double positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales a new double fixed point theorem is applied to investigate the existence of at least double positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale

multiple hamiltonian structures and soliton equations with explicit x dependence abstract it is known that a schrodinger operator d d x 2 u x has a family or hierarchy consisting of partial differential equations which preserve certain elements of its spectrum one such preserving equation is the korteweg de vries equation u t 1 2 3 u u u each system of the hierarchy is hamiltonian with respect to a pair of compatible local hamiltonian structures each hamiltonian structure is given by a skew symmetric matrix differential operator in this paper all this is generalized for second order scalar differential operators of the form l d d x 2 q x where is a complex parameter and it is assumed that q is analytic in a deleted neighborhood of with a pole of order at least 1 at in addition it is shown that the systems of certain hierarchies contain space dependent coefficients let x the following kortweg de vries like system is a preserving deformation of the operator l 2 1 x 2 q 1 1 q 2 2 let c 1 1 2 x 3 q 1 1 8 x then the equations of motion are given by these formulas q 1 t 1 2 3 q 1 c 1 2q 2 xq 2 and q 2 t q 2 q 2 c 1

estimates for lusin area and littlewood paley gλ functions over spaces of homogeneous type abstract let x d be a space of homogeneous type and x under the assumptions that the measure satisfies the volume regularity property p and the lusin area function s is bounded on l 2 x the authors prove without invoking any regularity on the kernels considered that if f belongs to bmo x s f is either infinite everywhere or finite almost everywhere and in the latter case s f 2 is bounded from bmo x into its proper subspace blo x as an application the authors also obtain the boundedness on l p with p 2 for the operator s furthermore exploiting the l p x boundedness of s the authors prove that if f belongs to a certain campanato space e p x with suitable indices s f is either infinite everywhere or finite almost everywhere and in the latter case s f 2 is bounded from e p x into e 2 p 2 x moreover the authors establish corresponding results for the littlewood paley g function without invoking any regularity of the kernels considered and the property p of x the authors also show that e p x is a proper subspace of e p x with suitable indices

random martingales and localization of maximal inequalities abstract let x d be a metric measure space for r 0 consider the hardy littlewood maximal operator m r f x def sup r r 1 b x r b x r f d we show that if there is an n 1 such that one has the microdoubling condition b x 1 1 n r b x r for all x x and r 0 then the weak 1 1 norm of m r has the following localization property m r l 1 x l 1 x sup r 0 m r r n r l 1 x l 1 x an immediate consequence is that if x d is ahlfors david n regular then the weak 1 1 norm of m r is n log n generalizing a result of stein and stromberg 1983 47 we show that this bound is sharp by constructing a metric measure space x d that is ahlfors david n regular for which the weak 1 1 norm of m 0 is n log n the localization property of m r is proved by assigning to each f l 1 x a distribution over random martingales for which the associated random doob maximal inequality controls the weak 1 1 inequality for m r

positive solutions of nonlinear m point boundary value problems on time scales in this paper by using fixed point theorems in a cone and the associated green s function we study the existence of at least two and three positive solutions to the m point boundary value problem bvp on time scales u d t f t u t 0 email protected 0 1 t bu 0 email protected d 0 0 u 1 email protected email protected iu e i m 3 where t is a time scale email protected c l d 0 1 x 0 0 b email protected 0 a email protected 0 for i 1 2 m 2 and e i satisfy 0 e 1 e 2 e m 2 r 1

three circle theorem and dimension estimate for holomorphic functions on kahler manifolds the classical hadamard three circle theorem is generalized to complete kahler manifolds more precisely we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle theorem two sharp monotonicity formulae are derived as corollaries among applications we obtain sharp dimension estimates with rigidity of holomorphic functions with polynomial growth when the holomorphic sectional curvature is nonnegative when the bisectional curvature is nonnegative the sharp dimension estimate was due to ni

polynomial growth harmonic functions on groups of polynomial volume growth we consider harmonic functions of polynomial growth of some order d on cayley graphs of discrete groups of polynomial volume growth of order d w r t the word metric and prove the optimal estimate for the dimension of the space of such harmonic functions more precisely the dimension of this space of harmonic functions is at most of order d d 1 as in the already known riemannian case this estimate is polynomial in the growth degree more generally our techniques also apply to graphs roughly isometric to cayley graphs of groups of polynomial volume growth

on the rate of convergence to the asymptotic cone for nilpotent groups and subfinsler geometry addressing a question of gromov we give a rate in pansu s theorem about the convergence to the asymptotic cone of a finitely generated nilpotent group equipped with a left invariant word metric rescaled by a factor we obtain a convergence rate measured in the gromov hausdorff metric of for nilpotent groups of class and for nilpotent groups of class 2 we also show that the latter result is sharp and we make a connection between this sharpness and the presence of so called abnormal geodesics in the asymptotic cone as a corollary we get an error term of the form for the volume of cayley balls of a general nilpotent group of class r we also state a number of related conjectural statements

coupled harry dym equations with multi hamiltonian structures the authors consider the isospectral flows of delta 2 sigma 1n upsilon i lambda i psi alpha psi using an unusual form of the lax approach they derive in a particularly simple manner a the second half of the lax pair b the associated hamiltonian structures c an infinite hierarchy of poisson commuting hamiltonians in this way they show that these equations possess n 1 compatible purely differential hamiltonian structures the case n 1 is just the bi hamiltonian harry dym hierarchy they thus extend the recent results on multi hamiltonian coupled kdv equations

multiple positive solutions for discrete nonlocal boundary value problems in this paper we investigate a second order nonlinear difference equation with sign changing nonlinearity subject to two different sets of nonlocal boundary conditions the explicit expressions of the associated green s functions are presented by using a recently developed fixed point theorem we establish sufficient conditions for the existence of multiple positive solutions of the boundary value problem

geometry and analysis of dirichlet forms let e be a regular strongly local dirichlet form on l2 x m and d the associated intrinsic distance assume that the topology induced by d coincides with the original topology on x and that x is compact satisfies a doubling property and supports a weak 1 2 poincare inequality we first discuss the non coincidence of the intrinsic length structure and the gradient structure under the further assumption that the ricci curvature of x is bounded from below in the sense of lott sturm villani the following are shown to be equivalent i the heat flow of e gives the unique gradient flow of u ii e satisfies the newtonian property iii the intrinsic length structure coincides with the gradient structure moreover for the standard resistance dirichlet form on the sierpinski gasket equipped with the kusuoka measure we identify the intrinsic length structure with the measurable riemannian and the gradient structures we also apply the above results to the coarse ricci curvatures and asymptotics of the gradient of the heat kernel

estimates for littlewood paley operators in bmo rn abstract let g f be the littlewood paley g function of f on r n in this paper the authors prove that if f bmo r n the space of functions with bounded mean oscillation then g f is either infinite everywhere or finite almost everywhere and in the latter case g f 2 is bounded from bmo r n into blo r n the space of functions with bounded lower oscillation which is a proper subspace of bmo r n moreover the authors also establish similar results for the lusin area function and the littlewood paley g function

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

harmonic functions and volume growth of fingerless ends let m be a noncompact complete riemannian manifold with finitely many ends in this paper we study the existence of green s function for the p laplace equation on m in terms of a certain volume growth we also show that the dimension of the linear space of polynomial growth harmonic functions is finite if a volume comparison condition and a mean value inequality for nonnegative subharmonic functions hold in sufficiently large parts of each end

existence and nonexistence of positive solutions for a class of nth order three point boundary value problems in banach spaces by using the fixed point principle in cone and the fixed point index theory for strict set contraction operator this paper investigates the existence nonexistence and multiplicity of positive solutions for a class of nonlinear three point boundary value problems of nth order differential equations in ordered banach spaces in addition an example is included to demonstrate the main results

multiple positive solutions of multi point boundary value problem for second order impulsive differential equations this paper is devoted to study the existence of multiple positive solutions for the second order multi point boundary value problem with impulse effects the arguments are based upon fixed point theorems in a cone an example is worked out to demonstrate the main results

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

three circles theorems for harmonic functions we proved two three circles theorems for harmonic functions on manifolds in integral sense as one application on manifold with nonnegative ricci curvature whose tangent cone at infinity is the unique metric cone with unique conic measure we showed the existence of nonconstant harmonic functions with polynomial growth this existence result recovered and generalized the former result of ding and led to a complete answer of ni s conjecture furthermore in similar context combining the techniques of estimating the frequency of harmonic functions with polynomial growth which were developed by colding and minicozzi we confirmed their conjecture about the uniform bound of frequency

on the existence of nonnegative solutions to an integral equation with applications to boundary value problems abstract by the use of a guo krasnoselskii theorem in cones existence of positive eigenvalues yielding nonnegative or positive solutions to an integral equation is studied the results are applied to a variety of boundary value problems concerning ordinary differential equations

positive solutions for a class of boundary value problem with integral boundary conditions in banach spaces this paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary value problem of second order differential equations with integral boundary conditions in ordered banach spaces the arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators the nonexistence of a positive solution is also studied

positive solution for m point boundary value problems in this paper we investigate an m point boundary value problem with sign changing nonlinearity the existence of an interval of parameters which ensures the problem has at least one positive solution is determined by constructing available operator and combining the method of lower solution with the method of topology degree moreover the associated green s function for the above problem is also given

existence of solutions of boundary value problems with integral boundary conditions for second order impulsive integro differential equations in banach spaces this paper investigates the existence of solutions for a class of second order boundary value problems with integral boundary conditions of nonlinear impulsive integro differential equations in banach spaces the arguments are based upon the fixed point theorem of strict set contraction operators meanwhile an example is worked out to demonstrate the main results

a priori holder and lipschitz regularity for generalized p harmonious functions in metric measure spaces abstract let x d be a proper metric measure space and let x be a bounded domain for each x we choose a radius 0 x dist x and let b x be the closed ball centered at x with radius x if r consider the following operator in c t u x 2 sup b x u inf b x u 1 b x b x u d under appropriate assumptions on x and the radius function we show that solutions u c of the functional equation t u u satisfy a local holder or lipschitz condition in the motivation comes from the so called p harmonious functions in euclidean domains

bounding dimension of ambient space by density for mean curvature flow for an ancient solution of the mean curvature flow we show that each time slice m t is contained in an affine subspace with dimension bounded in terms of the density and the dimension of the evolving submanifold recall that an ancient solution is a family m t that evolves under mean curvature flow for all negative time t

symmetric positive solutions of boundary value problems with integral boundary conditions under conditions weaker than those used by ma we establish various results on the existence and nonexistence of symmetric positive solutions to fourth order boundary value problems with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in a cone our results improve and extend that obtained in h ma symmetric positive solutions for nonlocal boundary value problems of fourth order nonlinear anal 68 2008 645 651 we illustrate our results by one example which cannot be handled using the existing results

solutions and green s functions for some linear second order three point boundary value problems in this paper we consider the green s functions for a second order linear ordinary differential equation with some three point boundary conditions we give exact expressions of the unique solutions for the linear three point boundary problems by the green s functions as applications we study the iterative solutions for some nonlinear singular second order three point boundary value problems

a class of three point boundary value problems for second order impulsive integro differential equations in banach spaces abstract in this paper we consider the following boundary value problems for second order three point nonlinear impulsive integro differential equation of mixed type in a real banach space e x t f t x t x t a x t b x t t j t t k x t t k i k x t k x t t k i k x t k x t k k 1 2 m x 0 x 1 x where is the zero element of e a x t 0 t g t s x s d s b x t 0 1 h t s x s d s g c d r d t s j j t s h c j j r and x t t k denotes the jump of x t at t t k x t t k denotes the jump of x t at t t k some new results are obtained for the existence and multiplicity of positive solutions of the above problems by using the fixed point index theory and fixed point theorem in the cone of strict set contraction operators meanwhile an example is worked out to demonstrate the main results

local spectral convergence in rcd k n spaces abstract in this paper we give necessary and sufficient conditions for the validity of the local spectral convergence in balls in the setting of rcd spaces

poincare inequalities for littlewood paley operators abstract in this paper the authors prove that the inequalities of poincare type are preserved under the action of the littlewood paley operators applications to boundedness of the littlewood paley operators on lipschitz spaces and hajlasz sobolev spaces are considered

fixed sign solutions for a system of singular focal boundary value problems we consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments using schauder fixed point theorem we establish criteria such that the system of boundary value problems has at least one fixed sign solution

positive solutions for a class of boundary value problems with integral boundary conditions this paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary value problems of fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in cone the nonexistence of positive solutions is also studied

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

coupled kdv equations with multi hamiltonian structures abstract we present a large class of systems of n equations which possess n 1 purely differential compatible hamiltonian structures our generic equations are isospectral to n 1 0 e i 2 i 2 n 1 0 i 2 i 2 n but our class also includes degenerate nondispersive systems which are unrelated to this linear problem embedded in this class for each n there are n distinct coupled kdv systems when n 2 our class includes 3 known equations dispersive water waves ito s equation and reduced benney s equations these equations are thus tri hamiltonian we also present 2 examples of 3 component quadri hamiltonian systems which generalise the above mentioned dispersive and nondispersive water waves

triple solutions for second order three point boundary value problems abstract we establish the existence of at least three positive solutions to the second order three point boundary value problem u f t u 0 u 0 0 u u 1 where 0 lt f 0 1 0 0 is continuous we accomplish this by making growth assumptions on f which can apply to many more cases than the sublinear and superlinear ones discussed in recent works

fredholm theory for elliptic operators on quasi asymptotically conical spaces we consider the mapping properties of generalized laplace type operators l r on the class of quasi asymptotically conical qac spaces which provide a riemannian generalization of the qale manifolds considered by joyce joy00 our main result gives conditions under which such operators are fredholm when between

existence results for nonlinear boundary value problems with integral boundary conditions in banach spaces abstract this paper investigates the multiplicity of positive solutions for a class of nonlinear boundary value problems of fourth order differential equations with integral boundary conditions in ordered banach spaces the arguments are based upon a specially constructed cone and the fixed point index theory in cone for strict set contraction operator the nonexistence of positive solution is also studied meanwhile an example is worked out to demonstrate the main results

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results

on the existence of positive solution for a kind of multi point boundary value problem at resonance abstract this paper concerns the existence of positive solution for a class of second order m point boundary value problems under different resonant conditions by using the leggett williams norm type theorem due to o regan and zima we obtain the existence of positive solution an example is given to demonstrate the main results

existence of multiple solutions for second order boundary value problems we give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y f x y y 0 x epsilon 0 1 y 0 0 y 1 in the special case f x y y f y greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions we give an example showing this latter result is sharp our results extend those of avery and of lakshmikantham et al

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

factorisation of energy dependent schrodinger operators miura maps and modified systems we consider the energy dependent schrodinger operator mathbb l sum limits i 0 n lambda i varepsilon i partial 2 u i which we have previously shown to be associated with multi hamiltonian structures 2 in this paper we use an unusual form of the lax approach to derive by asingle construction the time evolutions of the eigenfunctions of mathbb l the associated hamiltonian operators and the hamiltonian functionals we then generalise the well known factorisation of standard lax operators to the case of energy dependent operators the simple product of linear factors is replaced by a dependent quadratic form we thus generalise the resulting construction of miura maps and modified equations we show that for some of our systems there exists a sequence ofn such modifications therth modification possessing n r 1 hamiltonian structures

super extensions of energy dependent schrodinger operators we consider the energy dependent super schrodinger linear problem sum limits i 0 n lambda i varepsilon i partial 2 u i psi eta i phi 0 sum limits i 0 n lambda i varepsilon i partial phi eta i psi 0 which is a direct generalization of the purely even energy dependent schrodinger equation discussed in 1 we show that the isospectral flows of that problem possess n 1 compatible hamiltonian structures we also extend a generalised factorisation approach of 2 to this case and derive a sequence ofn modifications for the 2n component systems thenth such modification possesses n n 1 compatible hamiltonian structures