positive solutions to singular system with four point coupled boundary conditions abstract existence of positive solution to a nonlinear singular system with four point coupled boundary conditions of the type x t f t x t y t t 0 1 y t g t x t y t t 0 1 x 0 0 x 1 y y 0 0 y 1 x is established the nonlinearities f g 0 1 0 0 0 are continuous and singular at t 0 t 1 while the parameters satisfy 0 1 0 1 an example is included to show the applicability of our result

some more results on increments of the wiener process let w t for 0 leq t infty be a standard weiner process and suppose that c k and b k are fixed sequences of real numbers satisfying 0 leq c k b k infty let k omega be the set of limit points as t rightarrow infty of frac w b k omega w c k omega 2 b k c k lbrack log b k b k c k log log b k rbrack 1 2 where omega is a point in the probability space on which w t is defined we give necessary conditions on b k and c k to have k omega lbrack 1 1 rbrack a s we also give some related results and discuss sharpness

asymptotic analysis of gaussian integrals ii manifold of minimum points this paper derives the asymptotic expansions of a wide class of gaussian function space integrals under the assumption that the minimum points of the action form a nondegenerate manifold such integrals play an important role in recent physics this paper also proves limit theorems for related probability measures analogous to the classical law of large numbers and central limit theorem

positive solutions for 2p order and 2q order systems of singular boundary value problems with integral boundary conditions abstract in this paper we study the existence multiplicity and nonexistence of positive solutions for 2p order and 2q order systems of singular boundary value problems with integral boundary conditions the results are based upon the fixed point theorem of cone expansion and compression type due to krasnosel skill moreover it generalizes and includes some known results

non negative solutions for a class of non positone problems in the recent past many results have been established on non negative solutions to boundary value problems of the form where 0 f 0 0 positone problems in this paper we consider the impact on the non negative solutions when f 0 f u to be convex to guarantee uniqueness of positive solutions and f u to be appropriately concave for multiple positive solutions this is in contrast to the case of positone problems where the roles of convexity and concavity were interchanged to obtain similar results we further establish the existence of non negative solutions with interior zeros which did not exist in positone problems

multiplicity results for positive solutions of some semi positone three point boundary value problems in this paper some multiplicity results for positive solutions of some singular semi positone three point boundary value problem be obtained by using the fixed point index method

positive solutions of second order three point boundary value problems with change of sign we study the existence of positive solutions of the second order three point boundary value problems t a t f y t 0 0 t 1 y 0 0 y 1 y n where 0 1 0 1 we show the existence of at least one positive solution by applying the krasnoselskii fixed point theorem in a cone here a t is allowed to changes sign on 0 1 applications of our results are provided to yield positive radial solutions of some elliptic boundary value problems on an annulus

existence and uniqueness of positive radial solutions for the lane emden system in this article we consider component wise positive radial solutions of a weakly coupled system of elliptic equations in a ball with homogeneous nonlinearities the existence is well known in general we give a result for the remaining cases the uniqueness is less studied we complement the known results

three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second order ordinary differential equations abstract in this paper we consider the existence of at least three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second order ordinary differential equations the associated green s function for the boundary value problems is first given the proofs of our main results are based upon the leggett williams fixed point theorem finally we give an example to demonstrate our result

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

existence of positive solutions for second order semipositone differential equations on the half line in this paper by means of constructing a special cone we obtain a sufficient condition for the existence of positive solution for semipositone singular sturm liouville boundary value problem on the half line the results obtained generalize and improve the corresponding results of zhang and liu in papers x g zhang l s liu positive solutions of superlinear semipositone singular dirichlet boundary value problems j math anal appl 316 2006 525 537 y s liu existence and unboundedness of positive solutions for singular boundary value problems on half line appl math comput 144 2003 543 556

how big are the lag increments of a gaussian process abstract in this paper the limit theorems on lag increments of a wiener process due to chen kong and lin 1 are developed to the case of a gaussian process via estimating upper bounds of large deviation probabilities on suprema of the gaussian process

some results on increments of the wiener process with applications to lag sums of i i d random variables obtained for the wiener process but with n replacing t and sn replacing w t using the work of koml6s major and tusnady on the invariance principle we obtain the desired results for i i d sequences as immediate corollaries to our work for the wiener process 1 introduction the motivation for the work done here came from a specific statistical problem suppose xk is a sequence of random variables whose distribution functions approach in some appropriate sense a fixed distribution with mean it if the sequence is independent or is appropriately dependent then under mild regularity conditions sn n t almost surely there will usually be bias or non random error associated with the earlier xk s one might hope to reduce this bias by throwing away

answers to some questions about increments of a wiener process on obtient des resultats qui donnent une reponse affirmative aux questions posees par hanson et russo sans hypothese additionnelle 1983

positive solutions for singular m point boundary value problems with positive parameter in this paper some new existence results for positive solutions for a class of singular m point boundary value problems with parameter be obtained

positive solutions for singular boundary value problems of a coupled system of differential equations by using fixed point theorem of cone expansion and compression this paper investigates the existence of multiple positive solutions for singular boundary value problems of a coupled system of nonlinear ordinary differential equations