positive periodic solutions of singular systems with a parameter abstract the existence and multiplicity of positive periodic solutions for second order non autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter our results provide a unified treatment for the problem and significantly improve several results in the literature the proof of our results is based on the krasnoselskii fixed point theorem in a cone

hilbert space compression and exactness of discrete groups we show that the hilbert space compression of any unbounded finite dimensional cat 0 cube complex is 1 and deduce that any finitely generated group acting properly co compactly on a cat 0 cube complex is exact and hence has yu s property a the class of groups covered by this theorem includes free groups finitely generated coxeter groups finitely generated right angled artin groups finitely presented groups satisfying the b 4 t 4 small cancellation condition and all those word hyperbolic groups satisfying the b 6 condition another family of examples is provided by certain canonical surgeries defined by link diagrams

pullback and pushout constructions in c algebra theory abstract a systematic study of pullback and pushout diagrams is conducted in order to understand restricted direct sums and amalgamated free products of c algebras particular emphasis is given to the relations with tensor products both with the minimal and the maximal c tensor norm thus it is shown that pullback and pushout diagrams are stable under tensoring with a fixed algebra and stable under crossed products with a fixed group general tensor products between diagrams are also investigated the relations between the theory of extensions and pullback and pushout diagrams are explored in some detail the crowning result is that if three short exact sequences of c algebras are given with appropriate morphisms between the sequences allowing for pullback or pushout constructions at the levels of ideals algebras and quotients then the three new c algebras will again form a short exact sequence under some mild extra conditions as a generalization of a theorem of t a loring it is shown that each morphism between a pair of c algebras combined with its extension to the stabilized algebras gives rise to a pushout diagram this result has applications to corona extendibility and conditional projectivity finally the pullback and pushout constructions are applied to the class of noncommutative cw complexes defined by s eilers t a loring and g k pedersen j reine angew math 1998 499 101 143 to show that this category is stable under tensor products and under restricted direct sums

compression functions of uniform embeddings of groups into hilbert and banach spaces we construct finitely generated groups with arbitrary prescribed hilbert space compression alpha from the interval 0 1 for a large class of banach spaces e including all uniformly convex banach spaces the e compression of these groups coincides with their hilbert space compression moreover the groups that we construct have asymptotic dimension at most 3 hence they are exact in particular the first examples of groups that are uniformly embeddable into a hilbert space respectively exact of finite asymptotic dimension with hilbert space compression 0 are given these groups are also the first examples of groups with uniformly convex banach space compression 0

crossed products extensions of lp bounds for amenable actions abstract we will extend earlier transference results due to neuwirth and ricard from the context of noncommutative l p spaces associated with amenable groups to that of noncommutative l p spaces associated with crossed products of amenable actions namely if m g c is a completely bounded fourier multiplier on l p then it extends to the crossed product with similar bounds provided that the action is amenable and trace preserving furthermore our construction also allows to extend g equivariant completely bounded operators acting on the space part to the crossed product provided that the generalized folner sets of the action satisfy certain accretivity property as a corollary we obtain stability results for maximal l p bounds over crossed products we derive using that stability results an application to the boundedness of smooth multipliers in the l p spaces of group algebras

remarks on periodic orbits of dynamical systems with repulsive singularities abstract we study existence and multiplicity of periodic solutions with prescribed period in the case of conservative systems having several singularities of repulsive type these results are also used to prove existence and multiplicity of periodic bounce trajectories in exterior domains

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

positivity and lower and upper solutions for fourth order boundary value problems abstract this paper is devoted to the study the boundary value problem u 4 t f t u t for all t i 0 1 u 0 u 1 u 0 u 1 0 we prove the existence of at least one two or three solutions in the presence of a pair of not necessarily ordered lower and upper solutions the proof follows from maximum principles related to the operator u 4 m u and amann s three solutions theorem

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

the method of lower and upper solutions for fourth order two point boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u iv f x u x u x u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

implicit brain imaging we describe how implicit surface representations can be used to solve fundamental problems in brain imaging this kind of representation is not only natural following the state of the art segmentation algorithms reported in the literature to extract the different brain tissues but it is also as shown in this paper the most appropriate one from the computational point of view examples are provided for finding constrained special curves on the cortex such as sulcal beds regularizing surface based measures such as cortical thickness and for computing warping fields between surfaces such as the brain cortex all these result from efficiently solving partial differential equations pdes and variational problems on surfaces represented in implicit form the implicit framework avoids the need to construct intermediate mappings between 3 d anatomical surfaces and parametric objects such planes or spheres a complex step that introduces errors and is required by many other cortical processing approaches

periodic solutions for a fourth order p laplacian differential equation with a deviating argument abstract by means of mawhin s continuation theorem a kind of fourth order p laplacian differential equation with a deviating argument as follows p u t f u t u t g t u t u t t e t is studied under various assumptions the existence of periodic solutions is obtained

bifurcation from interval and positive solutions of a nonlinear fourth order boundary value problem abstract we study the existence of positive solutions of the nonlinear boundary value problem u 4 t f t u t u t t 0 1 u 0 u 1 u 0 u 1 0 which is not necessarily linearizable our approaches are based on krein rutman theorem topological degree theory and global bifurcation techniques

entropy of automorphisms arising from dynamical systems through discrete groups with amenable actions let g aut a be a discrete group which is exact that is admits an amenable action on some compact space then the entropy of an automorphism of the algebra a does not change by the canonical extension to the crossed product a g this is shown for the topological entropy of an exact c algebra a and for the dynamical entropy of an afd von neumann algebra a these have applications to the case of transformations on lebesgue spaces

necessary and sufficient conditions for the existence of symmetric positive solutions of singular boundary value problems abstract necessary and sufficient conditions are obtained for the existence of symmetric positive solutions to the boundary value problem u p 1 u f t u u u t 0 1 u 2 i 0 u 2 i 1 0 i 0 1 applications of our results to the special case where f is a power function of u and its derivatives are also discussed moreover similar conclusions for a more general higher order boundary value problem are established our results extend some recent work in the literature on boundary value problems for ordinary differential equations the analysis of this paper mainly relies on fixed point theorems on cones

continuous fields of c algebras coming from group cocycles and actions recently i have been attempting to formulate a suitable c algebraic framework for the subject of deformation quantization 3 19 continuous fields of c algebras provide one of the key elements for this framework the main examples of deformation quantizations which i have constructed up to now in this c algebra framework come from letting either cocycles on groups or actions of groups vary it has thus become necessary to show that one obtains in this way fields of c aigebras that are indeed continuous since this material is of a general nature and can be useful in other situations 4 6 11 13 it has seemed appropriate to give a separate exposition of it in the present article section 1 of this article contains a review of the published results on continuous fields which we will need as well as a discussion of the fact that the approach which we will take involves treating upper and lower semi continuity separately in sect 2 we discuss the continuity of fields of c algebras which arise from varying cocycles on groups while in sect 3 we do the same for actions which vary

exactness of locally compact groups we give some new characterizations of exactness for locally compact second countable groups in particular we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact hausdorff space this answers an open question by anantharaman delaroche

symmetric positive solutions for p laplacian fourth order differential equations with integral boundary conditions this paper investigates the existence and multiplicity of symmetric positive solutions for a class of p laplacian fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory for cones the nonexistence of a positive solution is also studied

existence of three positive pseudo symmetric solutions for a one dimensional p laplacian abstract we apply the five functionals fixed point theorem to verify the existence of at least three positive pseudo symmetric solutions for the three point boundary value problem g u a t f u 0 u 0 0 and u u 1 where g v v p 2 v with p 1 and 0 1

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

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when

constructions preserving hilbert space uniform embeddability of discrete groups uniform embeddability in a hilbert space introduced by gromov is a geometric property of metric spaces as applied to countable discrete groups it has important consequences for the novikov conjecture exactness introduced and studied extensively by kirchberg and wassermann is a functional analytic property of locally compact groups recently it has become apparent that as properties of countable discrete groups uniform embeddability and exactness are closely related we further develop the parallel between these classes by proving that the class of uniformly embeddable groups shares a number of permanence properties with the class of exact groups in particular we prove that it is closed under direct and free products with and without amalgam inductive limits and certain extensions

a homotopic deformation along p of a leray schauder degree result and existence for u p 2u ƒ t u 0 u 0 u t 0 p 1 soit f 0 1 r r une fonction continue et soit o p r r definie par o p s s p 2 s pour p fixe 1 on considere le probleme de dirichlet suivant o p u f t u 0 u 0 u t 0 ou t est un nombre reel positif

property a and affine buildings abstract yu s property a is a non equivariant generalisation of amenability introduced in his study of the coarse baum connes conjecture in this paper we show that all affine buildings of type a 2 b 2 and g 2 have property a together with results of guentner higson and weinberger this completes a programme to show that all affine building have property a in passing we use our technique to obtain a new proof for groups acting on a n buildings

three positive solutions for the one dimensional p laplacian in this paper nonlinear two point boundary value problems with p laplacian operators subject to dirichlet boundary condition and nonlinear boundary conditions are studied we show the existence of three positive solutions by the five functionals fixed point theorem

periodic solutions of second order non autonomous singular dynamical systems abstract in this paper we establish two different existence results of positive periodic solutions for second order non autonomous singular dynamical systems the first one is based on a nonlinear alternative principle of leray schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity the second one is based on schauder s fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions recent results in the literature are generalized and significantly improved

property a and cat 0 cube complexes property a is a non equivariant analogue of amenability defined for metric spaces euclidean spaces and trees are examples of spaces with property a simultaneously generalising these facts we show that finite dimensional cat 0 cube complexes have property a we do not assume that the complex is locally finite we also prove that given a discrete group acting properly on a finite dimensional cat 0 cube complex the stabilisers of vertices at infinity are amenable

a full description of property t of unital c crossed products abstract let be a discrete group that acts on a unital c algebra a through an action we study property t as well as its stronger variant of the full and the reduced crossed products we show that if a has a invariant tracial state then the reduced crossed product a r has strong property t if and only if has property t and a r a has strong property t if has the haagerup property the strong property t of a r a in the above statement can be replaced by that of a furthermore the strong property t of the full crossed product is shown to coincide with that of the reduced one in the case of property t we obtain the corresponding result when the group is either icc or abelian as an application a non compact locally compact group g is amenable if and only if c b g lt r g d does not have strong property t where g d is the group g equipped with the discrete topology and lt is the left translation action

non collision periodic solutions of second order singular dynamical systems we study the existence of non collision periodic solutions for second order singular dynamical systems the repulsive case and the attractive case are dealt with using a unified topological approach the proof is based on a well known fixed point theorem for completely continuous operators involving a new type of cone we do not need to consider so called strong force conditions moreover for the repulsive case the critical case can be covered recent results in the literature even in the scalar case are complemented generalized and improved

positive solutions of fourth order four point boundary value problems with p laplacian operator in this paper we consider the existence of positive solutions for the singular fourth order p laplacian equation p u t f t u t 0 t 1 with the four point boundary conditions u 0 0 u 1 au u 0 0 u 1 bu where p t t p 2t p 1 0 1 f c 0 1 0 0 may be singular at t 0 and or 1 and u 0 by using the upper and lower solution method and fixed point theorems the existence of positive solutions to the above the boundary value problem is obtained

multiplicity of positive solutions for second order three point boundary value problems we study the multiplicity of positive solutions for the second order three point boundary value problem u h t f u 0 t 0 1 u 0 0 u u 1 where 0 1 0 1 the methods employed are fixed point index theorems and leray schauder degree and upper and lower solutions

positive solutions of nonlinear fourth order boundary value problems with local and non local boundary conditions we establish new existence results for multiple positive solutions of fourth order nonlinear equations which model deflections of an elastic beam we consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non local boundary conditions with a unified approach our method is to show that each boundary value problem can be written as the same type of perturbed integral equation in the space c 0 1 involving a linear functional u but although we seek positive solutions the functional is not assumed to be positive for all positive u the results are new even for the classic boundary conditions of clamped or hinged ends when u 0 because we obtain sharp results for the existence of one positive solution for multiple solutions we seek optimal values of some of the constants that occur in the theory which allows us to impose weaker assumptions on the nonlinear term than in previous works our non local boundary conditions contain multi point problems as special cases and for the first time in fourth order problems we allow coefficients of both signs

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

fourth order two point boundary value problems estimates by two sided bounds on presente une methode simple pour transformer des problemes aux deux points limites d ordre 4 en problemes d ordre 2

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian f p x t q t f t x t x t 0 t 0 1 subject to the following boundary value conditions x 0 i 1n a ix x i x 1 i 1n b ix x i where f p s s p 2 s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

relative property a and relative amenability for countable groups abstract we define a relative property a for a countable group with respect to a finite family of subgroups many characterizations for relative property a are given in particular a relative bounded cohomological characterization shows that if g has property a relative to a family of subgroups h and if each h h has property a then g has property a this result leads to new classes of groups that have property a in particular groups are of property a if they act cocompactly on locally finite property a spaces of bounded geometry with any stabilizer of property a specializing the definition of relative property a an analogue definition of relative amenability for discrete groups is introduced and similar results are obtained

a necessary and sufficient condition for positive solutions for fourth order multi point boundary value problems with p laplacian abstractinthispaper weconsidertheexistenceofpositivesolutionsforaclassofsingularfourth order p laplacianequationwithmulti point boundary conditions by means of a monotone iterative technique a necessary and suf cient condition for the existence of apseudo c 3 0 1 positive solution is established also the existence and uniqueness of the pseudo c 3 0 1 positive solution theiterative sequence of the solution and an error estimation for the pseudo c 3 0 1 positive solution are obtained c 2007 elsevier ltd all rights reserved msc 34b15 34b25keywords necessary and suf cient condition p laplacian pseudo c 3 0 1 positive solutions cone 1 introductionin this paper we consider the existence of positive solutions for the singular fourth order multi point boundaryvalue problem with p laplacian p u 00 t 00 f 0 1u 0 m x 2i 1 a i u u 1 0 u 00 0 m x 2i 1 b u 00 u 00 1 0 1 1 where p t t p 2 t p 2 0 a i b i i

uniqueness of positive solutions for some nonlinear fourth order equations abstract in this paper we study the uniqueness question of positive solutions of the two point boundary value problem u 4 t f u t r 0 is fixed andf 0 0 is inc1 a uniqueness result is proved whenfsatisfies 0 0 some examples are also given

isoperimetry of group actions the isoperimetric profile of a discrete group was introduced by vershik however it is well defined only for a restrictive class amenable groups we generalize the notion of isoperimetric profile beyond the world of amenable groups by defining isoperimetric profiles of amenable actions of finitely generated groups on compact topological spaces this allows to extend the definition of the isoperimetric profile to all groups which are exact in such a way that for amenable groups it is equal to vershik s isoperimetric profile the main feature of our construction is that it preserves many of the properties known from the classical case we use these results to compute exact asymptotics of the isoperimetric profiles for several classes of non amenable groups

a bozejko picardello type inequality for finite dimensional cat 0 cube complexes abstract we prove a bozejko picardello type inequality for finite dimensional cat 0 cube complexes and as a consequence we obtain that a group acting properly on a finite dimensional cat 0 cube complex is weakly amenable with the cowling haagerup constant 1

on exactness and isoperimetric profiles of discrete groups abstract we introduce a quasi isometry invariant related to property a and explore its connections to various other invariants of finitely generated groups this allows to establish a direct relation between asymptotic dimension on one hand and isoperimetry and random walks on the other we apply these results to reprove sharp estimates on isoperimetric profiles of some groups and to answer some questions in dimension theory

principal non commutative torus bundles in this paper we study continuous bundles of c algebras which are non commutative analogues of principal torus bundles we show that all such bundles although in general being very far away from being locally trivial bundles are at least locally rkk trivial using earlier results of echterhoff and williams we shall give a complete classification of principal non commutative torus bundles up to t n equivariant morita equivalence we then study these bundles as topological fibrations forgetting the group action and give necessary and sufficient conditions for any non commutative principal torus bundle being rkk equivalent to a commutative one as an application of our methods we shall also give a k theoretic characterization of those principal t n bundles with h flux as studied by mathai and rosenberg which possess classical t duals

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

existence of three positive solutions for boundary value problems with p laplacian abstract by using fixed point theorem we study the following equation g u t a t f u 0 subject to boundary conditions where g v v p 2 v with p 1 the existence of at least three positive solutions is proved

existence of multiple positive solutions for one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for one dimensional p laplacian p u f t u 0 t 0 1 subject to the boundary value conditions p u 0 i 1 n 2 a i p u i u 1 i 1 n 2 b i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and a i b i satisfy a i b i 0 0 i 1 n 2 a i 1 and i 1 n 2 b i 1 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem

amenability and exactness for dynamical systems and their c algebras we study the relations between amenability resp amenability at infinity of c dynamical systems and equality or nuclearity resp exactness of the corresponding crossed products

existence of positive solutions for fourth order m point boundary value problems with a one dimensional p laplacian operator abstract this paper discusses the existence of positive solutions for fourth order m point boundary value problems with a one dimensional p laplacian operator p u t g t f u t 0 t 0 1 u 0 u 1 0 a u 0 b u 0 i 1 m 2 a i u i c u 1 d u 1 i 1 m 2 b i u i where p s s p 2 s p 1 f is a lower semi continuous function by using krasnoselskii s fixed point theorems in a cone the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is obtained

a novel method for nonlinear singular fourth order four point boundary value problems abstract in this paper a novel method is proposed for solving nonlinear singular fourth order four point boundary value problems bvps by combining advantages of the homotopy perturbed method hpm and the reproducing kernel method rkm some numerical examples are presented to illustrate the strength of the method

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

monotone iterative for fourth order p laplacian boundary value problems with impulsive effects sufficient conditions are given for the existence of a solution of fourth order p laplacian boundary value problems with impulsive effects the conditions assume the nonlinear function in equation is monotone and the existence of an upper lower solution pair the properties of p laplacian operator are employed

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

existence and uniqueness results for the bending of an elastic beam equation at resonance etude d un probleme non lineaire aux valeurs limites pour la flexion d une poutre elastique en appui simple aux deux extremites dans le cas de resonance theoremes d existence et d unicite

multiple positive solutions of the one dimensional p laplacian in this work we investigate the existence of positive solutions of the p laplacian using the quadrature method we prove the existence of multiple solutions of the one dimensional p laplacian for 0 and determine their exact number for 0 2005 elsevier inc all rights reserved

periodic solutions for a fourth order rayleigh type p laplacian delay equation abstract by applying mawhin s continuation theory and some new inequalities the existence of periodic solutions for a fourth order rayleigh type p laplacian delay equation is obtained moreover an example is given to illustrate the results

on ozawa kernels we write explicitly ozawa kernels for group extensions for discrete metric spaces of finite asymptotic dimension of large enough hilbert space compression and for suitable actions of countable groups on metric spaces we also obtain an alternative proof of stability results concerning yu s property a

e theory and kk theory for groups which act properly and isometrically on hilbert space a good deal of research in c algebra k theory in recent years has been devoted to the baum connes conjecture 3 which proposes a formula for the k theory of group c algebras that blends group homology with the representation theory of compact subgroups the conjecture has brought c algebra theory into close contact with manifold theory through its obvious similarity to the borel conjecture of surgery theory 9 31 and its links with the theory of positive scalar curvature 27 in addition there are points of contact with harmonic analysis particularly the tempered representation theory of semisimple groups although the proper relation between the baum connes conjecture and representation theory is not well understood the conjecture is most easily formulated for groups which are discrete and torsion free for such a group g there is a natural homomorphism

necessary and sufficient conditions for the existence of symmetric positive solutions of multi point boundary value problems abstract we study the nonlinear boundary value problem with multi point boundary condition u p 1 u f t u u u t 0 1 u 2 i 0 u 2 i 1 j 1 m a i j u 2 i t j i 0 1 necessary and sufficient conditions are obtained for the existence of symmetric positive solutions of this problem using fixed point theorems on cones applications of our results to the special case where f is a power function of u and its derivatives are also discussed moreover similar conclusions for a more general higher order boundary value problem are established our results extend some recent work in the literature on boundary value problems for ordinary differential equations

exotic crossed products and the baum connes conjecture we study general properties of exotic crossed product functors and characterise those which extend to functors on equivariant c algebra categories based on correspondences we show that every such functor allows the construction of a descent in kk theory and we use this to show that all crossed products by correspondence functors of k amenable groups are kk equivalent we also show that for second countable groups the minimal exact morita compatible crossed product functor used in the new formulation of the baum connes conjecture by baum guentner and willett 4 extends to correspondences when restricted to separable g c algebras it therefore allows a descent in kk theory for separable systems

on positive solutions of some nonlinear fourth order beam equations abstract the existence uniqueness and multiplicity of positive solutions of the following boundary value problem is considered u 4 t f t u t 0 for 0 where 0 is a constant f 0 1 0 0 is continuous

positive solutions of fourth order two point boundary value problems in this paper by using the krasnoselskii fixed point theorem we study the existence of one or multiple positive solution of the fourth order two point boundary value problem y 4 t f t y t y t y 0 y 1 y 0 y 1 0 we also give some examples to illustrate our results

lp compression traveling salesmen and stable walks we show that if h is a group of polynomial growth whose growth rate is at least quadratic then the lp compression of the wreath product z oh equals max 1 p 1 2 we also show that the lp compression of z oz equals max p 2p 1 2 3 and the lp compression of z oz 0 the zero section of z oz equipped with the metric induced from z o z equals max p 1 2p 3 4 the fact that the hilbert compression exponent of z o z equals 3 while the hilbert compression exponent of z o z 0 equals 3 4 is used to show that there exists a lipschitz function f z o z 0 l2 which cannot be extended to a lipschitz function defined on all of z o z

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension