multiple positive solutions for a functional second order boundary value problem by using the krasnoselskii fixed point theorem on cones in banach spaces some existence results of positive solutions of a boundary value problem concerning a second order functional differential equation are given

positive solutions of boundary value problems for third order functional difference equations the existence of positive solutions are established for the third order functional difference equation 3u n a n f n u w n 0 0 n t satisfying u n n n1 n 1 and u n n t 3 n n2 with 0 1 t 3 0 the results in this paper generalize and substantially improve recent work by agarwal and henderson on boundary value problems related to third order difference equations

existence of positive solutions for second order functional differential equations we afford a existence criterion of positive solutions of a boundary value problem concerning a second order functional differential equation by using the krasnoselskii fixed point theorem on cones in banach spaces moreover we also apply our results to establish several existence theorems of multiple positive solutions for some functional differential equations

existence of positive solutions for higher order functional differential equations abstract under suitable conditions on f t y t the boundary value problem of higher order functional differential equation fde of the form bvp fde y n t f t y t 0 t 0 1 a bc y i 0 0 0 i n 3 y n 2 t y n 1 t t t 0 y n 2 t y n 1 t t t 1 1 a has at least one positive solution where a is a fixed constant moreover we also apply this main result to establish several existence theorems which guarantee bvp has multiple positive solutions

positive solutions of nonlinear functional difference equations abstract in this paper we apply a cone theoretic fixed point theorem and obtain sufficient conditions for the existence of positive solutions to some boundary value problems for a class of functional difference equations we consider analogues of sublinear or superlinear growth in the nonlinear terms

positive solutions to a multi point boundary value problem with delay abstract the paper is concerned with the existence of positive solutions for the nonlinear multi point boundary value problems of a class of second order delay differential equations our results improve some recent results obtained in d q jiang multiple positive solutions for boundary value problems of second order delay differential equations appl math lett 15 2002 575 583 dingyong bai yuantong xu existence of positive solutions for boundary value problems of second order delay differential equations appl math lett 18 2005 621 630

positive solutions for boundary value problems of functional differential equations abstract we study the existence of positive solutions of the second order boundary values problems of functional differential equations x t f t x t 0 0 t t x 0 x t a where f 0 t c r r is a continuous function c r c r 0 and a r the proof of our main result is based upon the fixed point theorem in cones

theory and multipliers of stable algebras the main theorem is that if a is a c algebra with a countable approximate identity consisting of projections then the unitary group of m a k is contractible this gives a realization via the index map of ko a as components in the set of fredholm operators on ha for a c algebra a let ha ai i ai e a and eai ai converges in norm then ha becomes a right a module under the action ai b aib with the a valued inner product ai b1 ea bi ha is a hilbert a module y ha is the c algebra of operators on ha that have an adjoint k ha is an ideal of y ha called the compact operators on ha set 11 2 definition 4 operators in ha invertible modulo 3f ha are called fredholm and have an index that takes its values in ko a the paper is divided into two parts in part 1 we show that index a ko a is an isomorphism where t denotes the set of path components of the set of fredholm operators in part 2 we show that the unitary group of m a k is contractible when a has a countable approximate identity consisting of projections as 2 ha m a k this in particular implies that the unitary group of s ha is connected when a is unital this latter result is used to prove the isomorphism mentioned above the results of this paper were announced in 14 see remark 2 5 2 this research is based on the author s doctoral work done at dalhousie university under the supervision of professor p a fillmore the author also wishes to thank w j phillips for many useful suggestions part 1 the index of a fredholm operator 1 1 we describe the index map from fredholm operators on hilbert c modules to the corresponding k groups the principal ingredients of this construction have been discussed by several authors kasparov 12 miscenko and fomenko 15 and pimsner popa and voiculescu 17 however as we shall need refinements and variations of these constructions we will give a detailed account of the index map throughout this paper k or y h will denote the c algebra of compact operators on a separable infinite dimensional hilbert space h for any two c algebras a and b a b will denote the completion of the algebraic tensor product aob in the spatial or minimal c norm see e g effros and lance 8 2 received by the editors july 28 1983 and in revised form december 27 1985 1980 mathematics subject classification 1985 revision primary 46l05 46m20 01987 american mathematical society 0002 9947 87 1 00 25 per page

existence of solutions of boundary value problems for second order functional differential equations abstract in this paper we deal with the boundary value problem x f t x x t x x t x 0 x 0 c 1 c 2 c 1 c 2 r x j 0 x 1 x j 0 where f car j r c r r c r c r j 0 1 1 a j a 0 1 a j and a 0 1 are two special sets of functionals and x j is the restriction of x to j we find sufficient conditions for the existence of solutions of the above problem the proof is based on the leray schauder degree theory

existence of positive solutions for boundary value problem of second order fde abstract we use a fixed point theorem in cones to investigate the existence of positive solutions for boundary value problem of a second order functional differential equation fde with the form y t r t y t 0 0 y t y t t r t 0 y t y t n t 1 t 1 a where y t y t for a we allow that r t has the singularity at the endpoints t 0 and t 1 of 0 1 our results include the situations that f is either superlinear or sublinear

nonlinear boundary value problems in hilbert spaces abstract in this paper we examine nonlinear two point boundary value problems with sturm liouville type boundary conditions in a hilbert space our technique involves using the topological transversality theorem of a granas which relies on the notions of an essential map and a priori bounds on solutions we obtain existence results for a wide class of problems with our nonlinear term satisfying a bernstein nagumo growth condition

eigenvalue criteria for existence of multiple positive solutions to boundary value problems of second order delay differential equations abstract criteria are established for existence of multiple positive solutions to the boundary value problems expressed by second order delay differential equations of the form p t y t q t y t f t y t y t a t 0 1 y t y t t t 0 y t y t t t 1 1 a where 0 a 1 4 are suitably small p c 1 0 1 p 0 q c 0 1 and q 0

triple positive solutions for a class of boundary value problem of second order functional differential equations abstract we obtain sufficient conditions for the existence of at least three positive solutions for the functional differential equation x t q t f t x t x t 1 0 subject to some boundary conditions this is an application of a new fixed point theorem introduced by avery and peterson ann differential equations 8 1992 261 268

on positive solutions for second order boundary value problems of functional differential equations in this paper by using krasnoselskii fixed point theorem we obtain sufficient conditions for the existence of at least one or two positive solutions of a second order boundary value problem for a class of nonlinear functional differential equations examples are also included to illustrate our results

bouquet algebra of toric ideals abstract to any toric ideal i a encoded by an integer matrix a we associate a matroid structure called the bouquet graph of a and introduce another toric ideal called the bouquet ideal of a we show how these objects capture the essential combinatorial and algebraic information about i a passing from the toric ideal to its bouquet ideal via the graph theoretic properties of the bouquet graph allows us to classify several cases for example on the one end of the spectrum there are ideals that we call stable for which bouquets capture the complexity of various generating sets as well as the minimal free resolution on the other end of the spectrum lie toric ideals whose various bases e g minimal generating sets grobner graver bases coincide apart from allowing for classification type results bouquets provide a new way to construct families of examples of toric ideals with various interesting properties such as robustness genericity and unimodularity the new bouquet framework can be used to provide a characterization of toric ideals whose graver basis the universal grobner basis any reduced grobner basis and any minimal generating set coincide

triple positive solutions for a class of boundary value problems for second order neutral functional differential equations abstract we obtain sufficient conditions for the existence of at least three positive solutions for the second order neutral functional differential equation x t q t f t x t x t x t x t 0 0 t 1 0 subject to one of the following two pairs of boundary conditions x t t t 0 x 1 0 x t t t 0 x 1 0 and generalize and correct some conditions of theorem 3 2 in x b shu y t xu triple positive solutions for a class of boundary value problems of second order functional differential equations nonlinear anal 61 8 2005 1401 1411 this is an application of a new fixed point theorem introduced by avery and peeterson r i avery a c peeterson three positive fixed points of nonlinear operators on ordered banach spaces comput math appl 42 2001 313 322

existence of positive solutions for functional differential equations under suitable conditions on f t yt the boundary value problem of second order functional differential equation fde with the form fde y t f t yt 0 for t 0 1 a bc y t y t t for t 0 bvp y t y e t for t 1 1 a has at least one positive solution moreover we also apply this main result to establish several existence theorems which guarantee bvp has the multiple positive solutions