compactness characterization of operators in the toeplitz algebra of the fock space fαp abstract for 1 p let t p be the norm closure of the algebra generated by toeplitz operators with bounded symbols acting on the standard weighted fock space f p in this paper we will show that an operator a is compact on f p if and only if a t p and the berezin transform b a of a vanishes at infinity

berezin toeplitz quantization and composition formulas abstract extending results in l a coburn the measure algebra of the heisenberg group j funct anal 161 1999 509 525 l a coburn on the berezin toeplitz calculus proc amer math soc 129 11 2001 3331 3338 we derive composition formulas for berezin toeplitz operators with i g unbounded symbols in the range of certain integral transforms the question whether a finite product of berezin toeplitz operators is an operator of this type again can be answered affirmatively in several cases but there are also well known counter examples we explain some consequences of such formulas to c algebras generated by toeplitz operators

infinitely many solutions of p sublinear p laplacian equations abstract existence of infinitely many solutions of the p laplacian equation p u a x u q 2 u f x u u w 0 1 p is proved where 1 q p r n is a bounded domain with smooth boundary a c is allowed to change sign and f c for some 0 is a perturbation term which may not be odd in u

existence and multiplicity of solutions for a discontinuous problems with critical sobolev exponents abstract in this paper we consider the equation p u u p 2 u f x u in r n with discontinuous nonlinearity where 1 p n 0 is a real parameter and p n p n p is the critical sobolev exponent under proper conditions on f applying the nonsmooth critical point theory for locally lipschitz functionals we obtain at least one nontrivial nonnegative solution provided that 0 and for any k n it has k pairs of nontrivial solutions if k where 0 and k are positive numbers in particular we obtain the existence results for f is discontinuous in just one point

nontrivial solutions to semilinear elliptic problems involving two critical hardy sobolev exponents abstract in this paper we investigate a semilinear elliptic equation which involves doubly critical hardy sobolev exponents and a hardy type term by means of the linking theorem and delicate energy estimates the existence of nontrivial solutions to the problem is established

existence of a nontrivial weak solution to quasilinear elliptic equations with singular weights and multiple critical exponents abstract in this paper we consider the existence of a non trivial weak solution to a quasilinear elliptic equation with singular weights and multiple critical exponents in the whole space firstly we get the existence of a local palais smale sequence by verifying the geometric conditions of the mountain pass lemma secondly we study the concentration properties of the palais smale sequence of a zero weak limit thirdly we deduce by contradiction to eliminate the possibility of a zero weak limit case lastly applying a monotonic inequality we shall prove that the nontrivial weak limit of the palais smale sequence is indeed a weak solution

on the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions abstract we prove the existence of extremal solutions for the third order discontinuous functional nonlinear problem u t f t u u t u t for a e t a b u a a a r l 1 u u u a u b u a 0 l 2 u u a u b u b 0 by using a fixed point theorem after having established some existence results for some auxiliary second order nonlinear problems we observe that together with the discontinuities allowed on the spacial variable u with adequate modifications of technical type analogous results can be obtained when the equation has a second member not necessarily continuous in u

extremal functions and best constants to an inequality involving hardy potential and critical sobolev exponent abstract in this paper we study the asymptotic behavior of radial extremal functions to an inequality involving hardy potential and critical sobolev exponent based on the asymptotic behavior at the origin and the infinity we shall deduce a strict inequality between two best constants finally as an application of this strict inequality we consider the existence of a nontrivial solution of a quasilinear brezis nirenberg type problem with hardy potential and critical sobolev exponent

iterative solutions for a beam equation with nonlinear boundary conditions of third order a fourth order differential equation with nonlinear boundary conditions modeling beams on elastic foundations is considered iterative solutions are proved through the contraction principle some numerical simulations are also provided

on a class of boundary value problems involving the p biharmonic operator abstract a nonlinear boundary value problem involving the p biharmonic operator is investigated where p 1 it describes various problems in the theory of elasticity e g the shape of an elastic beam where the bending moment depends on the curvature as a power function with exponent p 1 we prove existence of solutions satisfying a quite general boundary condition that incorporates many particular boundary conditions which are frequently considered in the literature

monotone positive solutions for a fourth order equation with nonlinear boundary conditions abstract this work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions the results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions numerical simulations are also presented

oscillating solutions of a nonlinear fourth order ordinary differential equation we study the existence of periodic solutions for a nonlinear fourth order ordinary differential equation under suitable conditions we prove the existence of at least one solution of the problem applying coincidence degree theory and the method of upper and lower solutions

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

existence results for brezis nirenberg problems with hardy potential and singular coefficients abstract in this paper we consider the existence of non trivial solutions to semi linear brezis nirenberg type problems with hardy potential and singular coefficients first we shall study the corresponding eigenvalue problem and obtain some basic properties of eigenvalues and asymptotic estimates of the eigenfunctions and approximating eigenfunctions secondly we consider the extremal functions of the best embedding constant and get some crucial estimates for the cut off function of the extremal functions thirdly applying different variational theorems for distinct cases of those parameters appearing in the equation we obtain two existence results for non trivial solutions to semi linear brezis nirenberg type problems our existence results are divided into non resonant and resonant cases

toeplitz operators and quantum mechanics abstract toeplitz operators on the segal bargmann spaces of gaussian measure square integrable entire functions on complex n space c n are studied the c algebra generated by the weyl form of the canonical commutation relations consists precisely of the uniform limits of almost periodic toeplitz operators the question of which toeplitz operators admit a symbol calculus modulo the compact operators is raised and sufficient conditions are given for such a calculus these conditions involve a notion of slow oscillation at infinity

berezin transform and toeplitz operators on harmonic bergman spaces abstract for an operator which is a finite sum of products of finitely many toeplitz operators on the harmonic bergman space over the half space we study the problem does the boundary vanishing property of the berezin transform imply compactness this is motivated by the axler zheng theorem for analytic bergman spaces but the answer would not be yes in general because the berezin transform annihilates the commutator of any pair of toeplitz operators nevertheless we show that the answer is yes for certain subclasses of operators in order to do so we first find a sufficient condition on general operators and use it to reduce the problem to whether the berezin transform is one to one on related subclasses

toeplitz operators with bmo symbols on the segal bargmann space we show that zorboska s criterion for compactness of toeplitz operators with bmo 1 symbols on the bergman space of the unit disc holds by a different proof for the segal bargmann space of gaussian square integrable entire functions on n we establish some basic properties of bmot p for p 1 and complete the characterization of bounded and compact toeplitz operators with bmo 1 symbols via the bargmann isometry and results of lo and englis we also give a compactness criterion for the gabor daubechies windowed fourier localization operators on l 2 n dv when the symbol is in a bmo 1 sobolev type space finally we discuss examples of the compactness criterion and counterexamples to the unrestricted application of this criterion for the compactness of toeplitz operators

on a free boundary problem abstract in this paper we will be concerned with the existence of positive solutions of the following discontinuous problem p u f u h u in u h on where is the unit ball of r n n 3 and h is the heaviside function the problem is written in an equivalent integral equation form the shape of the free boundary problem x u x is studied for when is a positive real parameter f and h are given functions

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

elliptic problems with critical exponents and hardy potentials this paper is devoted to the existence of positive solutions of a dirichlet problem with critical exponent and a singular potential under various assumption on the domain omega which include some kinds of unbounded domains we prove the existence of ground states and of symmetric solutions c 2002 elsevier science usa all rights reserved

lower and upper solutions for a fully nonlinear beam equation abstract in this paper the two point fourth order boundary value problem is considered u i v f t u u u u 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r 4 r is a continuous function satisfying a nagumo type condition we prove the existence of a solution lying between lower and upper solutions using an a priori estimation lower and upper solutions method and degree theory the same arguments can be used with adequate modifications for any type of two point boundary value problem including all derivatives until order three with the second and the third derivatives given in different end points an application to the extended fisher kolmogorov problem will be obtained

on the schatten von neumann properties of some pseudo differential operators abstract we obtain a number of explicit estimates for quasi norms of pseudo differential operators in the schatten von neumann classes s q with 0 q 1 the estimates are applied to derive semi classical bounds for operators with smooth or non smooth symbols

a fixed point operator for a nonlinear boundary value problem we study a semilinear second order equation with a nonlinear boundary condition for the axial deformation of a nonlinear elastic beam in the presence of friction under appropriate conditions we define a fixed point operator in order to obtain solutions for this equation

the dual variational principle and elliptic problems with discontinuous nonlinearities on etudie des problemes aux valeurs limites elliptiques du type u f u p x x u 0 x ou r n est un domaine borne et f peut avoir des discontinuites on cherche des solutions en utilisant le principe d action duale de clarke

solutions for semilinear elliptic equations with critical exponents and hardy potential abstract in this paper we answer affirmatively an open problem cf theorem 4 in ferrero and gazzola j differential equations 177 2001 494 let 0 be an open bounded domain r n n 5 and assume that 0 n 2 2 2 n 2 n 2 then for all 0 there exists a nontrivial solution with critical level in the range 0 1 n s n 2 for the problem u u x 2 u u 2 2 u in u 0 on

compact vectorial toeplitz operators on the segal bargmann space abstract we provide a sufficient condition for the compactness of a toeplitz operator acting on the segal bargmann space of vector valued functions written in terms of an associated operator valued kernel

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

toeplitz quantization on fock space for toeplitz operators t f t acting on the weighted fock space h t 2 we consider the semi commutator t f t t g t t fg t where t 0 is a certain weight parameter that may be interpreted as planck s constant hbar in rieffel s deformation quantization in particular we are interested in the semi classical limit begin equation tag lim limits t to 0 t f t t g t t fg t t end equation it is well known that t f t t g t t fg t t tends to 0 under certain smoothness assumptions imposed on f and g this result was recently extended to f g in textup buc c n by bauer and coburn we now further generalize to not necessarily bounded uniformly continuous functions and symbols in the algebra textup vmo cap l infty of bounded functions having vanishing mean oscillation on mathbb c n our approach is based on the algebraic identity t f t t g t t fg t h bar f t h g t where h g t denotes the hankel operator corresponding to the symbol g and norm estimates in terms of the weighted heat transform as a consequence only f or likewise only g has to be contained in one of the above classes for to vanish for g we only have to impose limsup t to 0 h g t t infty e g g in l infty c n we prove that the set of all symbols f in l infty mathbb c n with the property that lim t rightarrow 0 t t ft t g t t fg t lim t rightarrow 0 t g t t f t t gf t t 0 for all g in l infty mathbb c n coincides with textup vmo cap l infty additionally we show that lim limits t to 0 t f t t f infty holds for all f in l infty c n finally we present new examples including bounded smooth functions where does not vanish

nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequalities abstract in this paper we develop a critical point theory for nonsmooth locally lipschitz functionals defined on a closed convex set extending this way the work of struwe variational methods springer berlin 1990 through a deformation result we obtain minimax principles producing critical points then we use the theory to obtain positive and negative solutions of nonlinear and semilinear hemivariational inequalities in this context we improve a result on positive solutions for semilinear elliptic problems due to nirenberg variational methods in nonlinear problems in topics in calculus of variations lecture notes in mathematics vol 1365 springer berlin 1987

existence and location results for hinged beam equations with unbounded nonlinearities abstract this work presents some existence non existence and location results for the problem composed by the fourth order fully nonlinear equation u 4 x f x u x u x u x u x s p x for x 0 1 where f 0 1 r 4 r and p 0 1 r are continuous functions and s is a real parameter with the lidstone boundary conditions u 0 u 1 u 0 u 1 0 this problem models several phenomena such as the bending of an elastic beam simply supported at the endpoints the arguments used apply a lower and upper solutions technique a priori estimations and topological degree theory in this paper we replace the usual bilateral nagumo condition by some one sided conditions which enables us to consider unbounded nonlinearities

heat flow bmo and the compactness of toeplitz operators abstract in this paper it is shown that the berezin toeplitz operator t g is compact or in the schatten class s p of the segal bargmann space for 1 p whenever g s c 0 c n vanishes at infinity or g s l p c n d v respectively for some s with 0 s 1 4 where g s is the heat transform of g on c n moreover we show that compactness of t g implies that g s is in c 0 c n for all s 1 4 and use this to show that for g bmo 1 c n we have g s is in c 0 c n for some s 0 only if g s is in c 0 c n for all s 0 this backwards heat flow result seems to be unknown for g bmo 1 and even g l finally we show that our compactness and vanishing backwards heat flow results hold in the context of the weighted bergman space l a 2 b n d v where the heat flow g s is replaced by the berezin transform b g on l a 2 b n d v for 1

multiple positive solutions for p laplace elliptic equations involving concave convex nonlinearities and a hardy type term abstract in this paper the following problem is considered p u u p 2 u x p f x u q 2 u g x u p 2 u x u 0 x where r n is a bounded domain such that 0 1 q p 0 f and g are nonnegative functions n p p p is the best hardy constant and p n p n p is the critical sobolev exponent by extracting the palais smale sequence in the nehari manifold the existence of multiple positive solutions to this equation is verified

a shooting method for a nonlinear beam equation abstract we study the existence of solutions for a nonlinear fourth order ode with nonlinear boundary condition that arises in beam theory using a shooting type argument we prove the existence of at least one solution of the problem

the dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation the dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation m r grossinho a b 1 st a tersian c 2 a departamento de matem atica iseg universidade t ecnica de lisboa rua do quelhas 6 1200 lisboa portugal b cmaf universidade de lisboa av prof gama pinto 2 1699 lisboa codex portugal c center of applied mathematics and informatics university of rousse 8 studentska str 7017 rousse bulgaria

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

second and higher order systems of boundary value problems abstract existence results for systems of kth order boundary value problems are presented our analysis is based on a nonlinear alternative of a granas and use of a priori bounds

on a nonsmooth fourth order boundary value problem abstract existence of solutions of the following boundary value problem is investigated by a variational approach u i v a u b u f t u u 0 a u 0 u 1 a u 1 u 0 u 1 j u 0 u 1 u 0 u 1 here f t 0 1 r r is a caratheodory mapping locally lipschitz with respect to the second variable and f t denotes the generalized clarke gradient of f t with respect to while j is assumed to be a proper convex lower semicontinuous function whose subdifferential is denoted by j this problem is a model for real beam shell applications

elliptic problems with discontinuities in this paper we prove two existence theorems for elliptic problems with discontinuities the first one is a noncoercive dirichlet problem and the second one is a neumann problem we do not use the method of upper and lower solutions for neumann problems we assume that f is nondecreasing we use the critical point theory for locally lipschitz functionals

periodic solutions to hamiltonian inclusions abstract we prove the existence of periodic trajectories of hamiltonian inclusions which reduce to the usual hamiltonian equations in the presence of smoothness this is accomplished via a direct variational principle involving a new action integral in an extended sense

toeplitz operators on the segal bargmann space in this paper we give a complete characterization of those functions on 2n dimensional euclidean space for which the berezin toeplitz quantizations admit a symbol calculus modulo the compact operators the functions in question are characterized by a condition of small oscillation at infinity