periodic solutions of the lienard equation with one sided growth restrictions in this article we are concerned with the problem of the existence of periodic solutions to the periodically forced scalar lienard equation x f x x g x e t d dt 1 where f g e r r are continuous functions and e is periodic we are looking for solutions of 1 having the same period of the forcing term e throughout the paper we assume without loss of generality see e g 22 36 p 693 that

periodic solutions of forced lienard equations with jumping nonlinearities under nonuniform conditions this paper is devoted to the existence of periodic solutions for the scalar forced lienard differential equation the key assumptions relate the asymptotic behaviour as x of g t x x to the critical values of the positively 1 homogeneous problem no condition on f except continuity is assumed our approach is based on leray schauder degree techniques and a priori estimates

nonresonance conditions for asymptotically positively homogeneous differential systems the fucik spectrum and its generalization in this article we propose how to define the fucik spectra for differential systems in rnwith jumping nonlinearities the propertyp a generalization of the non fucik spectra to positively homogeneous nonautonomous differential systems is also defined in the most general setting a quantitative estimate result concerning the parameterized completely continuous positively homogeneous perturbations of the identity in banach spaces is given in this article such a result is a generalization of one property in the spectrum theory for completely continuous linear operators using this estimate result we will give some significantly improved nonresonance results from the fucik spectra and propertypfor asymptotically positively homogeneous differential systems

quadratic forms weighted eigenfunctions and boundary value problems for non linear second order ordinary differential equations some known results for different kinds of boundary value problems for second order ordinary differential equations are generalised different approaches are compared with one another using topological and variational methods and the theory of weighted eigenvalue problems

existence of one signed periodic solutions of some second order differential equations via a krasnoselskii fixed point theorem this paper is devoted to study the existence of periodic solutions of the second order equation x 00 f t x where f is a caratheodory function by combining some new properties of green s function together with krasnoselskii fixed point theorem on compression and expansion of cones as applications we get new existence results for equations with jumping nonlinearities as well as equations with a repulsive or attractive singularity in this latter case our results cover equations with weak singularities and are compared with some recent results by i rachunkova m tvrdyand i vrkoc r 2002 elsevier science usa all rights reserved

stability and evolution of solitary waves in perturbed generalized nonlinear schrodinger equations in this paper we study the stability and evolution of solitary waves in perturbed generalized nonlinear schrodinger nls equations our method is based on the completeness of the bounded eigenstates of the associated linear operator in l2 space and a standard multiple scale perturbation technique unlike the adiabatic perturbation method our method details all instability mechanisms caused by perturbations of such equations and explicitly specifies when such instabilities will occur in particular our method uncovers the instability caused by bifurcation of nonzero discrete eigenvalues of the linearization operator as an example we consider the perturbed cubic quintic nls equation in detail and determine the stability regions of its solitary waves in the instability region we also specify where the solitary waves decay collapse develop movingfronts or evolve into a stable spatially localized and temporally periodic state the generalization of this method to other perturbed nonlinear wave systems is also discussed

stability and evolution of the quiescent and travelling solitonic bubbles abstract we simulate numerically the dynamics of the bubble like solitons of the cubic quintic nonlinear schrodinger equation in agreement with earlier predictions slow moving bubbles have been observed to be unstable in contrast to rapid bubbles which stabilize above a certain critical velocity the empirical formula for the critical velocity has been confirmed to a high degree of accuracy based on the choice of some critical perturbation we derive an integral criterion for stability of kinks and bubbles of the general nonlinear schrodinger equation which provides an explanation of the appearance of the critical velocity finally we follow numerically the nonlinear evolution of the unstable bubbles in one two and three dimensions

on the peroidic bvp for the forced duffing equation with jumping nonlinearity on etudie le probleme suivant u cu f t u e t p p sur 0 t u t u 0 0 u t u 0 0 c est une fonction arbitraire dans l 1 0 t r c r et l application non lineaire f est a saut

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

a continuation approach to superlinear periodic boundary value problems this paper deals with the problem of the existence of t periodic solutions for the first order differential system x i t x 1 1 where f 0 t x r r is a caratheodory function in what follows we prove some results for the solvability of the periodic bvp in the case when the dimension of the space is even such a limitation is motivated by our interest in applications to the second order equation d g t u u o 1 2 which takes the form of 1 1 when it is written as the equivalent system u v 0 g t u v 1 3

computer simulation of wave collapses in the nonlinear schro dinger equation abstract the self tuning numerical scheme for simulation of collapse phenomena in the framework of the nonlinear schrodinger equation is developed the scheme allows to reach extremely high field amplitudes 2 0 2 10 15 without lack of validity numerical results are compared with analytical predictions

an explicit method with improved stability property a new explicit method is presented this method has an enhanced stability property when compared with the previously published explicit method j eng mech 2007 133 7 748 760 which is unconditionally stable for linear elastic and any instantaneous stiffness softening systems based on linearized analysis whereas it is only conditionally stable for any instantaneous stiffness hardening system in contrast to the previously published explicit method the most important improvement of the new explicit method is that it can have unconditional stability for general instantaneous stiffness hardening systems in addition to linear elastic and instantaneous stiffness softening systems since these stability results are obtained from a linearized stability analysis they are applicable to the non linear systems that satisfied the simplifications used for the analysis this explicit method is also shown to be second order accurate it is computationally efficient in the solution of a general structural dynamic problem where the total response is dominated by low frequency modes when compared with explicit methods such as the newmark explicit method and the family of explicit methods developed by tamma et al comput methods appl mech eng 2003 192 257 290 and implicit methods such as the constant average acceleration method some numerical examples are used to confirm the enhanced stability property and the efficiency in computing copyright 2008 john wiley sons ltd

a new fixed point theorem and periodic solutions of nonconservative weakly coupled systems abstract in this paper we prove a new fixed point theorem for the coupling of twist conditions and poincare bohl type conditions as its applications we prove the existence of periodic solutions for various nonconservative mixed type weakly coupled systems

eigenvalue cutoff in the cubic quintic nonlinear schrodinger equation using theoretical arguments we prove the numerically well known fact that the eigenvalues of all localized stationary solutions of the cubic quintic 2 1 dimensional nonlinear schr odinger equation exhibit an upper cutoff value the existence of the cutoff is inferred using gagliardo nirenberg and h older inequalities together with pohozaev identities we also show that in the limit of eigenvalues close to zero the eigenstates of the cubic quintic nonlinear schr odinger equation behave similarly to those of the cubic nonlinear schr odinger equation

existence and localization of solution for second order elliptic bvp in presence of lower and upper solutions without any order abstract we prove an existence and localization result for a solution of a second order elliptic equations with dirichlet and regular oblique derivative boundary conditions the main result is obtained assuming the existence of a lower and an upper solution without particular order and a positively homogeneous asymptotic behaviour of the right hand member of the equation

periodic solutions for some nonlinear differential equations of neutral type where f ir x ir ir is a caratheodory function f x is 2n periodic for every x ci e r and r e io 2n this problem has been studied by sadovskii in 151 by hale and mawhin in 6 in the case ial 1 to the previous one our interest is particularly motivated by the fact that represents a simple and meaningful model for a general phenomenon which often arises in the study of functional differential equations in fact as is well known in some cases a delayed differential equation can be seen as a perturbation of an ordinary differential equation in particular this occurs when the delayed term in the equation can be considered smaller than the ordinary one or dominated by it when such domination is available many good properties can be proved and several results such as those of 6 and 16 take advantage of this fact on the contrary when no domination is present the situation is much more complicated and in general very little is known in problem the delayed term can be considered dominated by the ordinary one whenever ial 1 as a matter of fact in this case one can prove the invertibility of the differential operator l x x a r ux the compactness of its inverse and even some a priori estimates for the solutions consequently one can reduce to a fixed point problem and solve it by means of some topological degree argument however when 11 1 so that the weight of the two terms x t and x t t is the same the above properties fail and moreover for some delays the kernel of the differential operator lx x a r is infinite dimensional therefore one must look for different methods problem is thus a simple but nevertheless significant example of the considerations illustrated by hale in 5 about the difficulty of undertaking a unified approach in the study of functional differential equations at the same time it provides an analogy between neutral equations and the wave equation in the line suggested by hale in 5

periodic solutions for ordinary differential equations with sublinear impulsive effects abstract the continuation method of topological degree is used to investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects the applications of the abstract approach include the generalizations of some classical nonresonance theorem for impulsive equations for instance the existence theorem for asymptotically positively homogeneous differential systems and the existence theorem for second order equations with landesman lazer conditions

on periodic solutions of nonlinear second order vector differential equations this paper considers existence of periodic solutions for vector lienard differential equations in our main result we write where q t x is a symmetric matrix and h t x is sublinear the key assumption relates the asymptotic behaviour as x of the eigenvalues of q t x to the spectrum of the linear operator d 2 dt 2 several choices for q t x are considered which lead to known theorems and extend others in the case of the duffing equation the assumptions are weakened our approach is based on leray schauder s degree theory and a priori estimates

nonuniform nonresonance of semilinear differential equations abstract consider the dirichlet problem of nonlinear differential equations with the principal part the p laplacian when the nonlinearity satisfies some semilinearity conditions the usual nonuniform nonresonance conditions are obtained by comparing nonlinear equations with the classical eigenvalues in this article we will introduce some weighted eigenvalues the nonuniform nonresonance conditions proved in this article using weighted eigenvalues will improve the usual ones significantly

bifurcation surfaces stemming from the fucik spectrum abstract let r n be a bounded domain with smooth boundary and g r r be a nonlinear function we prove existence of two dimensional bifurcation surfaces for the elliptic boundary value problem u a u b u g x u in u 0 where u min 0 u u max 0 u and a b r 2 is a pair of parameters we show that these two dimensional bifurcation surfaces stem from the fucik spectrum of the main difficulty in doing that comes from non smoothness of the operators u u in order to overcome this difficulty a variant implicit function theorem and an abstract two dimensional bifurcation theorem are proved these two theorems do not require smoothness of operators and the abstract two dimensional bifurcation theorem can be regarded as an extension of the well known crandall rabinowitz bifurcation theorem and therefore are of interest for their own sake

resonant and nonresonant oscillations for some third order nonlinear ordinary differential equations on etudie l existence de solutions 2 periodiques des equations differentielles d ordre 3 x ax bx g t x p t x x x x ax bx t x x x x p t x x x x ax f x x g t x p t x x x

existence of periodic solutions of duffing equations on considere le probleme aux valeurs limites periodiques de type duffing u t ku t g t u t f t t 0 2 u 0 u 2 u 0 u 2 on demontre un resultat d existence general qui montre que si la croissance de g t u a l infini appartient a un ensemble avec la propriete p alors pour tout f l 1 0 2 le probleme a au moins une solution