positive soliton solutions for generalized quasilinear schrodinger equations with critical growth this paper is concerned with the positive solutions for generalized quasilinear schrodinger equations in rn with critical growth which have appeared from plasma physics as well as high power ultrashort laser in matter by using a change of variables and variational argument we obtain the existence of positive solutions for the given problem

stability and bifurcation for a delayed predator prey model and the effect of diffusion abstract we consider a predator prey system with one or two delays and a unique positive equilibrium e its dynamics are studied in terms of the local stability of e and of the description of the hopf bifurcation that is proven to exist as one of the delays taken as a parameter crosses some critical values we also consider a reaction diffusion system with neumann conditions resulting from adding one spatial variable and diffusion terms in the previous model the spectral and bifurcation analysis in the neighborhood of e now as a stationary point of this latter system is addressed and the results obtained for the case without diffusion are applied

positive steady states of the holling tanner prey predator model with diffusion this paper is concerned with the holling tanner prey predator model with diffusion subject to the homogeneous neumann boundary condition we obtain the existence and non existence of positive non constant steady states

dynamics in a diffusive predator prey system with ratio dependent predator influence abstract a diffusive predator prey system with predator functional response subject to neumann boundary conditions is considered existence nonexistence and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation hopf and steady state bifurcation analyses are carried out in detail these results provide theoretical evidences to the complex spatio temporal dynamics found by numerical simulation

the discrete frenkel kontorova model and its extensions i exact results for the ground states abstract we present a rigorous study of the classical ground states under boundary conditions of a class of one dimensional models generalizing the discrete frenkel kontorova model the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic quasi periodic and chaotic orbits for all boundary conditions we select among all the extremum solutions of the energy of the model those which correspond to the ground states of the infinite system we prove that these ground states are either periodic commensurate or quasi periodic incommensurate but are never chaotic we also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions the topological structure of the whole set of ground states is described in details in addition to physical applications consequences for twist map homeomorphisms are mentioned part ii s aubry p y ledaeron and g andre will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map

global stability for a class of predator prey systems this paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator prey systems the dulac s criterion is applied and liapunov functions are constructed to establish the global stability

existence of c 1 critical subsolutions of the hamilton jacobi equation let m be a c second countable manifold without boundary we denote by tm the tangent bundle and by tm m the canonical projection a point in tm will be denoted by x v with x m and v tx m 1 x in the same way a point of the cotangent space t m will be denoted by x p with x m and p t x m a linear form on the vector space tx m we will suppose that g is a complete riemannian metric on m for v tx m the norm v is g v v 1 2 we will denote by the dual norm on t x m we will also use the notations v x for v tx m and p x for v t x m we will assume in the whole paper that h t m r is a function of class at least c2 which satisfies the following three conditions 1 uniform superlinearity for every k 0 there exists c k r such that

towards a quantum analog of weak kam theory we discuss a quantum analogue of mather s minimization principle for lagrangian dynamics and provide some formal calculations suggesting the corresponding euler lagrange equation we then rigorously construct from the dual eigenfunctions of a certain non selfadjoint operator a candidate for a minimizer and recover aspects of weak kam theory in the limit as h 0 regarding our state as a quasimode we furthermore derive some error estimates although it remains an open problem to improve these bounds

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

rotation entropy and equilibrium states for a dynamical system x t and function f x rd we consider the corresponding generalised rotation set this is the convex subset of rd consisting of all integrals of f with respect to t invariant probability measures we study the entropy h e of rotation vectors e and relate this to the directional entropy lhl l of geller misiurewicz for x t a mixing subshift of finite type and f of summable variation we prove that if the rotation set is strictly convex then the functions h and h are in fact one and the same for those rotation sets which are not strictly convex we prove that 1h e and h e can differ only at non exposed boundary points e

decay estimates and strichartz estimates of fourth order schrodinger operator abstract we study time decay estimates of the fourth order schrodinger operator h 2 v x in r d for d 3 and d 5 we analyze the low energy and high energy behaviour of resolvent r h z and then derive the jensen kato dispersion decay estimate and local decay estimate for e i t h p a c under suitable spectrum assumptions of h based on jensen kato type decay estimate and local decay estimate we obtain the l 1 l estimate of e i t h p a c in 3 dimension by ginibre argument and also establish the endpoint global strichartz estimates of e i t h p a c for d 5 furthermore using the local decay estimate and the georgescu larenas soffer conjugate operator method we prove the jensen kato type decay estimates for some functions of h

steady states of a leslie gower model with diffusion and advection abstract this paper focuses on a stationary leslie gower model with diffusion and advection firstly some existence conditions of nonconstant positive solutions are obtained by means of the leray schauder degree theory as diffusion and advection of one of the species both tend to infinity we obtain a limiting system which is a semi linear elliptic equation with nonlocal constraint in the simplified 1d case the global bifurcation structure of nonconstant solutions of the limiting system is classified

bifurcation and spatiotemporal patterns in a homogeneous diffusive predator prey system abstract a diffusive predator prey system with holling type ii predator functional response subject to neumann boundary conditions is considered hopf and steady state bifurcation analysis are carried out in details in particular we show the existence of multiple spatially non homogeneous periodic orbits while the system parameters are all spatially homogeneous our results and global bifurcation theory also suggest the existence of loops of spatially non homogeneous periodic orbits and steady state solutions these results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulation

a diffusive predator prey model in heterogeneous environment abstract in this paper we demonstrate some special behavior of steady state solutions to a predator prey model due to the introduction of spatial heterogeneity we show that positive steady state solutions with certain prescribed spatial patterns can be obtained when the spatial environment is designed suitably moreover we observe some essential differences of the behavior of our model from that of the classical lotka volterra model that seem to arise only in the heterogeneous case

analysis on the existence of the steady states for an ecological mathematical model with predator prey dependent functional response abstract we establish a reaction diffusion ecological mathematical model with predator prey dependent functional response and the neumann boundary conditions first we study the bifurcation solution emitting from the unique positive constant solution by considering the local bifurcation finally we mainly analyze the coexistence of the prey and predator with the help of the fixed point index theory where we use a different approach in calculating one of the fixed point indices

non constant positive steady states of a diffusive predator prey system in homogeneous environment abstract in this paper we investigate the existence and non existence of non constant positive steady states of a diffusive predator prey interaction system under homogeneous neumann boundary condition in homogeneous environment we show that the predator prey model with leslie gower functional response has no non constant positive solution but the system with a general functional response may have at least one non constant positive steady state under some conditions

bifurcations in a predator prey system of leslie type with generalized holling type iii functional response abstract we consider a predator prey system of leslie type with generalized holling type iii functional response p x m x 2 a x 2 b x 1 by allowing b to be negative b 2 a p x is monotonic for b 0 and nonmonotonic for b 0 when x 0 the model has two non hyperbolic positive equilibria one is a multiple focus of multiplicity one and the other is a cusp of codimension 2 for some values of parameters and a degenerate bogdanov takens singularity focus or center case of codimension 3 for other values of parameters when there exist a multiple focus of multiplicity one and a cusp of codimension 2 we show that the model exhibits subcritical hopf bifurcation and bogdanov takens bifurcation simultaneously in the corresponding small neighborhoods of the two degenerate equilibria respectively different phase portraits of the model are obtained by computer numerical simulations which demonstrate that the model can have i a stable limit cycle enclosing two non hyperbolic positive equilibria ii a stable limit cycle enclosing an unstable homoclinic loop iii two limit cycles enclosing a hyperbolic positive equilibrium iv one stable limit cycle enclosing three hyperbolic positive equilibria or v the coexistence of three stable states two stable equilibria and a stable limit cycle when the model has a bogdanov takens singularity of codimension 3 we prove that the model exhibits degenerate focus type bogdanov takens bifurcation of codimension 3 these results not only demonstrate that the dynamics of this model when b 2 a are much more complex and far richer than the case when b 0 but also provide new bifurcation phenomena for predator prey systems

propagation in hamiltonian dynamics and relative symplectic homology the main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating hamiltonian is sufficiently large over the zero section the proof is based on floer homology and on the notion of a relative symplectic capacity applications include results about propagation properties of sequential hamiltonian systems periodic orbits on hypersurfaces hamiltonian circle actions and smooth lagrangian skeletons in stein manifolds

diffusion self diffusion and cross diffusion u1 x 0 u 1 0 x u2 x 0 u 2 0 x i n 0 where 2 n 1 2 x 2 is the laplace operator 0 is a bounded smooth domain of r n with n1 0 and 0 are the boundary and the closure of 0 respectively 0t 0 0 t and 0t 0 0 t for some t 0 is the outward unit normal vector on 0 di ai bi ci i 1 2 are all positive constants while ij i j 1 2 denote non negative constants the initial values u1 0 and u2 0 are non negative smooth func tions which are not identically zero the mathematical model 1 1 was proposed by shigesada et al 27 in their study of spatial segregation of interacting species where u1 and u2 represent the densities of two competing species d1 and d2 are their diffu sion rates a1 and a2 denote the intrinsic growth rates b1 and c2 account for intra specific competitions b2 and c1 are the coefficients of inter specific competitions 11 and 22 are usually referred as self diffusion pressures and 12 and 21 are cross diffusion pressures an interesting feature of 1 1 is that the movements of these two competing species are affected by the population pressures due to the mutual interference between the individuals and it was hoped that the nonlinear dispersive force due to the

convergence of the solutions of the discounted hamilton jacobi equation we consider a continuous coercive hamiltonian h on the cotangent bundle of the compact connected manifold m which is convex in the momentum if u lambda m rightarrow mathbb r is the viscosity solution of the discounted equation begin aligned lambda u lambda x h x mathrm d x u lambda c h end aligned where c h is the critical value we prove that u lambda converges uniformly as lambda rightarrow 0 to a specific solution u 0 m rightarrow mathbb r of the critical equation begin aligned h x mathrm d x u c h end aligned we characterize u 0 in terms of peierls barrier and projected mather measures as a corollary we infer that the ergodic approximation as introduced by lions papanicolaou and varadhan in 1987 in their seminal paper on homogenization of hamilton jacobi equations selects a specific corrector in the limit

stability and bifurcation in a reaction diffusion model with nonlocal delay effect in this paper the existence stability and multiplicity of spatially nonhomogeneous steady state solution and periodic solutions for a reaction diffusion model with nonlocal delay effect and dirichlet boundary condition are investigated by using lyapunov schmidt reduction moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

weak liouville arnol d theorems and their implications this paper studies the existence of invariant smooth lagrangian graphs for tonelli hamiltonian systems with symmetries in particular we consider tonelli hamiltonians with n independent but not necessarily involutive constants of motion and obtain two theorems reminiscent of the liouville arnol d theorem moreover we also obtain results on the structure of the configuration spaces of such systems that are reminiscent of results on the configuration space of completely integrable tonelli hamiltonians

stability and hopf bifurcation in a diffusive logistic population model with nonlocal delay effect abstract a reaction diffusion model with logistic type growth nonlocal delay effect and dirichlet boundary condition is considered and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior the stability of the positive spatially nonhomogeneous positive equilibrium and associated hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel

dynamics near an isolated m semi static homoclinic orbit abstract we show that there are infinitely many periodic orbits in any neighborhood of an isolated m semi static orbit homoclinic to an aubry set for time periodic positive lagrangian systems

the bifurcation structure of the holling tanner model for predator prey interactions using two timing the holling tanner model for predator prey systems has two hopf bifurcation points for certain parameters the dependence of the environmental parameters on the underlying bifurcation structure is uncovered using two timing emphasis is on how the bifurcation diagram changes as the hopf bifurcation points separate two degenerate cases require a modification of conventional two timing when the two hopf bifurcation points nearly coalesce the two stable periodic solution branches are shown to be connected as a ratio of linear growth rates varies the hopf bifurcation points separate further and one limit cycle becomes unstable this situation can correspond to an outbreak in populations the modified two timing analysis analytically captures the unstable and stable limit cycles of the new branch

birkhoff periodic orbits for small perturbations of completely integrable hamiltonian systems with convex hamiltonians pour des systemes a n degres de liberte on montre l existence d au moins n orbites periodiques distinctes avec un vecteur frequence rationnel admissible proche du tore correspondant du systeme non perturbe sous l hypothese que le hamiltonien du systeme non perturbe a des surfaces d energie convexes pour les variables action angle

one dimensional variational problems whose minimizers do not satisfy the euler lagrange equation in this paper we consider the problem of minimizing i u text int a b text f x u x u x dx 1 1 in the set a of absolutely continuous function u a b satisfying the end conditions u left a right text alpha text quad u left b right text beta text 1 2 where and are given constant in 1 1 a b is a finite interval denotes frac d dx and the integrand f f x u p is assumed to be smooth nonnegative and to satisfy the regularity condition f pp text 0 text 1 3

normal forms and hopf bifurcation for partial differential equations with delays the paper addresses the computation of normal forms for some partial functional differential equations pfdes near equilibria the analysis is based on the theory previously developed for autonomous retarded functional differential equations and on the existence of center or other invariant manifolds as an illustration of this procedure two examples of pfdes where a hopf singularity occurs on the center manifold are considered

spatiotemporal dynamics in a diffusive ratio dependent predator prey model near a hopf turing bifurcation point abstract spatiotemporal dynamics in a ratio dependent predator prey model with diffusion is studied by analytical methods normal forms associated with codimension two hopf turing bifurcation are derived which can be used to understand and classify the spatiotemporal dynamics of the model for values of parameters close to the hopf turing bifurcation point in the vicinity of this degenerate point a wealth of complex spatiotemporal dynamics are observed our theoretical results are confirmed by numerical simulations

global bifurcation analysis and pattern formation in homogeneous diffusive predator prey systems abstract the dynamics of a general diffusive predator prey system is considered existence and nonexistence of non constant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as non constant steady state solutions are studied

on m semi static homoclinic orbits abstract we study m semi static homoclinic orbits to aubry sets in positive definite lagrangian systems