a discretization technique for the solution of odes abstract a functional analytic technique was developed in the past for the establishment of unique solutions of odes in h 2 d and h 1 d and of difference equations in l 2 and l 1 this technique is based on two isomorphisms between the involved spaces in this paper the two isomorphisms are combined in order to find discrete equivalent counterparts of odes so as to obtain eventually the solution of the odes under consideration as an application the duffing equation and the lorenz system are studied the results are compared with numerical ones obtained using the 4th order runge kutta method the advantages of the present method are that it is accurate the only errors involved are the round off errors it does not depend on the grid used and the obtained solution is proved to be unique

on holder continuity of approximate solutions to parametric equilibrium problems abstract we establish verifiable sufficient conditions for holder continuity of approximate solutions to parametric equilibrium problems when solutions may be not unique many examples are provided to illustrate the need of considering approximate solutions instead of exact solutions and the essentialness of the imposed assumptions as applications we derive this holder continuity for constrained minimization variational inequalities and fixed point problems

diffusive logistic equations with indefinite weights population models in disrupted environments the dynamics of a population inhabiting a strongly heterogeneous environment are modelledby diffusive logistic equations of the form u t d u m x cu u in 0 where u represents the population density c d 0 are constants describing the limiting effects of crowding and the diffusion rate of the population respectively and m x describes the local growth rate of the population if the environment is bounded and is surrounded by uninhabitable regions then u 0 on 0 the growth rate m x is positive on favourablehabitats and negative on unfavourable ones the object of the analysis is to determine how the spatial arrangement of favourable and unfavourable habitats affects the population being modelled the models are shown to possess a unique stable positive steady state implying persistence for the population provided l d where is the principle positive eigenvalue for the problem m x in 0 on analysis of how depends on m indicates that environments with favourable and unfavourable habitats closely intermingled are worse for the population than those containing large regions of uniformly favourable habitat in the limit as the diffusion rate d 0 the solutions tend toward the positive part of m x c and if m is discontinuous develop interior transition layers the analysis uses bifurcation and continuation methods the variational characterisation of eigenvalues upper and lower solution techniques and singular perturbation theory

stable coexistence states in the volterra lotka competition model with diffusion we study the existence uniqueness and stability of coexistence states in the lotka volterra model with diffusion for two competing species we assume that the parameters describing the interactio

a remark on a standard and linear vector network equilibrium problem with capacity constraints in this paper weak vector equilibrium principle with capacity constraints is introduced a necessary condition that a vector minimum cost flow is a vector equilibrium flow with capacity constraints is obtained when the number of paths connecting with each pair of source and sink is less than or equal to 2 a sufficient condition for a vector minimum cost flow to be a vector equilibrium flow is also obtained a generalized weak vector equilibrium principle is also introduced without any additional assumption a necessary and sufficient condition for a weak vector minimum cost flow to be a generalized weak vector equilibrium flow is obtained

bounds for the first positive zero of a mixed bessel function abstract the present article is concerned with lower and upper bounds of the first positive zero of the function h z j z zj z where j gn z is the ordinary bessel function of order 1 and j z is the derivative of j z a lower bound found here improves and extends the range of validity of the order of a lower bound found in a previous work 8 also two upper bounds given here improve a previously known upper bound 8 in the particular case 0 these bounds lead to lower and upper bounds for the first positive zero j 1 of j z which improve well known bounds in the literature

absolute optimal solution for a compact and convex game abstract this paper investigates the existence of absolute optimal solutions for a partition p in continuous and quasiconcave games we show that the p consistency property introduced in the paper together with the quasiconcavity and continuity of payoffs permits the existence of p absolute optimal solutions in games with compact and convex strategy spaces the p consistency property is a general condition that cannot be dispensed with for the existence of p absolute optimal solutions we also characterize the existence of p absolute optimal solutions by providing necessary and sufficient conditions moreover we suggest an algorithm for efficiently computing p absolute optimal solutions

on the holder continuity of solutions to parametric multivalued vector equilibrium problems we consider parametric multivalued vector equilibrium problems of both weak and strong types in metric linear spaces sufficient conditions for the local uniqueness and holder continuity of the solutions are established as consequences some new results for variational inequalities are derived and compared with recent papers on the subject

a multicriteria pareto optimal path algorithm abstract in this paper we present an algorithm for finding in a multicriteria network pareto optimal paths one each for each efficient objective vector validation of the algorithm and two illustrative examples are included computational experience is also reported this algorithm is a generalization of an earlier one for the bicriterion case

inequalities involving bessel and modified bessel functions abstract some inequalities for the ratios j v 1 x j v x and i v 1 x i v x of bessel and modified bessel functions of the first kind and order v 1 are given the inequalities are found easily from a different definition of the ratios and improve many results obtained recently by several authors

the study of pareto equilibria for multiobjective games by fixed point and ky fan minimax inequality methods abstract in this paper we present two ways to study the existence of weight nash equilibria and pareto equilibria for multiobjective games one is the fixed point method which is well known and the second is the application of ky fan minimax inequality which is not often used in the study of optimization game theory and mathematical programming as results several existence theorems for weight nash equilibria and pareto equilibria are established which improve and unify the corresponding results in the recently existing literatures

vector equilibrium problem and vector optimization this paper examines the vector equilibrium model based on a vector cost consideration this is a generalization of the well known wardrop traffic equilibrium principle where road users choose paths based on just a single cost the concept of parametric equilibria is introduced and used to establish relations with parametric complementarity and variational inequality problems relations with some vector optimization problems via scalarization techniques are given under appropriate conditions some solution methods for solving vector equilibrium problems are also discussed

holder continuity and upper estimates of solutions to vector quasiequilibrium problems abstract in this paper we establish the holder continuity of solution mappings to parametric vector quasiequilibrium problems in metric spaces under the case that solution mappings are set valued our main assumptions are weaker than those in the literature and the results extend and improve the recent ones furthermore as an application of holder continuity we derive upper bounds for the distance between an approximate solution and a solution set of a vector quasiequilibrium problem with fixed parameters

convergence in competition models with small diffusion coefficients abstract it is well known that for reaction diffusion 2 species lotka volterra competition models with spatially independent reaction terms global stability of an equilibrium for the reaction system implies global stability for the reaction diffusion system this is not in general true for spatially inhomogeneous models we show here that for an important range of such models for small enough diffusion coefficients global convergence to an equilibrium holds for the reaction diffusion system if for each point in space the reaction system has a globally attracting hyperbolic equilibrium this work is planned as an initial step towards understanding the connection between the asymptotics of reaction diffusion systems with small diffusion coefficients and that of the corresponding reaction systems

on the common zeros of bessel functions using a functional analytic method we give some results concerning common zeros of the ordinary bessel functions j z of first kind with respect to and fixed z a lower bound for the common zero z of the bessel functions j z j z where are known is also given

the multiobjective equilibrium network design problem revisited a simulated annealing approach abstract in this paper we present a model for continuous multiobjective optimal design of a transportation network the model presented here explicitly incorporates user equilibrium constraints and takes the form of a difficult nonlinear nonconvex mathematical program the user equilibrium constraints form a finite set of nonlinear albeit nonconvex inequalities and give rise to a single level mathematical program as opposed to the now standard mathematical programming variational inequality representation which leads to a bilevel formulation of the equilibrium network design problem we show that simulated annealing is ideally suited for solving multiobjective versions of the equilibrium network design problem articulated in this fashion we employ the weighting method together with simulated annealing to generate the pareto optimal set a numerical example is provided to demonstrate the efficacy of this solution methodology

well posedness by perturbations of mixed variational inequalities in banach spaces in this paper we consider an extension of the notion of well posedness by perturbations introduced by zolezzi for a minimization problem to a mixed variational inequality problem in a banach space we establish some metric characterizations of the well posedness by perturbations we also show that under suitable conditions the well posedness by perturbations of a mixed variational inequality problem is equivalent to the well posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem also we derive some conditions under which the well posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution

upper bounds for the first zeros of bessel functions abstract an upper bound for the first positive zero of the bessel functions of first kind j z for 1 is given this upper bound is better than a number of upper bounds found recently by several authors the upper bound given in this paper follows from a step of the ritz s approximation method applied to the eigenvalue problem of a compact self adjoint operator defined on an abstract separable hilbert space some advantages of this method in comparison with other approximation methods are presented

sensitivity analysis for abstract equilibrium problems we develop the general framework of sensitivity analysis for equilibrium problems in the setting of vector topological normed space our approach does not make any recourse to geometrical properties and the obtained result can be viewed as an extension and generalization of the well known results on variational inequalities in the literature even though we have worked under arbitrary constraints k with holder property that have been decisive in our treatment we have obtained in a similar spirit of domokos j math anal appl 230 1999 382 389 the best lower bound for the continuity modulus despite of the properties of the boundary of k

concentration phenomena of a semilinear elliptic equation with large advection in an ecological model abstract we consider a reaction diffusion advection equation arising from a biological model of migrating species the qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined in particular a conjecture of cantrell cosner and lou on concentration phenomena is resolved under mild conditions applications to a related parabolic competition system are also discussed

positive steady states of reaction diffusion advection competition models in periodic environment abstract in this paper we consider the positive steady states for reaction diffusion advection competition models in the whole space with a spatially periodic structure under the spatially periodic setting we establish sufficient conditions for the existence of positive steady states of this model respectively by investigating the sign of the principal eigenvalue for some linearized eigenvalue problems as an application a lotka volterra reaction diffusion advection model for two competing species in a spatially periodic environment is considered finally some numerical simulations are presented to seek dynamical behaviors

generalized vector quasi equilibrium problems with applications in this paper we consider the generalized vector quasi equilibrium problem with or without involving condensing maps and prove the existence of its solution by using known fixed point and maximal element theorems as applications of our results we derive some existence results for a solution to the vector quasi optimization problem for nondifferentiable functions and vector quasi saddle point problem

spatial heterogeneity of resources versus lotka volterra dynamics abstract the problem is motivated by a consideration of two phenotypes of a species in a strongly heterogenous spatial environment the phenotypes vary in their diffusion rates and interspecific interactions the aim is to investigate the relative strengths of the diffusion and reaction effects the problem is thus of competing species type but there are many questions which arise which are not covered by standard theory we investigate in particular the stability of the equilibria and the existence of coexistence solutions with emphasis on cases where the spatial variation of the environment becomes large we discuss briefly the implications of our results for the principle of competitive exclusions and for the question of the evolution of diffusion discussed in dockery et al j math biol 37 1998 61 83

parabolic systems in unbounded domains i existence and dynamics abstract in this paper we investigate the existence uniqueness and asymptotic behavior of a solution for a class of coupled nonlinear parabolic equations in a general unbounded domain that includes the whole space r n the exterior of a bounded domain and a half space in r n the asymptotic behavior of the solution is with respect to a pair of quasi solutions of the corresponding elliptic system and when these two quasi solutions coincide the solution of the parabolic system converges to a unique solution of the elliptic system

differential and sensitivity properties of gap functions for minty vector variational inequalities the purpose of this paper is to investigate differential properties of a class of set valued maps and gap functions involving minty vector variational inequalities relationships between their contingent derivatives are discussed an explicit expression of the contingent derivative for the class of set valued maps is established optimality conditions of solutions for minty vector variational inequalities are obtained

uniqueness and complete dynamics in heterogeneous competition diffusion systems in this paper we study the interactions between diffusion and heterogeneity of the environment in the classical diffusive lotka volterra competition systems in the weak competition case we establish the uniqueness hence the global asymptotic stability of coexistence steady states under various circumstances and thereby we obtain a complete understanding of the change in dynamics when one of the interspecific competition coefficients is small

semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems abstract in this paper we establish sufficient conditions for the solution set of parametric multivalued vector quasiequilibrium problems to be semicontinuous all kinds of semicontinuity are considered lower semicontinuity upper semicontinuity hausdorff upper semicontinuity and closedness moreover we investigate both the weak and strong solutions of quasiequilibrium problems

analytic efficient solution set for multi criteria quadratic programs abstract we present active set methods to evaluate the exact analytic efficient solution set for multi criteria convex quadratic programming problems mcqp subject to linear constraints the idea is based on the observations that a strictly convex programming problem admits a unique solution and that the efficient solution set for a multi criteria strictly convex quadratic programming problem with linear equality constraints can be parameterized the case of bi criteria quadratic programming bcqp is first discussed since many of the underlying ideas can be explained much more clearly in the case of two objectives in particular we note that the efficient solution set of a bcqp problem is a curve on the surface of a polytope the extension to problems with more than two objectives is straightforward albeit some slightly more complicated notation two numerical examples are given to illustrate the proposed methods

iterative methods for variational and complementarity problems in this paper we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems included among such methods are the newton and several successive overrelaxation algorithms for the most part the study is concerned with the family of linear approximation methods these are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches the paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria finally several convergence results are obtained for some nonlinear approximation methods

perturbation analysis of error bounds for systems of conic linear inequalities in banach spaces for a general constrained or unconstrained system of conic inequalities we provide sufficient conditions to ensure the existence of a common error bound for each of the systems obtained from the original one when the given data undergoes a small perturbation moreover we also give some dual characterizations on the existence of error bounds for systems of conic inequalities

holder continuity of perturbed solution set for convex optimization problems abstract in this paper we first establish sufficient conditions for the local uniqueness and holder continuity of perturbed solution set for a scalar optimization problem then by using a linear scalarization method we obtain the holder continuity of two classes of perturbed solution sets for a multiobjective programming problem respectively we also give some examples to illustrate that our main results are applicable these examples are also given to illustrate that our main results are new and different from the ones in literature

convergence of an annealing algorithm the annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems including np hard combinatorial problems such as the travelling salesman steiner trees and others there is an appealing physical analogy for its operation but a more formal model seems desirable in this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1 we also show that there are cases where convergence takes exponentially long that is it is no better than a deterministic method we study how the convergence rate is affected by the form of the problem finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of practical confidence in the solution

the effects of diffusion and spatial variation in lotka volterra competition diffusion system i heterogeneity vs homogeneity abstract it is well known that the interactions between diffusion and spatial heterogeneity could create very interesting phenomena in this series of two papers using the classical lotka volterra competition system we will illustrate the combined effects of dispersal and spatial variations on the outcome of the competition in part i with the total resources being fixed at exactly the same level we first show that a heterogeneous distribution of resources is usually superior to its homogeneous counterpart in the presence of diffusion then we study the more general case when both species have heterogeneous carrying capacities but still with the same total resources limiting behaviors of co existence steady states as the dispersal rates tend to 0 or are also obtained in part ii we continue our investigation but under much broader situations including different strengths and distributions of the resources and with different competition abilities

global dynamics of the lotka volterra competition diffusion system diffusion and spatial heterogeneity i in the first part of this series of three papers we investigate the combined effects of diffusion spatial variation and competition ability on the global dynamics of a classical lotka volterra competition diffusion system we establish the main results that determine the global asymptotic stability of semitrivial as well as coexistence steady states hence a complete understanding of the change in dynamics is obtained immediately our results indicate confirm that when spatial heterogeneity is included in the model diffusion driven exclusion could take place when the diffusion rates and competition coefficients of both species are chosen appropriately 2015 wiley periodicals inc

advection mediated competition in general environments abstract we consider a reaction diffusion advection system of two competing species with one of the species dispersing by random diffusion as well as a biased movement upward along resource gradient while the other species by random diffusion only it has been shown that under some non degeneracy conditions on the environment function the two species always coexist when the advection is strong in this paper we show that for general smooth environment function in contrast to what is known there can be competitive exclusion when the advection is strong and we give a sharp criterion for coexistence that includes all previously considered cases moreover when the domain is one dimensional we derive in the strong advection limit a system of two equations defined on different domains uniqueness of steady states of this non standard system is obtained when one of the diffusion rates is large

elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena this paper is concerned with the asymptotic behaviour of the principal eigenvalue of some linear elliptic equations in the limit of high first order coefficients roughly speaking one of the main results says that the principal eigenvalue with dirichlet boundary conditions is bounded as the amplitude of the coefficients of the first order derivatives goes to infinity if and only if the associated dynamical system has a first integral and the limiting eigenvalue is then determined through the minimization of the dirichlet functional over all first integrals a parabolic version of these results as well as other results for more general equations are given some of the main consequences concern the influence of high advection or drift on the speed of propagation of pulsating travelling fronts

the effects of diffusion and spatial variation in lotka volterra competition diffusion system ii the general case abstract it is well known that the interactions between diffusion and spatial heterogeneity could create very interesting phenomena in this series of two papers using the classical lotka volterra competition system we will illustrate the combined effects of dispersal and spatial variations on the outcome of the competition in part i with the total resources being fixed at exactly the same level we first show that a heterogeneous distribution of resources is usually superior to its homogeneous counterpart in the presence of diffusion then we study the more general case when both species have heterogeneous carrying capacities but still with the same total resources limiting behaviors of co existence steady states as the dispersal rates tend to 0 or are also obtained in part ii we continue our investigation but under much broader situations including different strengths and distributions of the resources and with different competition abilities

a differential inequality for the positive zeros of bessel functions abstract let jv k be the kth positive zero of the bessel function jv z of the first kind and order v 1 we prove the differential inequalities where hn v x n 0 are the lommel polynomials watson 1966 as a consequence we obtain some new lower and upper bounds for jv k improving previously known results

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

stability of weak vector variational inequality abstract in this paper a key assumption is introduced by virtue of a parametric gap function then by using the key assumption sufficient conditions of the continuity and hausdorff continuity of a solution set map for a parametric weak vector variational inequality are obtained in banach spaces with the objective space being finite dimensional

on existence of vector equilibrium flows with capacity constraints of arcs in this paper we propose a weak vector equilibrium principle with capacity constraints of arcs by proving the existence of solutions for the weighted variational inequality we establish the existence results of weak vector traffic equilibrium flows with capacity constraints of arcs

does movement toward better environments always benefit a population abstract we study the effects of advection along environmental gradients on logistic reaction diffusion models for population growth the local population growth rate is assumed to be spatially inhomogeneous and the advection is taken to be a multiple of the gradient of the local population growth rate it is also assumed that the boundary acts as a reflecting barrier to the population we show that the effects of such advection depend crucially on the shape of the habitat of the population if the habitat is convex the movement in the direction of the gradient of the growth rate is always beneficial to the population while such advection could be harmful for certain non convex habitats

the holder continuity of solutions to generalized vector equilibrium problems in this paper by using a weaker assumption we discuss the holder continuity of solution maps for two cases of parametric generalized vector equilibrium problems under the case that the solution map is a general set valued one but not a single valued one these results extend the recent ones in the literature several examples are given for the illustration of our results