positive solutions for the boundary value problems of one dimensional p laplacian with delay this paper is concerned with the existence of positive solutions for the boundary value problem of one dimensional p laplacian with delay the proof is based on the guo krasnoselskii fixed point theorem in cones

bayesian and frequentist bartlett corrections for likelihood ratio and conditional likelihood ratio tests summary this paper characterizes priors under which the bayesian and frequentist bartlett corrections for the likelihood ratio and the conditional likelihood ratio clr statistics differ by o 1 it is seen that except for sample points with negligible probability the clr statistic has a posterior distribution for which a posterior bartlett correction exists this observation leads to an alternative proof of the existence of a frequentist bartlett correction for the clr statistic

frequentist validity of posterior quantiles in the presence of a nuisance parameter higher order asymptotics given a random sample from a distribution with density function that depends on an unknown parameter 1 2 we are concerned with frequentist validity up to o n 1 of posterior quantiles of 1 treating 2 as a nuisance parameter we propose to make the best choice of the prior on by matching as far as practicable the posterior and frequentist coverage probabilities up to o n 1

a singular boundary value problem for the one dimensionalp laplacian abstract the singular boundary value problem formula is studied in this paper whereg s s p 2s p 1 the singularity may appear atu 0 and att 0 ort 1 and the functionfmay be discontinuous the authors prove that for anyp 1 and for any positive nonincreasing functionfand nonnegative measurable functionkwith some integrability conditions the above mentioned problem has a unique solution also the properties of the solution are discussed in the paper

positive solutions for one dimensional p laplacian boundary value problems with dependence on the first order derivative abstract this paper presents sufficient conditions for the existence and multiplicity of positive solutions to the one dimensional p laplacian differential equation p u a t f u u 0 subject to some boundary conditions we show that it has at least one or two or three positive solutions under some assumptions by applying the fixed point theorem

multiple voting location and single voting location on trees abstract we examine voting location problems in which the goal is to place based on an election amongst the users a given number of facilities in a graph the user preference is modeled by shortest path distances in the graph a condorcet solution is a set of facilities to which there does not exist an alternative set preferred by a majority of the users recent works generalize the model to additive indifference and replaced user majority by proportion we show that for multiple voting location condorcet and simpson decision problems are 2 p complete and investigate the approximability of the simpson and the simpson score optimization problem further we contribute a result towards lower bounds on the complexity of the single voting location problem on the positive side we develop algorithms for the optimization problems on tree networks which are substantially faster than the existing algorithms for general graphs finally we suggest a generalization of the indifference notion to threshold functions

existence of positive solutions for singular boundary value problems involving the one dimensional p laplacian this paper studies the existence of positive solutions for singular dirichlet boundary value problems these results are obtained by using the global continuation theorem fixed point index theory and approximate method

on perturbed ellipsoidal and highest posterior density regions with approximate frequentist validity this paper considers in the multiparameter case perturbed ellipsoidal and highest posterior density regions with both bayesian and frequentist validity up to o n 1

twin solutions of boundary value problems for ordinary differential equations and finite difference equations a new twin fixed point theorem is applied first to obtain the existence of at least two positive solutions for the right focal boundary value problem y f ity 0 0 t 1 y 0 y 1 0 it is applied later to obtain the existence of at least two positive solutions for the analogous discrete right focal boundary value problem 2u k g u k 0 k 0 n u 0 u n 1 0

sharp conditions for the existence of sign changing solutions to equations involving the one dimensional p laplacian abstract we consider the boundary value problem involving the one dimensional p laplacian u p 2 u a x f u 0 0 x 1 u 0 u 1 0 where p 1 we establish sharp conditions for the existence of solutions with prescribed numbers of zeros in terms of the ratio f s s p 1 at infinity and zero our argument is based on the shooting method together with the qualitative theory for half linear differential equations

existence and iteration of monotone positive solutions for multipoint boundary value problem with p laplacian operator in the paper we obtain the existence of monotone positive solutions and establish acorresponding iterative scheme for the following multipoint boundary value problem with p laplacian operator f p u t q t f t u t 0 0

radial solutions for the p laplacian equation abstract we study the existence of positive solutions of the following nonlinear equation 1 a a p u u in 0 where p 1 0 p x x x p 2 and a satisfies some appropriate conditions our purpose is to give two existence results for the above equation subject to some boundary conditions where the nonlinear term is a nonnegative continuous function in 0 0 satisfying some adequate hypotheses

integer programming formulations for three sequential discrete competitive location problems with foresight abstract we deal with three competitive location problems based on the classical maximal covering location problem the environment of these problems consists of an open market with two firms leader and follower several customers and locations where facilities can be located in order to capture the demand of the customers the leader enters the market by locating a set of facilities knowing the potential locations where the follower can locate her facilities after the leader s decision we consider here three pairs of objective functions for the leader follower previously studied in the literature maximizing minimizing the demand captured by the leader minimizing maximizing the regret of the leader maximizing the demand captured by each firm also known as stackelberg for each model we propose an integer linear programming formulation with a polynomial number of variables and an exponential number of constraints the formulations are solved by branch and cut algorithms where the constraints are generated on demand by solving appropriate separation problems we report extensive computational experiments realized on instances inspired by those from the literature comparing our algorithms with the exact and heuristic algorithms previously published for these problems

the existence of positive solutions for some nonlinear equation systems abstract in this paper we consider the existence of positive solutions of the following boundary value problem 1 x a t f x y 0 2 y b t g x y 0 t 0 1 1 x 0 1 x 0 0 2 y 0 2 y 0 0 1 x 1 1 x 1 0 2 y 1 2 y 1 0 where 1 2 r r are the increasing homeomorphism and positive homomorphism and 1 0 0 2 0 0 we show the sufficient conditions for the existence of positive solutions by using the nome type cone expansion expression fixed point theorem

a branch and cut algorithm for the discrete r p centroid problem abstract the environment of the r p centroid problem is composed of two noncooperative firms a leader and a follower competing to serve the demand of customers from a given market the demand of each customer is totally served by a facility of the leader or follower according to a customer choice rule the goal of both the leader and the follower is to maximize its own market share the r p centroid problem consists of deciding where the leader should place p facilities knowing that the follower will react by placing r facilities the discrete version of the problem is a 2 p hard one where both the applicant facilities and the customers are nodes on a graph in spite of it we present an integer programming formulation with polynomially many variables and exponentially many constraints moreover we report several experiments with different number of customers and applicant facilities and different values of p and r our results show that our method requires less computational time than the two exact algorithms found in the literature being able to optimally solve 29 previously open instances with up to 100 customers 100 applicant facilities and p r 15

triple positive solutions of a boundary value problem for nonlinear singular second order differential equations of mixed type with p laplacian in this paper we establish the existence of triple positive solutions of a two point boundary value problem for the nonlinear singular second order differential equations of mixed type with a p laplacian operator we also demonstrate that the results obtained can be applied to study certain higher order mixed boundary value problems finally an example is given to demonstrate the use of the main results of this paper

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

positive solutions for a fourth order p laplacian boundary value problem abstract in this paper we study the existence multiplicity and uniqueness of positive solutions for the fourth order p laplacian boundary value problem u p 1 u f t u u 2 i 0 u 2 i 1 0 i 0 1 here p 0 and f c 0 1 r r r 0 based on a priori estimates achieved by utilizing properties of concave functions we use fixed point index theory to establish our main results

bayesian interval estimates which are also confidence intervals let y 1 y n denote independent observations each distributed according to a distribution depending on a scalar parameter suppose that we are interested in constructing an interval estimate for one approach is to use bayesian inference for a given prior density we can construct an interval such that the posterior probability that lies in the interval is some specified value in this paper a method is given for constructing a bayesian interval estimate such that the coverage probability or the interval is approximately equal to the posterior probability or the interval

on the relationship between bayesian and non bayesian interval estimates summary let y1 y denote independent observations each distributed according to a density depending on a scalar parameter 0 suppose that we are interested in constructing an interval estimate for 0 one approach is to construct a confidence region with a specified coverage probability based on the likelihood ratio test statistic another approach is to construct a highest posterior density region with a specified posterior probability the goal of this paper is to study the relationship between these two approaches in particular we derive asymptotic expansions for the posterior probability of confidence regions based on the likelihood ratio test statistic and for the coverage probability of highest posterior density regions conditions under which the two methods lead to identical regions at least approximately are also given

bayesian and frequentist confidence intervals arising from empirical type likelihoods summary for a general class of empirical type likelihoods for the population mean higher order asymp totics are developed with a view to characterizing its members which allow for any given prior the existence of a confidence interval that has approximately correct posterior as well as fre quentist coverage in particular it is seen that the usual empirical likelihood always allows such a confidence interval while many of its variants proposed in the literature do not enjoy this property an explicit form of the confidence interval is also given

on the level error after bartlett adjustment of the likelihood ratio statistic summary it is well known that bartlett adjustment reduces level error of the likelihood ratio statistic from order n l to order n3 2 in the present note we show that level error of the adjusted statistic is actually order n2

successive iteration and positive symmetric solution for a sturm liouville like four point boundary value problem with a p laplacian operator abstract in this paper we consider the following sturm liouville like four point p laplacian boundary value problem with the nonlinear term f depending on the first order derivative p u t q t f t u t u t 0 0 t 1 subject to the boundary conditions u 0 u 0 u 1 u 0 by using a monotone iterative technique the existence of symmetric positive solutions and corresponding iterative schemes are obtained

multiplicity results for the 1 dimensional generalized p laplacian abstract using energy relations we prove the existence and multiplicity of solutions of the boundary value problem formula

noninformative priors for one parameter of many summary we consider the problem of constructing a prior that is noninformative for a single parameter in the presence of nuisance parameters our approach is to require that the resulting marginal posterior intervals have accurate frequentist coverage stein 1985 derived nonrigorously a sufficient condition for such a prior through the use of orthogonal parameters we give a general form for the class of priors satisfying stein s condition the priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters this is in contrast to jeffreys 1946 invariant prior for the overall parameter which is proportional to the square root of the determinant of the information matrix several examples are given and comparisons are made to the reference priors of bernardo 1979

relaxation of the condorcet and simpson conditions in voting location abstract a condorcet point in voting location is a location point such that there is no other closer to more than half of the users however such condorcet solution does not necessarily exist this concept is based on two assumptions first two locations are indifferent only if they are at the same distance of the voter second the number of voters needed to reject a location is more than half of them we relax the condorcet condition in two ways first by considering that two locations are indifferent for every user if the difference of the distances to them is within a positive threshold secondly by considering that the proportion of users needed to reject a location is not one half we consider the resulting new solution concepts that arise by applying both relaxations at the same time and develop algorithms for obtaining them in the finite case

successive iteration and positive symmetric solutions for some sturm liouville like four point p laplacian boundary value problems this paper deals with the existence of positive solutions for some sturm liouville like four point p laplacian boundary value problems our approach is based on the fixed point theorem and the monotone iterative technique without the assumption of the existence of lower and upper solution we obtain not only the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

existence and iteration of positive solutions for some p laplacian boundary value problems abstract this paper deals with the existence and iteration of positive solutions for the following p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to one of the following boundary conditions p u 0 p u 0 0 p u 1 p u 1 0 or u 0 g 1 u 0 0 u 1 g 2 u 1 0 the main tool is the monotone iterative technique we obtain not only the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

on bartlett adjustments for approximate bayesian inference summary in wide generality the posterior distributions of the likelihood ratio statistic and the posterior ratio statistic are chi squared to error of order o n where n is sample size the error in the chi squared approximation can be reduced to order o n 2 by bartlett correction in this paper explicit formulae are derived for the bartlett adjustment factors of both statistics and the derivations are based on the tierney kass kadane 1989 asymptotic approximation for marginal posterior probability density functions the use of numerical differentiation to facilitate calculation of the bartlett adjustments is also described some applications are considered that concern inference about regression models from both complete and right censored data

positive solutions for a system of second order quasilinear boundary value problems abstract in this paper we study the existence and multiplicity of positive solutions for the system of second order quasilinear boundary value problems u p 1 f t u v v q 1 g t u v u 0 u 1 0 v 0 v 1 0 where p q 1 and f g c 0 1 r 2 r r 0 based on a priori estimates achieved by utilizing jensen s inequality for nonnegative concave functions and homogeneous operators we use fixed point index theory to establish the main results

r p centroid problems on paths and trees an instance of the r p centroid problem is given by an edge and node weighted graph two competitors the leader and the follower are allowed to place p and r facilities respectively into the graph users at the nodes connect to the closest facility a solution of the r p centroid problem is a leader placement such that the maximum total weight of the users connecting to any follower placement is as small as possible we show that the absolute r p centroid problem is np hard even on a path which answers a long standing open question of the complexity of the problem on trees hakimi 1990 10 moreover we provide polynomial time algorithms for the discrete r p centroid on paths and the 1 p centroid on trees and complementary hardness results for more complex graph classes

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

a decomposition for the likelihood ratio statistic and the bartlett correction a bayesian argument let l n 1 log p x be the log likelihood of an n dimensional x under a p dimensional let j be the mle under h j 1 1 0 j j 0 and 0 be the unrestricted mle define t j as 2n l j 1 1 2 sgn j j 1 j 0 let t t 1 t p then under regularity conditions the following theorem is proved under 0 t is asymptotically n n 1 2 a 0 n 1 a j n 1 o n 3 2 where j is the identity matrix the result is proved by first establishing an analogous result when is random and then making the prior converge to a degenerate distribution the existence of the bartlett correction to order n 3 2 follows from the theorem we show that an edgeworth expansion with error o n 2 for t involves only polynomials of degree less than or equal to 3 and hence verify rigorously lawley s 1956 result giving the order of the error in the bartlett correction as o n 2

positive solutions of higher order four point boundary value problem with p laplacian operator in this paper we consider the existence of positive solutions of the higher order four point singular boundary value problem and show the sufficient conditions for the existence of positive solutions by using the fixed point theorem due to bai and ge some new existence results are obtained

twin positive solutions for the one dimensional p laplacian boundary value problems abstract in this paper we study the existence of multiple positive solutions for the equation g u e t f u 0 where g v v p 2 v p 1 subject to nonlinear boundary conditions we show the existence of at least two positive solutions by using a new three functionals fixed point theorem in cones

double positive solutions for a nonlinear four point boundary value problem with a p laplacian operator in this paper we study the existence of positive solutions for a nonlinear four point boundary value problem with a p laplacian operator by using a three functionals fixed point theorem in a cone the existence of double positive solutions for the nonlinear four point boundary value problem with ap laplacian operator is obtained this is different than previous results

bifurcation of sign changing solutions for one dimensional p laplacian with a strong singular weight p sublinear at abstract in this paper we consider one dimensional p laplacian problems with a singular weight which may not be in l 1 using the properties of eigenfunctions and the global bifurcation theory we prove existence uniqueness nonexistence and multiplicity results of positive solutions as well as sign changing solutions specially when the nonlinear term is p linear near 0 and p sublinear at

multiple positive solutions of nonlinear two point boundary value problems we improve the results obtained by erbe hu and wang in a recent paper we show that there exist at least two positive solutions of two point boundary value problems under conditions weaker than those used by erbe hu and wang

positive solutions for a system of p laplacian boundary value problems this paper is concerned with the existence and multiplicity of positive solutions for the system of p laplacian boundary value problems u i p i 1 f i t u 1 u n u i 0 u i 1 0 i 1 n where n 2 p i 1 f email protected c 0 1 xr n r i 1 n r 0 based on a priori estimates achieved by utilizing the jensen integral inequalities and r n monotone matrices we use fixed point index theory to establish the existence and multiplicity of positive solutions for the above problem

a fundamentally simple approach to a singular boundary value problem abstract existence results by means of a simple approach for the 3rd order differential equation x t t f t x t x t x t 0 t 1 satisfying the three point boundary value conditions x 0 x x 1 0 are given where 0 1 is a fixed point in contrast to the usual case 1 2 1 f t x y z 0 for any t 0 1 x 0 y z r and the map t is positive on 0 1 and suitable singular at the end points furthermore the obtained solution x t is positive and concave on 0 1 in addition without any monotonicity assumption on the nonlinearity we prove the existence of a sequence of such solutions with lim n x n 0 our principal tools are very simple applications on the plane of the well known from combinatorial topology sperner s lemma in comparison with other classical approaches like fixed point or degree theorems

positive solution of three point boundary value problem for the one dimensional p laplacian with singularities abstract in the paper we deal with positive solutions of the following nonlinear three point singular boundary value problem with a p laplacian operator p u q t f t u 0 0 t 1 subject to u 0 g u 0 0 u 1 u 0 or u 0 u 0 u 1 g u 1 0 where f t u may be singular at u 0 and q t may be singular at t 0 1 new existence principles are established