existence of solutions to k n k 2 boundary value problems we provide very general existence criteria to solutions for a class of higher order boundary value problems our results supplement as well as improve several recent results established in the literature

on eigenvalue intervals and twin eigenfunctions of higher order boundary value problems abstract in this paper we shall consider the boundary value problem y n q t y y 1 y n 2 p t y y 1 y n 2 n 2 t 1 1 y i 0 0 0 i n 3 y n 2 0 y n 1 0 0 yy n 2 1 y n 1 1 0 where 0 and are constants satisfying 0 0 0 and 0 intervals of are determined to ensure the existence of a positive solution of the boundary value problem for 1 we shall also offer criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are obtained for special cases several examples are included to dwell upon the importance of the results obtained

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

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

bayesian inference for causal effects in randomized experiments with noncompliance for most of this century randomization has been a cornerstone of scientific experimentation especially when dealing with humans as experimental units in practice however noncompliance is relatively common with human subjects complicating traditional theories of inference that require adherence to the random treatment assignment in this paper we present bayesian inferential methods for causal estimands in the presence of noncompliance when the binary treatment assignment is random and hence ignorable but the binary treatment received is not ignorable we assume that both the treatment assigned and the treatment received are observed we describe posterior estimation using em and data augmentation algorithms also we investigate the role of two assumptions often made in econometric instrumental variables analyses the exclusion restriction and the monotonicity assumption without which the likelihood functions generally have substantial regions of maxima we apply our procedures to real and artificial data thereby demonstrating the technology and showing that our new methods can yield valid inferences that differ in practically important ways from those based on previous methods for analysis in the presence of noncompliance including intention to treat analyses and analyses based on econometric instrumental variables techniques finally we perform a simulation to investigate the operating characteristics of the competing procedures in a simple setting which indicates relatively dramatic improvements in frequency operating characteristics attainable using our bayesian procedures

identities on units of algebraic algebras let a be an algebraic algebra over an infinite field k and let u a be its group of units we prove a stronger version of hartley s conjecture for a namely if a laurent polynomial identity lpi for short f 0 is satisfied in u a then a satisfies a polynomial identity pi we also show that if a is non commutative then a is a pi ring provided f 0 is satisfied by the non central units of a in particular a is locally finite and thus the kurosh problem has a positive answer for k algebras whose unit group is lpi moreover f 0 holds in u a if and only if the same identity is satisfied in a the last fact remains true for generalized laurent polynomial identities provided that a is locally finite

eigenvalues of a general class of boundary value problem with derivative dependent nonlinearity we consider a general class of boundary value problem bvp comprising the differential equation y m t f t y t y t y t y q t t 0 1 where 1 q m 1 and 0 together with multi point boundary conditions y 0 y 0 y 0 y q 1 0 0 a i y q t j y q 1 t j y m 1 t j 0 j r 0 1 i m q where 0 t 0 t 1 t r 1 particular cases of this general bvp include the well known abel gontscharoff focal m p sturm liouville and complementary lidstone bvps it is noted that bvps with derivative dependent nonlinear terms are less investigated in the literature due to technical difficulty in this paper a new technique is developed to characterize the eigenvalues so that the bvp has a positive solution explicit eigenvalue intervals are also established we include several well known examples in the literature to illustrate the results obtained

double positive solutions of n p boundary value problems for higher order difference equations abstract we shall provide existence criteria for double positive solutions of the n p boundary value problem n y f k y y n 2 y g k y y n 1 y n 1 k n i y 0 0 0 i n 2 p y n n p 0 where n 2 and 0 p n 1 is fixed upper and lower bounds for the two positive solutions are also established for a particular boundary value problem when n 2 several examples are included to dwell upon the importance of the results obtained

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

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

singular nonlinear boundary value problems for second order ordinary differential equations abstract the boundary value problem y f x y 0 y 0 y 0 0 y 1 y 1 0 is studied under conditions which are modeled on the problem y a x y p 0y 0 y 1 0 or y 0 y 1 0 which occurs in a number of applications the technical arguments involve properties of solutions i e concavity and the use of iterative techniques a new fixed point theorem for cones for decreasing mappings is proved and used it is of interest in its own right since most such theorems are for monotone increasing mappings

free products of units in algebras i quaternion algebras abstract letabe a quaternion algebra over a commutative unital ring we find sufficient conditions for pairs of units ofato generate a free group using the well known isomorphism betweenso 3 r and the group of real quaternions of norm 1 we obtain free groups of rotations of the euclidean 3 space specialization techniques allow us to find similar free subgroups in skew polynomial rings a consequence is the following letkgbe the group algebra of a residually torsion free nilpotent groupgover a fieldkwhose characteristic is not 2 ifxandyare any pair of noncommuting elements ofg andc d k then 1 cxand 1 dygenerate a free subgroup of the malcev neumann field of fractions ofkg

on eigenvalue intervals of higher order boundary value problems with a sign changing nonlinear term in the paper we shall consider the boundary value problem u n la t f t u u u u 3 u n 2 0 n 2 t 0 1 u i 0 0 0 i n 3 au n 2 0 bu n 1 0 0 cu n 2 1 du n 1 1 0 where l 0 a b c and d are constants satisfying a c 0 and b d 0 intervals of l are determined to ensure the existence of a positive solution of the boundary value problem according to the signs of a t and f

bounds for positive solutions for a focal boundary value problem we will be concerned with the focal boundary value problem 1 n n p t ny t n f h t y t n 1y t iy 0 n iy b 1 0 0 i n 1 using cone theory in a banach space we show that under certain assumptions on f this focal boundary value problem has two positive solutions in the special case 2y t 1 h2 y t y t y 0 b 1 0 where 0 1 we are able to exhibit upper and lower bounds for these two positive solutions

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

positive solutions and nonlinear eigenvalue problems for third order difference equations first solutions that lie in a cone intersected with an annular type region are obtained for the third order difference equation 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 in the cases that f is either superlinear or sublinear the second part is devoted to determining values of for which there exist positive solutions of 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 when both limx 0 f x x and limx f x x exist as positive real numbers

on subnormal subgroups of skew fields abstract if d is a skew field with infinite center z and d z then any subnormal subgroup of d which satisfies a laurent generalized polynomial identity is central