on multiple solutions of a semilinear schrodinger equation with periodic potential abstract this paper is concerned with the semilinear schrodinger equation s u v x u f x u u h 1 r n where v and f are periodic in the x variables f is a superlinear and subcritical nonlinearity and 0 lies in a spectral gap of u v it is shown that if f is odd in u then s has infinitely many large energy solutions the proof relies on a generalized variant fountain theorem for strongly indefinite functionals established in this paper

cantor families of periodic solutions for wave equations via a variational principle abstract we prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a cantor set of asymptotically full measure via a variational principle a lyapunov schmidt decomposition reduces the problem to a finite dimensional bifurcation equation variational in nature defined on a cantor set of non resonant parameters the cantor gaps are due to small divisors phenomena to solve the bifurcation equation we develop a suitable variational method in particular we do not require the typical arnold non degeneracy condition of the known theory on the nonlinear terms as a consequence our existence results hold for new generic sets of nonlinearities

periodic second order superlinear hamiltonian systems abstract we consider periodic solutions for superlinear second order non autonomous dynamical systems including both kinetic and potential terms we study the existence of nontrivial and ground state solutions

local linearization filters for non linear continuous discrete state space models with multiplicative noise in this paper the local linearization method for the approximate computation of the prediction and filtering estimates of continuous discrete state space models is extended to the general case of non linear non autonomous models with multiplicative noise the approximate prediction and filter estimates are obtained by applying the optimal linear filter to the piecewise linear state space model that emerges from a local linearization of both the non linear state equation and the non linear measurement equation in addition the solutions of the differential equations that describe the evolution of the first two conditional moments between observations are obtained and an algorithm for their numerical computation is also given the performance of the ll filters is illustrated by mean of numerical experiments

su 3 chern simons vortex theory and toda systems motivated by the study of the asymptotic properties of non topological condensates in the non abelian chern simons vortex theory see 26 we analyze the su 3 toda system p 1 2 zj j e 2i 1kijzi me i 12kijzi 1 on m mzj 0j 1 2 where m r2 z2 k kij 2 1 12 is the su 3 cartan matrix and j are positive parameters we study the variational problem associated with the system p 1 2 in a range of parameters where the trivial solution is a strict local minimum and the corresponding sobolev type inequality fails to apply in this situation a lack of compactness may occur due to concentration phenomena nonetheless we are able to establish the existence of a non trivial solution for p 1 2 which is not a minimizer

on nonlinear schrodinger poisson equations with general potentials abstract we study the existence of infinitely many finite energy radial solutions to the nonlinear schrodinger poisson equations u u x u f u 0 in r 3 u 2 0 lim x x 0 in r 3 nspe for short under some structure conditions on the nonlinearity function f as consequences of the main result we can provide examples of f which guarantee the existence of infinitely many finite energy solutions but i f t grows faster than t 2 and slower than t p for all p 2 or ii f t is the same as t t when t t 0 for arbitrarily given t 0 0 if f t t p 1 t it is known that nspe admits no finite energy nontrivial solutions when p 1 2 and admits infinitely many finite energy solutions when p 2 5 so examples i and ii show some interesting features of nspe

superlinear schrodinger operators abstract we find nontrivial and ground state solutions for the nonlinear schrodinger equation under conditions weaker than those previously assumed

on a free boundary problem for minimal surfaces forc 4 embedded manifoldss 3 which are differmorphic to the standard sphere in 3 the existence of non constant minimal surfaces bounded bys and intersectings orthogonally along their boundaries is deduced

stationary partitioning of convex bodies on considere une version particuliere du probleme de partage soit 7b b un corps convexe dans r 3 de volume m 3 7b b une surface de type disque s est a l interieur de 7b b divisant cet interieur en deux cellules simplement connexes 7b b et 7b b de volumes m 3 7b b m 3 7b b m 3 7b b 1 m 3 7b b 0 1 on considere comme fixee et on etudie les cas ou s a l aire la plus petite possible

large solutions for harmonic maps in two dimensions we seek critical points of the functionale u mathop smallint limits omega u 2 where is the unit disk in 2 andu s2 satisfies the boundary conditionu on we prove that if is not a constant thene has a local minimum which is different from the absolute minimum we discuss in more details the case where x y rx ry sqrt 1 r 2 andr 1

a direct method for minimizing the yang mills functional over 4 manifolds a direct method is employed to minimize the yang mills functional over a 4 dimensional manifold the limiting connection is shown to be yang mills but in a possibly new bundle we show that a topological invariant of the bundle is preserved by the minimizing process this implies the existence of an absolute minimum of the yang mills functional in a wide class of bundles

multiple solutions of h systems and rellich s conjecture soit x y r 2 x 2 y 2 1 on considere une fonction u r 3 satisfaisant le systeme h u 2hu x u y sur avec l une des conditions suivantes soit dirichlet u sur soit plateau u x 2 u y 2 u x u y 0 sur u et u non decroissante sur

properties of the matrix a xy abstract the main topic of this paper is the matrix v a xy where a is a nonsingular complex k k matrix and x and y are k p complex matrices of full column rank because properties of the matrix v can be derived from those of the matrix q i xy we will consider in particular the case where a i for the case that y x i so that q is singular we will derive the moore penrose inverse of q the moore penrose inverse of v in case y a 1 x i then easily follows finally we will focus on the eigenvalues and eigenvectors of the real matrix d xy with d diagonal

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2