positive solutions of mixed type multi point non homogeneous bvps for p laplacian equations abstract this paper is concerned with the mixed type multi point boundary value problem x t f t x t x t t 0 1 x 0 x 0 1 x 1 i 1 m i x i 2 new sufficient conditions to guarantee the existence of at least three positive solutions of above mentioned bvp are established an example is presented to illustrate the main result it is the purpose of this paper to show that the approach to get positive solutions of bvps by using multi fixed point theorems can be extended to treat this more general problem

impulsive boundary value problems with integral boundary conditions and one dimensional p laplacian abstract by using the classical fixed point index theorem for compact maps some sufficient conditions for the existence of multiple positive solutions for a class of second order impulsive differential equations with p laplacian and integral boundary conditions are established which are the complement of previously known results meanwhile the existence of many solutions is also studied

existence and uniqueness of a nontrivial solution for a class of third order nonlinear p laplacian m point eigenvalue problems on time scales abstract in this paper we study the existence and uniqueness of a nontrivial solution for the following third order p laplacian m point eigenvalue problems on time scales p u f t u t u t 0 t 0 t u 0 u 0 0 u t i 1 m 2 a i u i u 0 0 where p s is p laplacian operator i e p s s p 2 s p 1 p 1 q 1 p 1 q 1 0 is a parameter 0 1 m 2 t we obtain several sufficient conditions of the existence and uniqueness of nontrivial solution of the above eigenvalue problems when is in some interval our approach is based on the leray schauder nonlinear alternative as an application some examples to demonstrate our results are given the conditions we used in the paper are different from those in z c hao l debnath on eigenvalue intervals and eigenfunctions of fourth order singular boundary value problems appl math lett 18 2005 543 553 d jiang r p agarwal a uniqueness and existence theorem for a singular third order boundary value problem on 0 1 appl math lett 15 2002 445 451 s h li positive solutions of nonlinear singular third order two point boundary value problem j math anal appl 323 2006 413 425 z liu j s ume d r anderson s m kang twin monotone positive solutions to a singular nonlinear third order differential equation j math anal appl 334 2007 299 313 q yao positive solutions to a special singular second order boundary value problem math comput model in press q yao successive iteration of positive solution for a discontinuous third order boundary value problem comput math appl 53 2007 741 749

equivariant stable homotopy and segal s burnside ring conjecture analogous results were proved later for ko in the generality of compact lie groups by atiyah and segal 8 and for kfq the algebraic k theory spectrum associated to the finite field fq by rector 29 using quillen s 26 computation of it kfq in each case the answer involves an appropriate completed representation ring of g and the cohomology theory in question is constructed from the permutative category of finite dimensional vector spaces over a field see 31 if one considers cohomology theories constructed from other permutative categories one expects to find analogous computations in terms of a completed representation ring of g in the given category appropriately defined in particular stable cohomotopy ts is constructed from the category of finite sets 31 and for this category the analogue of the representation ring is a well known object the burnside ring a g 13 a g is a commutative ring with augmentation so one may speak of a g the completed burnside ring moreover there is

rough paths and 1d sde with a time dependent distributional drift application to polymers motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions like the kardar parisi zhang kpz equation we reconsider the unique solvability of one dimensional stochastic differential equations the drift of which is a distribution by means of rough paths theory existence and uniqueness are established in the weak sense when the drift reads as the derivative of a holder continuous function regularity of the drift part is investigated carefully and a related stochastic calculus is also proposed which makes the structure of the solutions more explicit than within the earlier framework of dirichlet processes

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

the limits of sinai s simple random walk in random environment we study the sample path asymptotics of a class of recurrent diffusion processes with random potentials including examples of sinai s simple random walk in random environment and brox s diffusion process with brownian potential the main results consist of several integral criteria which completely characterize all the possible levy classes therefore providing a very precise image of the almost sure asymptotic behaviors of these processes

the mean velocity of a brownian motion in a random levy potential a brownian motion in a random levy potential v is the informal solution of the stochastic differential equation dx t db t 1 2v x t dt where b is a brownian motion independent of v we generalize some results of kawazu tanaka who considered for v a brownian motion with drift by proving that x t t converges almost surely to a constant the mean velocity which we compute in terms of the levy exponent of v defined by e e mv t e t m

on the period matrix of a riemann surface of large genus with an appendix by j h conway and n j a sloane riemann showed that a period matrix of a compact riemann surface of genusg 1 satisfies certain relations we give a further simple combinatorial property related to the length of the shortest non zero lattice vector satisfied by such a period matrix see 1 13 in particular it is shown that for large genus the entire locus of jacobians lies in a very small neighborhood of the boundary of the space of principally polarized abelian varieties

subalgebras of the steenrod algebra and the action of matrices on truncated polynomial algebras let a t be the subalgebra of the steenrod algebra generated by sqi i 2t we determine which a module indecomposable summands of f2 x1 xn are free over a t by first showing this to be equivalent to the group theoretic question of determining which irreducible modular representations of mn f2 or gln f2 occur as composition factors in the truncated polynomial algebra f2 x1 xn x12 xn2 the second question is then answered

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

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 for m point boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u q t f t u 0 t 0 1 subject to the boundary conditions u 0 i 1 m 2 a i u i u 1 i 1 m 2 b i u i where p s s p 2 s by using a fixed point theorem in a cone we present sufficient conditions for the existence of multiple positive solutions for the above boundary value problem

existence of triple positive solutions for multi point boundary value problems with a one dimensional p laplacian in this paper we consider the existence of multiple positive solutions for multi point boundary value problems with a one dimensional p laplacian f p u t q t f t u t u t 0 01 a email protected email protected i email protected email protected m 2 0 i 1 m email protected i i 1 m email protected email protected 0 1 0 x 1 x 2 x m 2 1 by the fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

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

positive solutions for third order sturm liouville boundary value problems with p laplacian in this paper by using the fixed point index method we establish the existence of at least one or at least two positive solutions for the third order sturm liouville boundary value problem with p laplacian f p u t f t u t 0 email protected 0 1 au 0 email protected 0 0 cu 1 email protected 1 0 u 0 0 where f p s s p 2s p 1 as an application an example is given to demonstrate the main result

a symmetric solution of a multipoint boundary value problem with one dimensional p laplacian at resonance abstract we apply an extension of mawhin s continuation theorem due to ge to show the existence of at least one symmetric solution of the multipoint boundary value problem for the one dimensional p laplacian at resonance p x t f t x t x t t 0 1 subject to the boundary conditions x 0 i 1 n i x i x 1 i 1 n i x i where p s s p 2 s p 1 0 1 2 n 1 2 i i 1 i 1 2 n i 1 n i 1 f 0 1 r 2 r with f t u v f 1 t u v for t u v 0 1 r 2 satisfying the caratheodory conditions

slow movement of random walk in random environment on a regular tree we consider a recurrent random walk in random environment on a regular tree under suitable general assumptions upon the distribution of the environment we show that the walk exhibits an unusual slow movement the order of magnitude of the walk in the first n steps is log n 3

positive solutions for nonlinear operator equations and several classes of applications in this paper we study a class of nonlinear operator equations x ax x 0 on ordered banach spaces where a is a monotone generalized concave operator using the properties of cones and monotone iterative technique we establish the existence and uniqueness of solutions for such equations in particular we do not demand the existence of upper lower solutions and compactness and continuity conditions as applications we study first order initial value problems and two point boundary value problems with the nonlinear term is required to be monotone in its second argument in the end applications to nonlinear systems of equations and to nonlinear matrix equations are also considered

hecke algebras and cohomotopical mackey functors in this paper we define the concept of the cohomotopical mackey functor which is more general than the usual cohomological mackey functor and show that hecke algebra techniques are applicable to cohomotopical mackey functors our theory is valid for any possibly infinite discrete group some applications to topology are also given

the multiple positive solutions for p laplacian multipoint bvp with sign changing nonlinearity on time scales abstract in this paper we consider the following p laplacian multipoint boundary value problem on time scales p u t a t f t u t 0 t 0 t t p u 0 i 1 n 2 a i p u i u t i 1 n 2 b i u i where p s s p 2 s p 1 i 0 t t 0 1 2 n 2 t by using fixed point index we provide some sufficient conditions for the existence of multiple positive solutions to the above boundary value problem especially the nonlinear term f t u is allowed to change sign as an application an example is given to demonstrate our result

existence of solutions for weighted p t laplacian system multi point boundary value problems abstract this paper investigates the existence of solutions for weighted p t laplacian system multi point boundary value problems our method is based on leray schauder s degree we give the existence of solutions when the nonlinearity term f t satisfies sub p growth condition or general growth condition respectively moreover the existence of nonnegative and positive solutions has been discussed

multiplicity of symmetric positive solutions for a multipoint boundary value problem with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u t q t f t u t u t 0 t 0 1 subject to the boundary conditions u 0 i 1 n i u i u 1 i 1 n i u i where p s s p 2 s p 1 i 0 0 i 1 n i 1 0 1 2 n 1 2 i i 1 i 1 2 n applying a fixed point theorem of functional type in a cone we study the existence of at least three symmetric positive solutions to the above boundary value problem the interesting point is that the nonlinear term f contains the first order derivative explicitly

impulsive boundary value problems involving the one dimensional p laplacian abstract by using the classical fixed point index theorem for compact maps some sufficient conditions for the existence of multiple positive solutions for a class of second order impulsive differential equations with p laplacian are established which are complement of previously known results

decomposing thick subcategories of the stable module category let underline rm mod kg be the stable category of finitely generated modular representations of a finite group g over a field k we prove a krull remak schmidt theorem for thick subcategories of underline rm mod kg it is shown that every thick tensor ideal mathcal c of underline rm mod kg i e a thick subcategory which is a tensor ideal has a usually infinite unique decomposition mathcal c coprod i in i mathcal c i into indecomposable thick tensor ideals this decomposition follows from a decomposition of the corresponding idempotent kg module e mathcal c into indecomposable modules if mathcal c mathcal c w is the thick tensor ideal corresponding to a closed homogeneous subvariety w of the maximal ideal spectrum of the cohomology ring h g k then the decomposition of mathcal c reflects the decomposition w bigcup i 1 nw i of w into connected components

fine mesh limit of the vrjp in dimension one and bass burdzy flow we introduce a continuous space limit of the vertex reinforced jump process vrjp in dimension one which we call linearly reinforced motion lrm on mathbb r it is constructed out of a convergent bass burdzy flow the proof goes through the representation of the vrjp as a mixture of markov jump processes as a by product this gives a representation in terms of a mixture of diffusions of the lrm and of the bass burdzy flow itself we also show that our continuous space limit can be obtained out of the edge reinforced random walk errw since the errw and the vrjp are known to be closely related compared to the discrete space processes the lrm has an additional symmetry in the initial local times initial occupation profile changing them amounts to a deterministic change of the space and time scales

existence of three positive solutions for m point boundary value problems with one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u q t f t u t u t 0 t 0 1 subject to the boundary conditions u 0 0 u 1 i 1 m 2 a i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 m 2 1 and a i 0 1 0 i 1 m 2 a i 1 using a fixed point theorem due to avery and peterson we study the existence of at least three positive solutions to the above boundary value problem the interesting point is that the nonlinear term f explicitly involves a first order derivative

existence of solutions for a first order p laplacian bvp on time scales we introduce a first order delta dynamic equation on time scales involving the one dimensional p laplacian and prove the existence of at least one positive solution an example applying our result is also given

existence of positive solutions of nonlinear m point bvp for an increasing homeomorphism and positive homomorphism on time scales in this paper we will consider the following multipoint boundary value problem for the following second order dynamic equations on time scales f u d a t f t u t 0 t 0 t u 0 i 1m 2a iu x i f u d t i 1m 2b i f u d x i where f r r is an increasing homeomorphism and positive homomorphism and f 0 0 by using fixed point theorems we obtain an existence theorem of positive solutions for the above boundary value problem which includes and improve some related results in the relevant literature as an application an example to demonstrate our results is given

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

representations of the double burnside algebra and cohomology of the extraspecial p group ii abstract let e be the extraspecial p group of order p 3 and exponent p where p is an odd prime we determine the mod p cohomology h x f p of a summand x in the stable splitting of p completed classifying space be in the previous paper hida and yagita 2014 7 we determined this cohomology modulo nilpotence in this paper we consider the whole of the cohomology moreover we consider the stable splittings of bg for some finite groups with sylow p subgroup e related to the three dimensional linear group l 3 p

the relative burnside module and the stable maps between classifying spaces of compact lie groups tom dieck s burnside ring of compact lie groups is generalized to the relative case for any g d n a compact lie group and its normal subgroup a g n is defined to be an appropriate set of the equivalence classes of compact g enr s with free n action in such a way that i a g d n 7g n so b n g where b n g is the classifying space of principal n g bundle under the product situation i e g f x k n k a f x k d k is also denoted by a f k as it turns out to be the usual a f k when both f and k are finite then a couple of applications are given to the study of stable maps between classifying spaces of compact lie groups a conceptual proof of feshbach s double coset formula and a density theorem on the map ap a l h a a bl bh p for any compact lie groups l k when p is odd some restriction is applied to l when p 2 this latter result may be regarded as the pushout of feshbach s density theorem and the theorem of may snaith zelewski over the celebrated carlsson solution of segal s burnside ring conjecture 0 introduction even before the arrival of carlsson s celebrated paper c the segal conjecture for finite groups was known to imply the complete calculation of the stable maps between classifying spaces of finite groups agm lmm more recently snaith s2 got interested in the stable maps between classifying spaces of compact lie groups while studying his explicit brauer induction problem see s2 which is a nice reference on this topic snaith s research led to the further generalization of the segal conjecture by msz theorem a msz let f and j be finite groups and let k be a compact lie group then a induces the isomorphism a a f x j k a j fxj bfj bfk f where a f x j k is the grothendieck a f x j module of principal f x j k bundles over finite f x j sets and aj fxj is the completion of received by the editors june 23 1993 1991 mathematics subject classification primary 55p42 55r35 57s15 secondary 55q91 55r9 1

a one dimensional diffusion process in a wiener medium we consider a one dimensional diffusion process in a random medium which is itself generated by a wiener process the asymptotic behaviour is investigated using the self similarity of the medium process the results are analogous to the lattice case

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

discrete schemes for processes in random media we present discrete schemes for processes in random media we prove two results the first one is the convergence of sinai s random walks in random environments to the brox model the second one is the convergence of random walks in media with random gates to a continuous process in a poisson potential the proofs are based on the following idea we consider the discrete media as random potentials for continuous models

the limit distribution of sinai s random walk in random environment abstract recently sinai proved that if x n is a one dimensional random walk in random environment which is recurrent then log n 2 x n converges in distribution here we calculate the limit distribution explicitly

minami webb splittings and some exotic p local finite groups we give a new proof of the minami webb formula for classifying spaces of finite groups by exploiting symonds s resolution of webb s conjecture the methods are applicable to obtain a stable decomposition of minami s type for the classifying spaces of the three exotic p local finite groups which were introduced by ruiz and viruel at the prime 7 we obtain a similar decomposition for the classifying spaces of a family of exotic p local finite groups which were constructed by broto levi and oliver

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

existence of multiple positive solutions for nonlinear m point boundary value problems abstract in this paper we afford some sufficient conditions to guarantee the existence of multiple positive solutions for the nonlinear m point boundary value problem for the one dimensional p laplacian p u a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 a i u i

systems of fixed point sets let g be a compact lie group a canonical method is given for constructing a c space from homotopy theoretic information about its fixed point sets the construction is a special case of the categorical bar construction applications include easy constructions of certain classifying spaces as well as c eilenbergmac lane spaces and postnikov towers 0 introduction let g be a compact lie group and x a g space the equivariant homotopy theory of x is reflected to a remarkable extent in its system of fixed point sets defined as a functor from a certain category 0g to top the category of topological spaces our spaces will be compactly generated weak hausdorff they may or may not be equipped with a basepoint depending on the context these functors or systems have considerable technical advantages over g spaces it is easy to apply most homotopy theoretic constructions to them whereas in many cases it is unclear how to proceed for g spaces it is the purpose of this paper to present a canonical way of recovering from any system a g space which preserves all the homotopy theoretic structure of the system this allows us to give easy equivariant versions of some standard topological constructions such as eilenberg mac lane spaces and postnikov towers and to simplify other equivariant constructions 1 1 statements of the main theorems throughout g is a fixed compact lie group definitions the category of canonical orbits written 0g is a topological category with discrete object space 0g g 77 77 a closed subgroup of g and morphisms the g maps topologized by requiring the natural bijection hoxn0cig h g k g k h to be a homeomorphism by an oc space we shall mean a continuous contravariant functor from 0g to top these functors form the objects of a topological category in the usual manner we will also consider gg rings oc groups etc defined similarly definition let a1 be a g space the fixed point set system of x written x is an gg space defined as follows g 77 x received by the editors october 30 1981 and in revised form april 26 1982 1980 mathematics subject classification primary 57s10 55n25

categorifying induction formulae via divergent series abstract we show how to get explicit induction formulae for finite group representations and more generally for rational green functors by summing a divergent series over dwyer s subgroup and centralizer decomposition spaces this results in formulae with rational coefficients the former space yields a well known induction formula the latter yields a new one as essentially immediate corollaries of the existing literature we get similar formulae in group cohomology and stable splittings of classifying spaces

patterns in sinai s walk sinai s random walk in random environment shows interesting patterns on the exponential time scale we characterize the patterns that appear on infinitely many time scales after appropriate rescaling a functional law of iterated logarithm the curious rate function captures the difference between one sided and two sided behavior

triple positive solutions for a multi point boundary value problem with a one dimensional p laplacian in this paper we consider the multiplicity of positive solutions for a one dimensional p laplacian differential equation with sturm liouville like boundary conditions by means of a fixed point theorem for cones in banach spaces we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problems