nilpotent and high order approximations of vector field systems this paper is concerned with the study of structurally stable properties associated with systems described by one or several real analytic vector fields via approximating systems which retain inf

averaging results and the study of uniform asymptotic stability of homogeneous differential equations that are not fast time varying within the liapunov framework a sufficient condition for uniform asymptotic stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the v function taken along solutions of the system may have positive and negative values it is shown that the proposed condition is useful for the study of uniform asymptotic stability of homogeneous systems with order tau 0 in particular it is established that asymptotic stability of the averaged homogeneous system implies local uniform asymptotic stability of the original time varying homogeneous system this shows that averaging techniques play a prominent role in the study of homogeneous not necessarily fast time varying systems

tdgl and mkdv equations for jamming transition in the lattice models of traffic abstract the lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena they are the lattice versions of the hydrodynamic model of traffic two lattice models are presented one is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other is the difference equation in which both time and space variables are discrete we apply the linear stability theory and the nonlinear analysis to the lattice models it is shown that the time dependent ginzburg landau tdgl equation is derived to describe the traffic flow near the critical point a thermodynamic theory is formulated for describing the phase transitions and critical phenomena it is also shown that the perturbed modified korteweg de vries mkdv equation is derived to describe the traffic jam

an averaging theorem for time periodic degree zero homogeneous differential equations abstract this paper considers the stability of the differential equation dot x ex t x e x r n where x t x e is a time periodic degree zero homogeneous vector field and e 0 is a parameter it is shown that asymptotic stability of the time averaged equation implies asymptotic stability of the original system for e sufficiently small

analysis of car following model considering driver s physical delay in sensing headway abstract an extended car following model is proposed by taking into account the delay of the driver s response in sensing headway the stability condition of this model is obtained by using the linear stability theory the results show that the stability region decreases when the driver s physical delay in sensing headway increases the kdv equation and mkdv equation near the neutral stability line and the critical point are respectively derived by applying the reductive perturbation method the traffic jams could be thus described by soliton solution and kink antikink soliton solution for the kdv equation and mkdv equation respectively the numerical results in the form of the space time evolution of headway show that the stabilization effect is weakened when the driver s physical delay increases it confirms the fact that the delay of driver s response in sensing headway plays an important role in jamming transition and the numerical results are in good agreement with the theoretical analysis

mean field flow difference model with consideration of on ramp and off ramp abstract in this paper an extended lattice hydrodynamic model is proposed by incorporating the effects of mean field flow difference on ramp and off ramp the linear stability condition is obtained through linear stability theory and the mkdv equation is derived by using nonlinear analysis method therefore the propagation behavior of traffic jam can be described by the kink antikink soliton solution of the mkdv equation furthermore the theoretical findings are verified with the use of numerical simulation which confirms that the stability of traffic flow can be efficiently improved with the consideration of the effects of mean field flow difference on ramp and off ramp

modeling and application analysis of car following model with predictive headway variation abstract this work proposes an improved microscopic model by taking the predictive driving behavior of the preceding car into account firstly we use the linear method to investigate performance of the proposed model deduce the critical linear stability conditions and obtain a neutral curve accounting for stability of the new model then using the nonlinear analysis technique we derive the equations of burgers the korteweg de vries kdv and the modified kdv mkdv respectively to describe the triangular shock wave soliton density wave and the kink antikink density wave finally numerical experiments unfold from two aspects one for verifying the theoretical analysis results and another for testing the impact of predictive driving behavior of the preceding car on traffic stability simulation results show that the new model can stabilize traffic flow compared with the fvd model and confirm that the existence of three kinds of density waves in different phase diagram regions

analysis of social optimum for staggered shifts in a single entry traffic corridor with no late arrivals abstract this paper investigates the traffic flow dynamics under the social optimum so principle in a single entry traffic corridor with staggered shifts from the analytical and numerical perspectives the lwr lighthill whitham and richards model and the greenshield s velocity density function are utilized to describe the dynamic properties of traffic flow the closed form so solution is analytically derived and some numerical examples are used to further testify the analytical solution the optimum proportion of the numbers of commuters with different desired arrival times is further discussed where the analytical and numerical results both indicate that the cumulative outflow curve under the so principle is piecewise smooth

asymptotic solutions for a multi anticipative car following model abstract using a long wave expansion we study the asymptotic solutions near a critical point of a multi anticipative car following model a suitable rescaling of the variables then yields a modified korteweg de vries mkdv equation with higher order corrections an equation of this general form has already been investigated in detail in case of a simple model which allows us to use these results we are thus led to the conclusion that the characteristic features of the multi interaction model in the congested state can be obtained from the simple model by appropriately scaling the results

an asymmetric full velocity difference car following model abstract this paper presents a car following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream the problems of the prevalent general force gf model and the full velocity difference fvd model were solved furthermore the optimal velocity ov model the gf model and the fvd model are proved to be the special cases of the proposed asymmetric full velocity difference afvd model the mathematical model is presented followed by simulation analysis which demonstrates the properties of the afvd model

a new car following model for autonomous vehicles flow with mean expected velocity field abstract due to the development of the modern scientific technology autonomous vehicles may realize to connect with each other and share the information collected from each vehicle an improved forward considering car following model was proposed with mean expected velocity field to describe the autonomous vehicles flow behavior the new model has three key parameters adjustable sensitivity strength factor and mean expected velocity field size two lemmas and one theorem were proven as criteria for judging the stability of homogeneousautonomous vehicles flow theoretical results show that the greater parameters means larger stability regions a series of numerical simulations were carried out to check the stability and fundamental diagram of autonomous flow from the numerical simulation results the profiles hysteresis loop and density waves of the autonomous vehicles flow were exhibited the results show that with increased sensitivity strength factor or field size the traffic jam was suppressed effectively which are well in accordance with the theoretical results moreover the fundamental diagrams corresponding to three parameters respectively were obtained it demonstrates that these parameters play almost the same role on traffic flux i e before the critical density the bigger parameter is the greater flux is and after the critical density the opposite tendency is in general the three parameters have a great influence on the stability and jam state of the autonomous vehicles flow

analysis of optimal velocity model with explicit delay we analyze the optimal velocity model ovm with explicit delay the properties of congestion and the delay time of car motion are investigated by analytical and numerical methods it is shown that the small explicit delay time has almost no effects in the case of the large explicit delay time a new phase of congestion pattern of ovm seems to appear

multiple positive solutions for a semilinear elliptic equation with critical sobolev exponent in this paper we study a class of semilinear elliptic equations with hardy potential and critical sobolev exponent by means of the ekeland variational principle and mountain pass theorem multiple positive solutions are obtained

proportional differential effects in traffic car following model system abstract traffic flow system s stability analysis can be seen as a typical control system problem which has three kinds of damping ratio properties from the viewpoint of control theory to discover the damping ratio characteristics of traffic flow system under sudden outer impulse firstly we proposed a new method to build the traffic flow model based on state space theory secondly we deduced one form of state transfer matrix from system closed loop transfer function reversely lastly we fully investigated the proportional differential effects in the traffic car following model system analytically and numerically for unsteady traffic flow system with the proportional differential pd term in order to suppress the traffic jam we derived a kind of decoupled delay feedback control algorithm which used h norm and the numerical simulation method to find the feedback gain k and delay time the traffic flow system s transient performance formula was presented with and without pd term and we found out the important impact of pd term on traffic flow system stability the numerical simulation results substantiate our theoretical and analytical results

asymmetric optimal velocity car following model abstract taking the asymmetric characteristic of the velocity differences of vehicles into account we present an asymmetric optimal velocity model for a car following theory the asymmetry between the acceleration and the deceleration is represented by the exponential function with an asymmetrical factor which agrees with the published experiment this model avoids the disadvantage of the unrealistically high acceleration appearing in previous models when the velocity difference becomes large this model is simple and only has two independent parameters the linear stability condition is derived and the phase transition of the traffic flow appears beyond the critical density the strength of interaction between clusters is shown to increase with the asymmetry factor in our model

kdv burgers equation in a new continuum model based on full velocity difference model considering anticipation effect abstract in this paper a new continuum model based on full velocity difference car following model is developed with the consideration of driver s anticipation effect by applying the linear stability theory the new model s linear stability is obtained through nonlinear analysis the kdv burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line numerical simulation shows that the new model possesses the local cluster and it is capable of explaining some particular traffic phenomena numerical results show that when considering the effects of anticipation the traffic jams can be suppressed efficiently the key improvement of this new model is that the anticipation effect can improve the stability of traffic flow

theoretical analysis of the density wave in a new continuum model and numerical simulation abstract considered the effect of traffic anticipation in the real world a new anticipation driving car following model ad cf was proposed by zheng et al based on ad cf model adopted an asymptotic approximation between the headway and density a new continuum model is presented in this paper the neutral stability condition is obtained by applying the linear stability theory additionally the korteweg de vries kdv equation is derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the neutral stability line the numerical simulation and the analytical results show that the new continuum model is capable of explaining some particular traffic phenomena

modified kdv equation for jamming transition in the continuum models of traffic abstract continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway they are the simplified versions of the hydrodynamic model of traffic two continuum models are presented one is described by the partial differential equations and the other is the discrete lattice version the linear stability theory and the nonlinear analysis are applied to the continuum models the modified korteweg de vries equation kdv near the critical point is derived using the reduction perturbation method it is shown that the jamming transition and the density wave in the congested traffic flow are described by the modified kdv equation the solutions of the kdv equations obtained from the two models are compared with that of the optimal velocity model car following model

nonlinear perturbations of a periodic elliptic problem with critical growth abstract using the well known mountain pass theorem due to ambrosetti and rabinowitz we establish conditions for the existence of a positive solution for a class of nonlinear elliptic problems in r n with critical growth

monotone methods for semilinear elliptic equations in unbounded domains abstract monotone methods in conjuction with upper and lower solutions have proved to be extremely powerful tools in the study of nonlinear elliptic boundary value problems in bounded domains in this paper the theory is extended to unbounded not necessarily exterior domains and general linear boundary conditions

stabilization effect of traffic flow in an extended car following model based on an intelligent transportation system application an extended car following model is proposed by incorporating an intelligent transportation system in traffic the stability condition of this model is obtained by using the linear stability theory the results show that anticipating the behavior of more vehicles ahead leads to the stabilization of traffic systems the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by applying the reductive perturbation method the traffic jam could be thus described by the kink antikink soliton solution for the mkdv equation from the simulation of space time evolution of the vehicle headway it is shown that the traffic jam is suppressed efficiently with taking into account the information about the motion of more vehicles in front and the analytical result is consonant with the simulation one

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

nonlinear analysis for a modified continuum model considering electronic throttle et and backward looking effect abstract in this research a new car following model is developed by considering the influences of electronic throttle et dynamics and backward looking effect the improved car following model is transformed into a new continuum model through the relationship between the microscopic variables and macroscopic variables the linear stability condition of the extended continuum model can be obtained according to the linear stability theory the neutral stability curve shows that backward looking effect will improve the stability of traffic flow the kdv burgers equation is derived by the nonlinear analysis which can be used to describe the spreading behavior of traffic flow density wave in traffic congestion nearby the neutral stability line numerical experiments have been carried out including the shock waves rarefaction waves and energy consumption the numerical simulation results indicate that the traffic flow stability can be enhanced by considering et dynamics and backward looking effect in addition the above two factors can also effectively reduce energy consumption

stabilization analysis and modified korteweg de vries equation in a cooperative driving system two lattice traffic models are proposed by incorporating a cooperative driving system the lattice versions of the hydrodynamic model of traffic flow are described by the differential difference equation and difference difference equation respectively the stability conditions for the two models are obtained using the linear stability theory the results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink anti kink soliton solutions obtained from the mkdv equations

the backward looking effect in the lattice hydrodynamic model abstract the novel lattice hydrodynamic model is presented by incorporating the backward looking effect the stability condition for the the model is obtained using the linear stability theory the result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model the korteweg de vries kdv for short equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kdv soliton solution obtained from the kdv equation the simulation result is consistent with the nonlinear analysis

stabilization and enhancement of traffic flow by the next nearest neighbor interaction the car following model of traffic is extended to take into account the car interaction before the next car ahead the next nearest neighbor interaction the traffic behavior of the extended car following model is investigated numerically and analytically it is shown that the next nearest neighbor interaction stabilizes the traffic flow the jamming transition between the freely moving and jammed phases occurs at a higher density than the threshold of the original car following model by increasing the maximal velocity the traffic current is enhanced without jam by the stabilization effect the jamming transition is analyzed with the use of the linear stability and nonlinear perturbation methods the traffic jam is described by the kink solution of the modified korteweg char21 de vries equation the theoretical coexisting curve is in good agreement with the simulation result

nontrivial solutions for a class of semilinear biharmonic problems involving critical exponents in this paper we will discuss the existence of a nontrivial solution of the following class of semilinear biharmonic problem involving critical exponents 6u a x u h x u q 1u k x u p 1u in r u h r n 5 p where 1iqip 2 1 n 4 n 4 and a h k rn r are bounded nonnegative and continuous functions we recall that semilinear and quasilinear problems for second order equations have been extensively studied in the last years for laplace operator and subcritical case they have been studied for instance by rabinowitz 30 coti zelati and rabinowitz 14 kryszewski and szulkin 21 alama and li 1 when a h and k are 1 periodic while in the paper 25 montecchiari has dropped the periodicity condition on a h and

a new lattice model of traffic flow with the consideration of the traffic interruption probability abstract in this paper we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways the stability condition of the new model is obtained by the linear stability analysis and the modified korteweg de vries kdv equation is derived through nonlinear analysis thus the space will be divided into three regions stable metastable and unstable the simulation results also show that the traffic interruption probability could stabilize traffic flow

the effect of headway variation tendency on traffic flow modeling and stabilization abstract advanced communications technology enables us to obtain the headway variation tendency hvt of the next moment in a car following scenario to maximize the benefits of the new technology we developed a new traffic flow model that takes into consideration the effect of hvt first linear analysis method is used to derive the linear stability condition that determines whether the hvt can improve traffic system stability then using the reductive perturbation method a modified kdv mkdv equation is obtained and the kink antikink solutions are derived the phase diagram of driver sensitivity against equilibrium headway is also plotted by using the neutral stability line derived from linear analysis and the coexisting line derived from nonlinear analysis this diagram demonstrates that hvt does have the ability to improve the stability of traffic stream finally the effect of hvt is validated through numerical simulations where it is evident that the information of hvt can smooth the traffic stream and prevent the formation of traffic congestion

boundedness properties for time varying nonlinear systems a liapunov theorem guaranteeing uniform boundedness and uniform ultimate boundedness for a time varying nonlinear system dot x t f x t t has been established the study of uniform boundedness and uniform ultimate boundedness of particular classes of time varying nonlinear systems dot x t f x t t is reduced to the study of the corresponding time invariant frozen systems dot x t f x t sigma for all sigma in mathbb r this approach is illustrated for time varying homogeneous systems with a positive order for particular classes of time varying nonhomogeneous systems and for time varying lotka volterra equations

an optimal velocity estimation ove model based on non empirical formula abstract in many research of optimal velocity model the optimal velocity is estimated by empirical formulas there are several aspects of this approach that need to be improved on the one hand the physical significance of such empirical formulas is not clear enough on the other hand the empirical formula of macro results is not detailed enough at the micro level in this paper we derived an equation to estimate the optimal velocity from two basic assumptions based on this equation the optimal velocity estimation ove model was established to verify the rationality of ove model we conducted two single file pedestrian experiments from the results of experiments we find that pedestrians pursue a consistent velocity and a comfortable distance between pedestrians in single file movement and the comfortable distance is proportional to the square of the steady velocity these conclusions provide support for our assumptions in addition we simulated the experiments with the ovm model and a traditional ov model by comparison the ovm model can reproduce macro results very well further the ovm model has a better performance than traditional ov model in micro level in view of the clear physical meanings our ovm model has an important significance in studying the influencing factors of pedestrian movement

homogeneous state feedback stabilization of homogenous systems we show that for any asymptotically controllable homogeneous system in euclidean space not necessarily lipschitz at the origin there exists a homogeneous control lyapunov function and a homogeneous possibly discontinuous state feedback law stabilizing the corresponding sampled closed loop system if the system satisfies the usual local lipschitz condition on the whole space we obtain semiglobal stability of the sampled closed loop system for each sufficiently small fixed sampling rate if the system satisfies a global lipschitz condition we obtain global exponential stability for each sufficiently small fixed sampling rate the control lyapunov function and the feedback are based on the lyapunov exponents of a suitable auxiliary system and admit a numerical approximation

a new car following model with the consideration of anticipation optimal velocity abstract in this paper a new anticipation optimal velocity model aovm is proposed by considering anticipation effect on the basis of the full velocity difference model fvdm for car following theory on single lane the linear stability condition is derived from linear stability analysis starting and braking process is investigated for the car motion under a traffic signal which shows that the results accord with empirical traffic values especially aovm can avoid the disadvantage of the unrealistically high deceleration appearing in fvdm furthermore numerical simulation shows that aovm might avoid the disadvantage of negative velocity and headway that occur at small sensitivity coefficients in the fvdm since the anticipation effect is taken into account in aovm which means that collision disappears with the consideration of an appropriate anticipation parameter

an extended continuum model considering optimal velocity change with memory and numerical tests in this paper an extended continuum model of traffic flow is proposed with the consideration of optimal velocity changes with memory the new model s stability condition and kdv burgers equation considering the optimal velocities change with memory are deduced through linear stability theory and nonlinear analysis respectively numerical simulation is carried out to study the extended continuum model which explores how optimal velocity changes with memory affected velocity density and energy consumption numerical results show that when considering the effects of optimal velocity changes with memory the traffic jams can be suppressed efficiently both the memory step and sensitivity parameters of optimal velocity changes with memory will enhance the stability of traffic flow efficiently furthermore numerical results demonstrates that the effect of optimal velocity changes with memory can avoid the disadvantage of historical information which increases the stability of traffic flow on road and so it improve the traffic flow stability and minimize cars energy consumptions

multiplicity of solutions for a class of quasilinear equations with exponential critical growth abstract this paper deals with some results of existence and multiplicity of solutions for quasilinear problems involving the n laplacian operator when the nonlinearity has exponential critical growth to obtain our results we utilize ekeland variational principle mountain pass theorem and inequalities of the type trudinger moser bounded and unbounded domains are considered

design of homogeneous time varying stabilizing control laws for driftless controllable systems via oscillatory approximation of lie brackets in closed loop a constructive method for time varying stabilization of smooth driftless controllable systems is developed it provides time varying homogeneous feedback laws that are continuous and smooth away from the origin these feedbacks make the closed loop system globally exponentially asymptotically stable if the control system is homogeneous with respect to a family of dilations and using local homogeneous approximation of control systems locally exponentially asymptotically stable otherwise the method uses some known algorithms that construct oscillatory control inputs to approximate motion in the direction of iterated lie brackets that we adapt to the closed loop context

kdv burgers equation in the modified continuum model considering anticipation effect abstract the new continuum model mentioned in this paper is developed based on optimal velocity car following model which takes the drivers anticipation effect into account the critical condition for traffic flow is derived and nonlinear analysis shows density waves occur in traffic flow because of the small disturbance near the neutral stability line the kdv burgers equation is derived and one of the solutions is given numerical simulation is carried out to show the local cluster described by the model

social optimum for evening commute in a single entry traffic corridor with no early departures abstract in this paper we investigate the evening commute behaviors on the social optimum so state in a single entry traffic corridor with no early departures differing from the previous studies on evening commute the dynamic properties of traffic flow are analyzed with the lwr lighthill whitham richards model the properties of optimum cumulative inflow curve with general desired departure time distribution curve are deduced and then the analytic solutions for common desired departure time in so are obtained three numerical examples are carried out to capture the characteristics of evening commuting behaviors under different values of time the analytic and numerical results both indicate that the rarefaction wave originating from the first entry point influences the whole or part of the outflow curve no shock wave exists through the commuting process in addition the cost curves show that the trip cost increases and the departure delay cost decreases with departure time whereas the travel time cost first increases then decreases with departure time under the so principle

diffusion in the presence of a pole from the continuous gaussian to a discrete lattice model abstract the continuous gaussian model with delta function potentials which has been used to describe the effects that interacting centers poles bring to the diffusion of a random walker provides an exact solution only in dimension d 1 its application in dimension d 2 is in need of introduction of cutoffs coming from the finite sizes of poles we therefore formulate an analogous discrete model in the d dimensional lattice space where no cutoffs or their regularization are necessary the discrete model is amenable to numerical treatment and the green s function its first moments and properties derived from them can be determined numerically to all dimensionalities in the one dimensional 1 d case in the presence of a single center the outcomes of the gaussian model are compared with the corresponding results of the discrete lattice model the possibility of extension of the lattice model to higher dimension permits the study of the two dimensional 2 d case too the intensities of interactions considered before to obtain positive values are extended to negative values in order to describe attractions also

stability of the car following model on two lanes in the case of two lane traffic vehicle drivers always worry about the lane changing actions from neighbor lane this paper studies the stability of a car following model on two lanes which incorporates the lateral effects in traffic the stability condition of the model is obtained by using the linear stability theory the modified korteweg de vries equation is constructed and solved and three types of traffic flows in the headway sensitivity space stable metastable and unstable are classified both analytical and simulation results show that the anxiousness about lane changing from neighbor lane indeed has influence upon people s driving behavior and the consideration of lateral effects could stabilize the traffic flows on both lanes

a duality principle for homogeneous vectorfields with applications we introduce a duality principle for homogeneous vectorfields as an application of this duality principle stability and boundedness results for negative order homogeneous differential equations are obtained starting from known results for positive order homogeneous differential equations

the influence of continuous historical velocity difference information on micro cooperative driving stability abstract in this paper a new micro cooperative driving car following model is proposed to investigate the effect of continuous historical velocity difference information on traffic stability the linear stability criterion of the new model is derived with linear stability theory and the results show that the unstable region in the headway sensitivity space will be shrunk by taking the continuous historical velocity difference information into account through nonlinear analysis the mkdv equation is derived to describe the traffic evolution behavior of the new model near the critical point via numerical simulations the theoretical analysis results are verified and the results indicate that the continuous historical velocity difference information can enhance the stability of traffic flow in the micro cooperative driving process

exponential stabilization of driftless nonlinear control systems using homogeneous feedback this paper focuses on the problem of exponential stabilization of controllable driftless systems using time varying homogeneous feedback the analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control lie algebra it can be shown that any continuous time varying controller that achieves exponential stability relative to the euclidean norm is necessarily non lipschitz despite these restrictions we provide a set of constructive sufficient conditions for extending smooth asymptotic stabilizers to homogeneous exponential stabilizers the modified feedbacks are everywhere continuous smooth away from the origin and can be extended to a large class of systems with torque inputs the feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

multiple solutions for nonhomogeneous elliptic equations involving critical sobolev exponent we consider the following problem where is continuous on r n and h x 0 by using ekeland s variational principle and the mountain pass theorem without ps conditions through a careful inspection of the energy balance for the approximated solutions we show that the probelm has at least two solutions for some 0 and 0 in particular if p 2 in a different way we prove that problem with 1 and h x 0 has at least two positive solutions as

full velocity difference model for a car following theory in this paper we present a full velocity difference model for a car following theory based on the previous models in the literature to our knowledge the model is an improvement over the previous ones theoretically because it considers more aspects in car following process than others this point is verified by numerical simulation then we investigate the property of the model using both analytic and numerical methods and find that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion

effect of looking backward on traffic flow in an extended multiple car following model abstract in this paper a new car following model is proposed by incorporating the backward looking effect under certain conditions and multiple information of preceding cars in traffic flow and the neutral stability condition of this model can be obtained by using the linear stability theory numerical simulation shows that the proposed model is theoretically an improvement over previous ones

on a nonhomogeneous elliptic system with changing sign data abstract in this paper we give some existence results for multiple positive solutions to the following nonhomogeneous elliptic system s u a u 1 u u 1 v 1 f x in v b v 1 u 1 v v 1 g x in u v 0 on where is a regular bounded domain in r n n 3 0 a b nonnegative reals and are positive parameters and f g are given changing sign functions