positive solutions of periodic boundary value problems for nonlinear first order impulsive differential equations abstract motivated by liu y liu further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations j math anal appl 327 2007 435 452 li et al x li x lin d jiang x zhang existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects nonlinear anal 62 2005 683 701 and liu and ge y liu w ge stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients nonlinear anal 57 2004 363 399 this paper is concerned with the periodic boundary value problem pbvp for short for the nonlinear impulsive differential equation x t a t x t f t x t a e t 0 t t 1 t p x t k x t k x t k i k x t k k 1 p x t x 0 we obtain new sufficient conditions for the existence of at least one two or three positive solutions of the above pbvp respectively examples are presented to illustrate the main results

some more results on induced fuzzy topological spaces abstract the concept of induced fuzzy topological space introduced by weiss j math anal appl 50 1975 142 150 was defined with the notions of a lower semi continuous function the purpose of this paper is to present some new results on induced fuzzy topological spaces with the notion of open sets introduced by njastad pacific j math 15 1965 961 970 we also study the connections between some covering properties of an ordinary topological space x t and its corresponding induced fuzzy topological space x w t in the last section we also introduce a new class of fuzzy supra topological spaces induced fuzzy supra topological space ifst space and study the properties

asymptotically periodic solutions of n competing species problem with time delays abstract a general nonautonomous lotka volterra system of integro differential equations with infinite delay is considered and sufficient conditions for uniform stability and asymptotic stability of solutions are investigated these limiting equations are used to obtain the existence of asymptotically periodic solutions of the corresponding system of equations where lower limit in the integration is zero

some good dilutions of fuzzy compactness abstract the obvious generalisation of compactness to fuzzy topology is known not to be a good extension in the sense of lowen following lowen s approach to defining a good fuzzy compactness definitions are suggested for fuzzy almost nearly and weak compactness which are proved to satisfy goodness fuzzy s closedness and rs compactness are treated to a similar approach

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

the singular set for the composite membrane problem in this paper we study the behavior of the singular set u nabla u 0 for solutions u to the free boundary problem delta u f chi u geq 0 g chi u 0 with f 0 f x g x 0 and c0 0 such that the density assumption u 0 cap b r z geq c 0r 2 qquad forall r r 0 holds then z is isolated the density assumption can be motivated by the following example u x 1 2 quad f 2 quad g 2 quad hbox and u 0 emptyset

mean square almost periodic solution for impulsive stochastic nicholson s blowflies model with delays in this paper a class of impulsive stochastic nicholson s blowflies model is investigated by applying cauchy matrix under proper conditions the existence and exponential stability of square mean almost periodic solutions for the model with multiple nonlinear harvesting terms and delays moreover an example is provided to illustrate the effectiveness of the results

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes we consider the following eigenvalue optimization problem given a bounded domain and numbers 0 a 0 find a subset d of area a for which the first dirichlet eigenvalue of the operator d is as small as possible

an unstable elliptic free boundary problem arising in solid combustion we prove a regularity result for the unstable elliptic free boundary problem u u 0 0 1 related to traveling waves in a problem arising in solid combustion the maximal solution and every local minimizer of the energy are regular that is u 0 is locally an analytic surface and u u 0 u u 0 are locally analytic functions moreover we prove a partial regularity result for solutions that are non degenerate of second order here u 0 is analytic up to a set of hausdorff dimension n 2 we discuss possible singularities ams classification 35r35 35j60 35b65

dynamics of multi species competition predator system with impulsive perturbations and holling type iii functional responses abstract we investigate the dynamics of a class of multi species predator prey interaction models with holling type iii functional responses based on systems of nonautonomous differential equations with impulsive perturbations sufficient conditions for existence of a positive periodic solution are investigated by using a continuation theorem in coincidence degree theory which have been extensively applied in studying existence problems in differential equations and difference equations in addition sufficient criteria are established for the global stability and the globally exponential stability of the system by using the comparison principle and the lyapunov method

on a stochastic logistic equation with impulsive perturbations a stochastic logistic model with impulsive perturbations is proposed and investigated first we give a new definition of a solution of an impulsive stochastic differential equation isde which is more convenient for use than the existing one using this definition we show that our model has a global and positive solution and obtain its explicit expression then we establish the sufficient conditions for extinction non persistence in the mean weak persistence persistence in the mean and stochastic permanence of the solution the critical value between weak persistence and extinction is obtained in addition the limit of the average in time of the sample path of the solution is estimated by two constants afterwards the lower growth rate and the upper growth rate of the solution are estimated finally sufficient conditions for global attractivity are established

lagrangian approach to the study of level sets application to a free boundary problem in climatology we study the dynamics and regularity of level sets in solutions of the semilinear parabolic equation u t delta u in a mathbb h u mu quad rm in quad q it omega times 0 t where omega subset mathbb r n is a ring shaped domain a and are given positive constants mathbb h cdot is the heaviside maximal monotone graph mathbb h s 1 if s 0 mathbb h 0 0 1 mathbb h s 0 if s 0 such equations arise in climatology the so called budyko energy balance model as well as in other contexts such as combustion we show that under certain conditions on the initial data the level sets it gamma mu mathbf x t u mathbf x t mu are n dimensional hypersurfaces in the x t space and show that the dynamics of is governed by a differential equation which generalizes the classical darcy law in filtration theory this differential equation expresses the velocity of advancement of the level surface through spatial derivatives of the solution u our approach is based on the introduction of a local set of lagrangian coordinates the equation is formally considered as the mass balance law in the motion of a fluid and the passage to lagrangian coordinates allows us to watch the trajectory of each of the fluid particles

asymptotic stability of competitive systems with delays and impulsive perturbations abstract a general impulsive nonautonomous lotka volterra system of integro differential equations with infinite delay is considered the impulses are realized at fixed moments of time sufficient conditions for uniform stability and asymptotic stability of solutions are investigated the main results are obtained by using the comparison principle and the lyapunov method

on the singularities of a free boundary through fourier expansion in this paper we are concerned with singular points of solutions to the unstable free boundary problem delta u chi u 0 quad hbox in b 1 the problem arises in applications such as solid combustion composite membranes climatology and fluid dynamics

cross shaped and degenerate singularities in an unstable elliptic free boundary problem abstract we investigate singular and degenerate behavior of solutions of the unstable free boundary problem u u 0 first we construct a solution that is not of class c 1 1 and whose free boundary consists of four arcs meeting in a cross shaped singularity this solution is completely unstable repulsive from above and below which would make it hard to get by the usual methods and even numerics is nontrivial we also show existence of a degenerate solution this answers two of the open questions in the paper r monneau g s weiss an unstable elliptic free boundary problem arising in solid combustion http arxiv org abs math ap 0507315 submitted for publication

fuzzy alpha sets and alpha continuous maps abstract in this paper we generalize the notion of sets to fuzzy spaces we also introduce the concepts of fuzzy continuous and fuzzy open mappings and discuss their relations with fuzzy continuous and other weaker forms of fuzzy continuous mappings counterexamples are given to show the non coincidence of these mappings

permanence and global stability for nonautonomous n species lotka volterra competitive system with impulses and infinite delays abstract in this paper we consider a class of nonautonomous n species lotka volterra competitive systems with impulses and infinite delays by developing the methods given in teng 2002 25 we give sufficient conditions for permanence and global attractivity of the system

a lower epiperimetric inequality for area minimizing surfaces the epiperimetric inequality introduced by e r reifenberg in 3 gives a rate of decay at a point for the decreasing k density of area of an area minimizing integral k cycle while dilating the cycle at that point this rate of decay holds once the configuration is close to a tangent cone configuration and above the limiting density corresponding to that configuration this is why we propose to call the reifenberg epiperimetric inequality an upper epiperimetric inequality a direct consequence of this upper epiperimetric inequality is the statement that any point possesses a unique tangent cone the upper epiperimetric inequality was proven by b white in 5 for area minimizing 2 cycles in n in the present paper we introduce the notion of a lower epiperimetric inequality this inequality gives this time a rate of decay for the decreasing k density of area of an area minimizing integral k cycle while dilating the cycle at a point once the configuration is close to a tangent cone configuration and below the limiting density corresponding to that configuration our main result in the present paper is to prove the lower epiperimetric inequality for area minimizing 2 cycles in n as a consequence of this inequality we prove the splitting before tilting phenomenon for calibrated 2 rectifiable cycles which plays a crucial role in the proof of the regularity of 1 1 integral currents in 4 2004 wiley periodicals inc

theory of possibility as a basis for analysing business experience process abstract the aim of this paper is to introduce the theory of possibility in the analysis of professional abilities creations by the labor market when an individual performs a job he can acquire new abilities and is able to obtain other jobs it is shown how career possibilities secure a dynamic property of the labor market structure due to the business experience process the model we have defined indicates that the labor market structure converges in possibility towards a stable state

some results on boundary value problems for fuzzy differential equations with functional dependence abstract we calculate the exact solution for a class of boundary value problems for first order linear fuzzy differential equations with impulses under hukuhara differentiability by finding green s function some conclusions can be derived for impulsive fuzzy differential equations including a term with functional dependence for which existence and uniqueness results are proved

lyapunov method for boundedness of solutions of nonlinear impulsive functional differential equations sufficient conditions are investigated for boundedness of solutions of nonlinear impulsive functional differential equations with impulses at fixed moments the main tools are lyapunov functions and gronwall type of inequality

the singular set of 1 1 integral currents we prove that 2 dimensional integer multiplicity 2 dimensional rectifiable currents which are almost complex cycles in an almost complex manifold admitting locally a compatible positive symplectic form are smooth surfaces aside from isolated points and therefore are j holomorphic curves

existence and stability of periodic solution of a lotka volterra predator prey model with state dependent impulsive effects according to biological and chemical control strategy for pest we investigate the dynamic behavior of a lotka volterra predator prey state dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds by using poincare map and the properties of the lambert w function we prove that the sufficient conditions for the existence and stability of semi trivial solution and positive periodic solution numerical simulations are carried out to illustrate the feasibility of our main results

partial persistence and extinction in n dimensional competitive systems abstract in this paper we first consider an n dimensional system slightly more general than the lotka volterra system and give conditions that imply strong persistence of all species using this result we then give computable conditions on the coefficients which imply the ultimate extinction of certain species in an n dimensional lotka volterra system

global attractivity of the almost periodic solution of a delay logistic population model with impulses in this paper we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations by using a comparison theorem and constructing a suitable lyapunov functional a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained as applications some special models are studied our new results improve and generalize former results

second method of lyapunov and existence of integral manifolds for impulsive differential difference equations by means of piecewise continuous functions which are analogues of lyapunov s functions sufficient conditions are obtained for the existence of integral manifolds for impulsive differential difference equations with variable impulsive perturbations

regularity of the minimizers in the composite membrane problem in r 2 we study the regularity of the minimizers to the problem a infu h01 u 2 1 d a du 2 du2 we prove that in the physical case c is analytic where c is the constant such that d u c up to a zero measure set

existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model abstract by means of the cauchy matrix we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population