nonlinear boundary value problems at resonance soit un espace de mesure fini et h l 2 l espace des fonctions a valeurs reelles de carre integrable mesurables de lebesgue sur on considere l equation lu r n u g u h ou h h l dom l h h est un operateur lineaire auto adjoint densement defini r n appartient au spectre l g r r est une fonction qui peut etre non lineaire on donne des resultats d existence generaux

on a class of functionals invariant under a zn action abstract this document considers a system of ordinary differential equations of the form q v sub q t q f t where f and v are periodic in t v is periodic in the components of q q sub 1 q sub m and the mean value of f vanishes by showing that a corresponding functional is invariant under a natural z sub n action a simple variational argument yields at least n 1 distinct periodic solutions of more general versions of are also treated as is a class of neumann problems for semilinear elliptic partial differential equations

polynomials of meixner s type in infinite dimensions jacobi fields and orthogonality measures abstract the classical polynomials of meixner s type hermite charlier laguerre meixner and meixner pollaczek polynomials are distinguished through a special form of their generating function which involves the laplace transform of their orthogonality measure in this paper we study analogs of the latter three classes of polynomials in infinite dimensions we fix as an underlying space a non compact riemannian manifold x and an intensity measure on it we consider a jacobi field in the extended fock space over l 2 x whose field operator at a point x x is of the form x x x x x x x where is a real parameter here x and x are respectively the annihilation and creation operators at the point x we then realize the field operators as multiplication operators in l 2 d where d is the dual of d c 0 x and is the spectral measure of the jacobi field we show that is a gamma measure for 2 a pascal measure for 2 and a meixner measure for is a levy noise measure the isomorphism between the extended fock space and l 2 d is carried out by infinite dimensional polynomials of meixner s type we find the generating function of these polynomials and using it we study the action of the operators x and x in the functional realization

multiple solutions of a class of neumann problem for semilinear elliptic equations abstract the multiplicity results are obtained for solutions of the neumann problem for nonlinear elliptic equations with unbounded nonlinearity by the implicit function theorem and the morse theory

entropic measure and wasserstein diffusion we construct a new random probability measure on the circle and on the unit interval which in both cases has a gibbs structure with the relative entropy functional as hamiltonian it satisfies a quasi invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval respectively the associated integration by parts formula is used to construct two classes of diffusion processes on probability measures on the sphere or the unit interval by dirichlet form methods the first one is closely related to malliavin s brownian motion on the homeomorphism group the second one is a probability valued stochastic perturbation of the heat flow whose intrinsic metric is the quadratic wasserstein distance it may be regarded as the canonical diffusion process on the wasserstein space

a rademacher type theorem on l2 wasserstein spaces over closed riemannian manifolds abstract let p be any borel probability measure on the l 2 wasserstein space p 2 m w 2 over a closed riemannian manifold m we consider the dirichlet form e induced by p and by the wasserstein gradient on p 2 m under natural assumptions on p we show that w 2 lipschitz functions on p 2 m are contained in the dirichlet space d e and that w 2 is dominated by the intrinsic metric induced by e we illustrate our results by giving several detailed examples

gibbs states over the cone of discrete measures we construct gibbs perturbations of the gamma process on r d which may be used in applications to model systems of densely distributed particles first we propose a definition of gibbs measures over the cone of discrete radon measures on r d and then analyze conditions for their existence our approach works also for general levy processes instead of gamma measures to this end we need only the assumption that the first two moments of the involved levy intensity measures are finite also uniform moment estimates for the gibbs distributions are obtained which are essential for the construction of related diusions moreover we prove a mecke type characterization for the gamma measures on the cone and an fkg inequality for them

laplace operators on the cone of radon measures abstract we consider the infinite dimensional lie group g which is the semidirect product of the group of compactly supported diffeomorphisms of a riemannian manifold x and the commutative multiplicative group of functions on x the group g naturally acts on the space m x of radon measures on x we would like to define a laplace operator associated with a natural representation of g in l 2 m x here is assumed to be the law of a measure valued levy process a unitary representation of the group cannot be determined since the measure is not quasi invariant with respect to the action of the group g consequently operators of a representation of the lie algebra and its universal enveloping algebra in particular a laplace operator are not defined nevertheless we determine the laplace operator by using a special property of the action of the group g a partial quasi invariance we further prove the essential self adjointness of the laplace operator finally we explicitly construct a diffusion process on m x whose generator is the laplace operator

a clebsch gordan formula for sl3 c and applications to rationality abstract if r s t are irreducible sl 3 c representations we give an easy and explicit description of a basis of the space of equivariant maps r s t theorem 3 1 we apply this method to the rationality problem for invariant function fields in particular we prove the rationality of the moduli space of plane curves of degree 34 this uses a criterion which ensures the stable rationality of some quotients of grassmannians by an sl action proposition 5 4

an infinite dimensional analogue of the lebesgue measure and distinguished properties of the gamma process abstract we define a one parameter family l of sigma finite finite on compact sets measures in the space of distributions these measures are equivalent to the laws of the classical gamma processes and invariant under an infinite dimensional abelian group of certain positive multiplicators this family of measures was first discovered by gelfand graev vershik in the context of the representation theory of current groups here we describe it in direct terms using some remarkable properties of the gamma processes we show that the class of multiplicative measures coincides with the class of zero stable measures which is introduced in the paper we give also a new construction of the canonical representation of the current group sl 2 r x

existence and multiplicity for solutions of neumann problem for semilinear elliptic equations the existence and multiplicity results are obtained for solutions of neumann problem for semilinear elliptic equations by the least action principle and the minimax methods respectively

invariant measures for the continual cartan subgroup abstract we construct and study the one parameter semigroup of finite measures l 0 on the space of schwartz distributions that have an infinite dimensional abelian group of linear symmetries this group is a continual analog of the classical cartan subgroup of diagonal positive matrices of the group sl n r the parameter is the degree of homogeneity with respect to homotheties of the space we prove uniqueness theorem for measures with given degree of homogeneity and call the measure with degree of homogeneity equal to one the infinite dimensional lebesgue measure l the structure of these measures is very closely related to the so called poisson dirichlet measures pd and to the well known gamma process the nontrivial properties of the lebesgue measure are related to the superstructure of the measure pd 1 which is called the conic poisson dirichlet measure cpd this is the most interesting finite measure on the set of positive convergent monotonic real series

pairs of nontrivial solutions for resonant neumann problems abstract we study a semilinear neumann problem which is resonant at with respect to any eigenvalue different from the first and the second eigenvalue of n the negative neumann laplacian using a combination of variational methods with morse theoretic techniques we show that the problem has at least two nontrivial smooth solutions

existence and continuation of solutions for a nonlinear neumann problem abstract in this article we study the existence continuation and bifurcation from infinity of nonconstant solutions for a nonlinear neumann problem we apply the leray schauder degree and the degree for s o 2 equivariant gradient operators defined by the second author in s rybicki s o 2 degree for orthogonal maps and its applications to bifurcation theory nonlinear anal tma 23 1 1994 83 102

existence of a nontrivial solution for a class of hemivariational inequality problems at double resonance abstract in this paper we discuss a class of semilinear elliptic hemivariational inequality problems by using the nonsmooth minimax principle for locally lipschitz functions we establish the existence of a nontrivial solution for the semilinear elliptic hemivariational inequality problem where incomplete double resonance occurs at infinity between two distinct consecutive eigenvalues

existence and multiplicity results to neumann problems for elliptic equations involving the p laplacian abstract in this paper existence results of positive solutions to a neumann problem involving the p laplacian are established multiplicity results are also pointed out the approach is based on variational methods

on resonant neumann problems we consider semilinear neumann problems at resonance and prove existence and multiplicity theorems the existence theorems allow resonance with respect to any eigenvalue of the negative neumann laplacian the multiplicity theorems concern problems resonant at 0 the principal eigenvalue or at the first nonzero eigenvalue our approach uses tools from critical point theory and from morse theory

multiplicity of solutions for resonant neumann problems with an indefinite and unbounded potential we examine semilinear neumann problems driven by the laplacian plus an unbounded and indefinite potential the reaction is a caratheodory function which exhibits linear growth near we allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue and we prove several multiplicity results our approach uses critical point theory morse theory and the reduction method the lyapunov schmidt method