basic universal amplitude ratios are studied afresh for three dimensional nearest neighbor ising models in revising earlier work modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes c for the susceptibility 1 for the correlation length 1 a for the specific heat c t and b for the spontaneous magnetization m0 we find c c 4 95 0 15 1 1 1 960 0 01 a a 0 523 0 009 a c b 0 0581 0 0010 while a 1 3 verifies hyperuniversality to within 0 8 a method for calculating amplitude ratios which allows for corrections to scaling yields estimates for c c and 1 1 in excellent agreement with those derived from the individual amplitudes finally explicit formulae are given for the numerical evaluation of t 1 t c t and m0 t over the full temperature range from criticality to t 0 and corresponding plots and convenient near critical representations are also presented

on multiple fixed sign solutions of a discrete system with hermite boundary conditions abstract we consider the discrete system m u i k p i k u 1 k u 2 k u n k k 0 1 n 1 i n together with hermite boundary conditions j u i k 0 j 0 m 1 1 r 1 i n where r 2 m 1 for 1 r 1rm m and k s are integers such that 0 k1

multiple fixed sign solutions for a system of difference equations with sturm liouville conditions we consider the following system of difference equations d mu i k p i k u 1 k u 2 k u n k 0 k 0 1 n i 1 2 ntogether with sturm liouville boundary conditions d ju i 0 0 0 2 n m 1 z 0 w 0 h 0 d w z w n 1 z d h w 0 by using two different fixed point theorems we develop criteria for the existence of three solutions of the system which are of fixed signs on 0 1 n m examples are also included to illustrate the results obtained

analytic approach to the critical density in cellular automata for traffic flow the jamming transition in the stochastic traffic cellular automaton of nagel and schreckenberg j phys i 2 2221 1992 is examined we argue that most features of the transition found in the deterministic limit do not persist in the presence of noise and suggest instead to define the transition to take place at that critical density ensuremath rho c at which a large initial jam just fails to dissolve we show that ensuremath rho c v j v j v f where v f is the velocity of noninteracting vehicles and v j is the speed of the dissolution wave moving into the jam an approximate analytic calculation of v j in the framework of a simple renormalization scheme is presented which explicitly displays the effect of the interaction between vehicles during the acceleration stage of the nagel schreckenberg rules with maximum velocity v mathrm max g1 the analytic prediction is compared to numerical simulations we find a remarkable correspondence between the analytic expression for v j and a phase diagram obtained numerically by l ubeck et al phys rev e 57 1171 1998

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

existence of positive solutions of bvps for third order discrete nonlinear difference systems in this paper we consider the following boundary value problem of discrete email protected 3u 1 k f 1 k u 1 k u 2 k 0 email protected 0 t d 3u 2 k f 2 k u 1 k u 2 k 0 email protected 0 t with the dirichlet boundary conditionu 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 some new results of the existence nonexistence and multiplicity are obtained by using krasnosel skii s fixed point theorem in a cone in particular it is proved that the above boundary value problem has n positive solutions under suitable conditions where n is an arbitrary positive integer

amplitude ratios and β estimates from general dimension percolation moments low concentration series are generated for moments of the percolation cluster size distribution gamma j sj 1 s is the number of sites on a cluster for j 2 8 and general dimensionality d these diverge at pc as gamma j approximately aj pc p gamma j with gamma j gamma j gamma j 2 delta where delta gamma beta is the gap exponent the series yield new accurate values for delta and beta delta 2 23 or 0 05 2 10 or 0 04 2 03 or 0 05 and beta 0 44 or 0 15 0 66 or 0 09 0 83 or 0 08 at d 3 4 5 in addition ratios of the form ajak aman with j k m n are shown to be universal new values for some of these ratios are evaluated from the series from the epsilon expansion epsilon 6 d and exactly in d 1 and on the bethe lattice the results are in excellent agreement with each other for all dimensions results for different lattices at d 2 3 agree very well these amplitude ratios are much better behaved than other ratios considered in the past and should thus be more useful in characterising percolating systems

positive solutions of bvps for third order nonlinear difference systems abstract in this paper we consider the following discrete system boundary value problems 3 u 1 k f 1 k u 1 k u 2 k 0 k o t 3 u 2 k f 2 k u 1 k u 2 k 0 k o t with the dirichlet boundary condition u 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 some sufficient conditions are obtained for the existence of one or two positive solutions to the above system by using a nonlinear alternative of leray schauder type and krasnosel skii s fixed point theorem in a cone

stabilization of solutions of a degenerate nonlinear diffusion problem i 4 u f u in l l x r u tl t o in r u x 0 uo x in l l where m 1 is a parameter f is locally lipschitz continuous f 0 0 and u is bounded problems of this form arise in a number of areas of science for instance in models for gas or fluid flow in porous media 2 and for the spread of certain biological populations 13 161 this paper is divided into two parts in part i we consider what may be called the motivating example problem i which consists of problem i with the special choice f u u 1 u u a 1 for suitably restricted parameters a we begin by describing in detail the set l of nonnegative equilibrium solutions of problem i clearly 8 l contains the trivial solution u 0 for all l 0 write 8 l e l o in the description of z l there are two critical parameter values lo and l1 with 0 lo l1 j we show that i g l 4 for 0 l lo

upper and lower solution method for fourth order four point boundary value problems this paper is concerned with the fourth order ordinary differential equation u 4 t f t u t u t 0 0 some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique

triple positive solutions of conjugate boundary value problems ii we consider the following boundary value problems 1 n py n a t h y n 2 t 0 1 y i 0 0 0 i p 1 y i 1 0 0 i n p 1 and 1 n p ny f k y y n 1y n 2 0 k m iy 0 0 i p 1 iy m p 1 0 0 i n p 1 where 1 p n 1 is fixed by employing fixed point theorems for operators on a cone existence criteria are developed for multiple at least three positive solutions of the boundary value problems as an application we also establish the existence of radial solutions of certain partial difference equations several examples are included to dwell upon the importance of the results obtained

multiple positive solutions of singular second order m point boundary value problems abstract the existence of multiple positive solutions about the singular second order m point boundary value problem x h x f x 0 0 x 1 subject to some m point boundary value conditions is considered h x is allowed to be singular at x 0 and x 1

multiple positive solutions of bvps for third order discrete difference systems this paper is concerned with the following email protected 3u 1 k f 1 k u 1 k u 2 k 0 email protected 0 t d 3u 2 k f 2 k u 1 k u 2 k 0 email protected 0 t with the dirichlet boundary conditionu 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 by using leggett williams fixed point theorem sufficient conditions are obtained for the existence of three positive solutions to the above system

eigenvalues and eigenfunctions of discrete conjugate boundary value problems abstract we consider the following boundary value problem 1 n p n y f k y y n 1 y n 2 0 k m i y 0 0 0 i p 1 i y m n i 0 0 i n p 1 where 1 p n 1 is fixed and 0 a characterization of the values of is carried out so that the boundary value problem has a positive solution next for 1 criteria are developed for the existence of two positive solutions of the boundary value problem in addition for particular cases we also offer upper and lower bounds for these positive solutions several examples are included to dwell upon the importance of the results obtained

existence of positive solutions to second order time scale systems in this paper the author consider the following dynamic system on a measure chain u i d d t f i t u 1 s t u 2 s t u n s t 0 email protected a b satisfying sturm liouville boundary conditions a iu i a email protected iu i d a 0 c iu i s b email protected iu i d s b 0 i 1 2 n some new results are obtained for the existence of single twin and triple positive solutions of the above system by using nonlinear alternative of leray schauder type krasnosel skii s fixed point theorem in a cone and leggett williams fixed point theorem

existence of positive solutions of bvps for second order nonlinear difference systems this paper is concerned with the following system d 2u i k f i k u 1 k u 2 k u n k 0 k 0 t i 1 2 nwith the dirichlet boundary conditionu i 0 u i t 2 0 i 1 2 n some new results are obtained for the existence and multiplicity of positive solutions to the above system by using nonlinear alternative of leray schauder type krasnosel skii s fixed point theorem in a cone and leggett williams fixed point theorem in particular it proves that the above system has n positive solutions under suitable conditions where n is an arbitrary integer

numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures numerical methods for strongly oscillatory and singular functions are given in this paper beside a summary of standard methods and product integration rules we consider a class of complex integration methods several applications of quadrature processes in problems in telecom munications and physics are also presented 1998 elsevier science ltd all rights reserved integration oscillatory kernel singular kernel orthogonal polynomials product rules gaussian quaclratures error function bessel functions legendre functions

a novel method of calculating amplitude ratios by series expansions the author introduces a new method of calculating critical amplitude ratios using series which is both simple and powerful this method which gives estimates for the amplitude ratios that are neither biased by the values of the critical points nor by the critical exponents is applied to several models it is shown that this method produces results where no reliable estimates from series expansion exist in particular one finds 0 025 or 0 001 for at b2 for the 3d ising model and 220 or 10 for c c for the two dimensional percolation model in agreement with and with more accuracy than values obtained by other methods

critical temperatures of the d 3 s 1 2 ising model the effect of confluent corrections to scaling much attention has been paid to the d 3 s 1 2 ising model on the bcc lattice in recent years because the best high temperature series expansions were available for this lattice however in order to compare series estimates of critical exponents and temperatures with independent evaluations via the monte carlo method lattices of lower coordination number must be considered since monte carlo studies are usually made on these a study of extant susceptibility series on the fcc sc diamond and tetrahedron lattices is reported on and some comments are made on aspects of recent monte carlo analyses of the d 3 s 1 2 ising model on the sc and diamond lattices

general lidstone problems multiplicity and symmetry of solutions abstract for the 2mth order lidstone boundary value problem y 2 m t f y t y t y 2 i t y 2 m 1 t t 0 1 y 2 i 0 y 2 i 1 0 0 i m 1 where 1 mf r m 0 thinsp is continuous growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions this generalizes earlier papers which have applied avery s generalization of the leggett williams theorem to lidstone problems we then prove the analogous result for difference equations

a three point boundary value problem for nonlinear fourth order differential equations abstract in this paper the authors consider the nonlinear fourth order ordinary differential equation e u t g t f u 0 with the boundary conditions b u 0 u 1 u 0 u p u 1 0 some results on the existence and nonexistence of positive solutions to problem e b are obtained results on the existence of infinitely many positive solutions are also presented examples are included to demonstrate that the results are sharp

three symmetric solutions of lidstone boundary value problems for difference and partial difference equations we consider the boundary value problem 2my k m f y k 2y k 1 2iy k 1 2 m 1 y k m 1 k a 1 b 1 2iy a 1 m 2iy b 1 m 2i 0 0 i m 1 where m 1 and 1 m f rm 0 is continuous by using amann and leggett williams fixed point theorems we develop growth conditions on f so that the boundary value problem has triple positive symmetric solutions the results obtained are then applied in the investigation of radial solutions for certain partial difference equation subject to lidstone type conditions

triple solutions of focal boundary value problems on time scale we consider the following differential equation on a time scale t y d d t p t y s t 0 t a b t together with focal boundary conditions y a 0 y d s b 0 where a b e t and a s b by using two different fixed point theorems criteria are established for the existence of triple positive solutions of the boundary value problem we also include some examples to illustrate the results obtained