coupled fixed point results for ψ φ weakly contractive mappings in ordered g metric spaces in this paper we establish coupled coincidence and common coupled fixed point theorems for j f weakly contractive mappings in ordered g metric spaces presented theorems extend generalize and improve many existing results in the literature an example is given

on solutions of the initial value problem for the nonlinear schrodinger equations on considere le probleme aux valeurs initiales pour l equation de schrodinger non lineaire de la forme iu t u f u 2 u t x r r n u 0 x x x r n on etudie la regularite des solutions quand les fonctions initiales ne sont pas regulieres

on the derivative nonlinear schro dinger equation abstract in this paper we discuss the cauchy problem for the derivative nonlinear schrodinger equation i t 2i x 2 0 0 x x where 0 under an explicit smallness condition of the initial data we prove the unique global existence of solutions to this problem in the usual sobolev spaces in the weighted sobolev spaces and in the schwartz class we describe the smoothing effect in detail furthermore for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction

smoothing effects and dispersion of singularities for the schrodinger evolution group we describe smoothing effects and dispersion of singularities for the schrodinger evolution group in the weighted sobolev spaces under a fairly general assumption on the potential it is shown that all singularities in the wavefunction vanish instantly whenever the initial state has sufficient decay we measure the regularity gained by the wavefunction by the decay property of the initial state no assumptions on the regularity of the initial state are imposed throughout the paper

fixed point theorem for asymptotic contractions of meir keeler type in complete metric spaces abstract in this paper we introduce the notion of asymptotic contraction of meir keeler type and prove a fixed point theorem for such contractions which is a generalization of fixed point theorems of meir keeler and kirk in our discussion we use the characterization of meir keeler contraction proved by lim on characterizations of meir keeler contractive maps nonlinear anal 46 2001 113 120 we also give a simple proof of this characterization

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

global well posedness for schrodinger equation with derivative in h 1 2 r abstract in this paper we consider the cauchy problem of the cubic nonlinear schrodinger equation with derivative in h s r this equation was known to be the local well posedness for s 1 2 takaoka 1999 27 ill posedness for s 1 2 biagioni and linares 2001 1 etc and global well posedness for s 1 2 i team 2002 10 in this paper we show that it is global well posedness in the endpoint space h 1 2 r which remained open previously the main approach is the third generation i method combined with a new resonant decomposition technique the resonant decomposition is applied to control the singularity coming from the resonant interaction

on generalized weakly g contraction mapping in g metric spaces in this paper we establish some common fixed point results for two self mappings f and g on a generalized metric space x to prove our results we assume that f is a generalized weakly g contraction mapping of types a and b with respect to g

landau lifshitz and higher order nonlinear systems gauge generated from nonlinear schrodinger type equations new landau lifshitz ll and higher order nonlinear systems gauge generated from nonlinear schrodinger ns type equations are presented the consequences of gauge equivalence between different dynamical systems are discussed the gauge connections among various ll and ns equations are found and depicted through a schematic representation

on common fixed points in g metric spaces using e a property in this paper we introduce some new types of pairs of mappings f g on g metric spaces called g weakly commuting of type g f and g r weakly commuting of type g f we obtain also several common fixed point results by using the e a property

analyticity and global existence of small solutions to some nonlinear schrodinger equations in this paper we will study the nonlinear schrodinger equations begin gathered i partial t u tfrac 1 2 delta u left u right 2 u t x in mathbb r times mathbb r x n hfill u 0 x phi x x in mathbb r x n hfill end gathered it is shown that the solutions of exist and are analytic in space variables fort 0 if x h2n 1 2 xn decay exponentially as x andn 2

on cyclic meir keeler contractions in metric spaces abstract cyclic meir keeler contractions are considered under the recently introduced wuc and hw properties on pairs of subsets of metric spaces we show that in contrast with previous results in the theory best proximity point theorems under these properties do not directly extend from cyclic contractions to cyclic meir keeler contractions we obtain however a positive result for cyclic meir keeler contractions under additional properties which is shown to be an extension of already existing results for cyclic contractions moreover we give examples supporting the necessity of our additional conditions

global existence of small analytic solutions to nonlinear schrodinger equations in this paper we consider the following nonlinear schrodinger equation in r n n 2 i u 1 2 u f u u u t x er r n u 0 x x xer n

long range scattering for nonlinear schrodinger equations in one space dimension we consider the scattering problem for the nonlinear schrodinger equation in 1 1 dimensions open image in new window where x r 0 r p 3 we show that modified wave operators for exist on a dense set of a neighborhood of zero in the lebesgue spacel2 r or in the sobolev spaceh1 r the modified wave operators are introduced in order to control the long range nonlinearity u 2u

common fixed point results for noncommuting mappings without continuity in generalized metric spaces using the setting of a generalized metric space a fixed point theorem is proved for one map and several fixed point theorems are proved for two maps these results generalize several well known comparable results in the literature

common fixed point of mappings satisfying e a property in generalized metric spaces abstract in this paper using the setting of generalized metric spaces existence of unique common fixed point is established for mappings satisfying e a property under generalized strict contractive condition as well as under some generalized contractions obtained results are proper extensions of the existing ones in metric space we also provide example to support concepts and results presented herein

on solutions of the initial value problem for the nonlinear schrodinger equations in one space dimension t 0 xe has a regularizing property that the solutions become smooth instantly for t 0 even if their initial data are not smooth for example in l n our aim of this paper is to show that the nls equation 1 1 1 2 has a similar regularizing effect more precisely all solutions of finite energy to 1 1 1 2 are smooth for tq 0 provided the initial functions in hi n or in

invariants in a resonant derivative nonlinear schrodinger model a broad class of derivative nonlinear schrodinger equations which incorporate a de broglie bohm type quantum potential is considered it is shown that a wave packet ansatz inserted into these equations leads to an integrable hamiltonian dynamical sub system

global solvability of the derivative nonlinear schrodinger equation the derivative nonlinear schrodinger equation dnls iqt qxx q q2 x i q x t i a77xr z jffjt was first derived by plasma physicists 9 10 this equation was used to in terpret the propagation of circular polarized nonlinear alfven waves in plasma kaup and newell obtained the soliton solutions of dnls in 1978 5 the au thor obtained the local solvability of dnls in his dissertation 6 in this paper we obtain global existence in time of schwartz class solutions of dnls if the z 2 norm of the generic initial data q x 0 is bounded

generalized meir keeler type contractions on g metric spaces in this manuscript we introduce generalized meir keeler type contractions over g metric spaces moreover we show that every orbitally continuous generalized meir keeler type contraction has a unique fixed point on complete g metric spaces we illustrate our results by some given examples

coupled fixed point theorems for a generalized meir keeler contraction in partially ordered metric spaces abstract let x be a non empty set and f x x x be a given mapping an element x y x x is said to be a coupled fixed point of the mapping f if f x y x and f y x y in this paper we consider the case when x is a complete metric space endowed with a partial order we define generalized meir keeler type functions and we prove some coupled fixed point theorems under a generalized meir keeler contractive condition some applications of our obtained results are given the presented theorems extend and complement the recent fixed point theorems due to bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

coupled common fixed point results in two generalized metric spaces in this paper study of necessary conditions for the existence of unique coupled common fixed point of contractive type mappings in the context of two generalized metric spaces is initiated these results generalize several comparable results from the current literature we also provide illustrative examples in support of our new results

best proximity point theorems for cyclic orbital meir keeler contraction maps abstract we introduce a notion of cyclic orbital meir keeler contraction and give sufficient conditions for the existence of fixed points and best proximity points of such a map our main result is a generalization of a best proximity point result due to di bari et al c di bari t suzuki c vetro best proximity points for cyclic meir keeler contractions nonlinear anal 69 2008 3790 3794