weak singularities may help periodic solutions to exist abstract in a periodically forced semilinear differential equation with a singular nonlinearity a weak force condition enables the achievement of new existence criteria through a basic application of schauder s fixed point theorem the originality of the arguments relies in that contrary to the customary situation in the available references a weak singularity facilitates the arguments of the proofs

nonlinear periodic boundary value problems with sign changing green s function abstract we study the existence and nonexistence of positive solutions of nonlinear periodic boundary value problems u a t u b t f u a e t 0 t u 0 u t u 0 u t where b 0 a 0 and the green s function g t s of the linear problem u a t u 0 a e t 0 t u 0 u t u 0 u t may change sign on 0 t 0 t

cone theoretic generalization of total positivity abstract this paper is devoted to the generalization of the theory of total positivity we say that a linear operator a r n r n is generalized totally positive gtp if its jth exterior power j a preserves a proper cone k j j r n for every j 1 n we also define generalized strictly totally positive gstp operators we prove that the spectrum of a gstp operator is positive and simple moreover its eigenvectors are localized in special sets the existence of invariant cones of finite ranks is shown under some additional conditions some new insights and alternative proofs of the well known results of gantmacher and krein describing the properties of tp and stp matrices are presented

dynamics for a class of general hematopoiesis model with periodic coefficients abstract sufficient conditions are obtained for the existence and global attractivity of a unique positive periodic solution x t of x t a t x t b t 1 x n t t t 0 where n 1 a and b are continuous positive periodic function also some sufficient conditions are established for oscillation of all positive solutions of about x t for the proof of existence and uniqueness of x t the method used here is better than contraction mapping principle

multiplicity of positive periodic solutions to superlinear repulsive singular equations abstract in this paper we study positive periodic solutions to the repulsive singular perturbations of the hill equations it is proved that such a perturbation problem has at least two positive periodic solutions when the anti maximum principle holds for the hill operator and the perturbation is superlinear at infinity the proof relies on a nonlinear alternative of leray schauder type and on krasnoselskii fixed point theorem on compression and expansion of cones

probability and time trade off probability and time are integral dimensions of virtually any decision to treat them together we consider the prospect of receiving outcome x with a probability p at time t we define risk and time distance and show that if these two distances are traded off linearly then preferences are characterized by three functions a value function a probability discount rate function and a psychological distance function the concavity of the psychological distance function explains the common ratio and common difference effects a decreasing probability discount rate accounts for the magnitude effect the discount rate and the risk premium depend on the shape of these three functions this paper was accepted by peter wakker decision analysis

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

existence of positive solutions for first order discrete periodic boundary value problems with delay abstract let t 3 be a positive integer and t 0 1 2 t 1 we prove the existence of positive periodic solutions of the nonlinear discrete boundary value problem u t a t g u t u t b t f u t t t t u 0 u t our approach is based upon the global bifurcation techniques

periodic solutions for damped differential equations with a weak repulsive singularity abstract this paper deals with the existence of positive t periodic solutions for the following damped differential equation x p t x q t x f t x c t where p q c l 1 r are t periodic functions and f car r r r is t periodic in the first variable we will prove that a weak repulsive singularity enables the achievement of new existence criteria through a basic application of schauder s fixed point theorem

multiplicity of positive radial solutions for an elliptic inclusion system on an annulus in this paper we present the sufficient conditions for existence and multiplicity of positive radial solutions for elliptic inclusion systems our results are obtained by utilizing the generalization of leggett and williams s fixed point theorem established in this paper for the norm type cone expansion and compression of multivalued operators

two periodic solutions of neutral difference systems depending on two parameters in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order neutral difference systems our approach is based on a fixed point theorem in cones as well as some analysis techniques

existence of multiple positive periodic solutions for functional differential equations abstract in our paper by employing krasnoselskii fixed point theorem we investigate the existence of multiple positive periodic solutions for functional differential equations x t a t x t x t f t x t where 0 is a parameter some easily verifiable sufficient criteria are established

positive periodic solutions of functional differential equations with impulses and a parameter by applying the well known leggett williams multiple fixed point theorem this paper investigates the existence of multiple positive periodic solutions of functional differential equations with impulses and a parameter

positive solutions to superlinear attractive singular impulsive differential equation abstract in this paper we study positive periodic solutions to impulsive differential equation with the attractive singular perturbation the existence theorem is proved using the leray schauder alternative principle and the fixed point theorem the perturbation term in the equation we are mainly interested in is that it has not only an attractive singularity but also the superlinearity

existence of positive solutions for second order functional differential equations we afford a existence criterion of positive solutions of a boundary value problem concerning a second order functional differential equation by using the krasnoselskii fixed point theorem on cones in banach spaces moreover we also apply our results to establish several existence theorems of multiple positive solutions for some functional differential equations

periodic solutions of lienard equations with singular forces of repulsive type in this paper we will use the coincidence degree to give an existence result of periodic solutions for the scalar lienard equations with singular forces of repulsive type the main result of this paper clearly describes what balance conditions between the singular force at the singularity and at the infinity should be imposed if the equation has a periodic solution as an application we will improve the results of ding ye and wang for the brillouin electron beam focusing system

positive periodic solutions of singular systems of first order ordinary differential equations the existence and multiplicity of positive periodic solutions for first non autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter the proof of our results is based on the krasnoselskii fixed point theorem in a cone

positive periodic solutions of first order singular systems abstract we establish a complete structure for the existence of positive periodic solutions of first order non autonomous singular system u i t a i t u i t b i t f i u t i 1 n the methods employed are fixed point index theorems leray schauder degree and lower and upper solutions method

positive periodic solutions of delayed differential equations abstract in this paper we are concerned with the existence multiplicity and nonexistence of positive periodic solutions of the following equation u t a t u u t b t f u t t t r where a c r r r is a periodic function with respect to the first variable b c r 0 c r r all are periodic functions f c 0 0 and f s 0 for s 0 0 is a parameter the proof of our main results is based upon fixed point index theory

periodic solutions of functional dynamic equations with infinite delay abstract in this paper sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale is the set of the real numbers or the integers respectively the approach is mainly based on the krasnosel ski fixed point theorem which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in studying dynamic equations on time scales this study shows that one can unify such existence studies in the sense of dynamic equations on general time scales

on the axiomatization of the satiation and habit formation utility models we propose a preference condition called shifted difference independence to axiomatize a general habit formation and satiation model ghs this model allows for a general habit formation and satiation function that contain many functional forms in the literature as special cases since the ghs model can be reduced to either a general satiation model gsa or a general habit formation model gha our theory also provides approaches to axiomatize both the gsa model and the gha model furthermore by adding extra preference conditions into our axiomatization framework we obtain a ghs model with a linear habit formation function and a recursively defined linear satiation function

positive periodic solution of second order neutral functional differential equations abstract in this paper we consider two types of second order neutral functional differential equations by choosing available operators and applying krasnoselskii s fixed point theorem we obtain sufficient conditions for the existence of periodic solutions to such equations

periodic solutions of first order functional differential equations with periodic deviations the paper is concerned with the functional differential equation u t a t g u h 1 t u t lb t f u h 2 t where l 0 a t b t h 1 t and h 2 t are periodic functions applying leggett williams fixed point theorem to the equation we show the explicit open intervals of l such that the equation has at least three nonnegative periodic solutions

existence and multiplicity results for nonlinear periodic boundary value problems abstract this paper studies the existence of positive solutions for periodic boundary value problems the criteria for the existence nonexistence and multiplicity of positive solutions are established by using the global continuation theorem fixed point index theory and approximate method the results obtained herein generalize and complement some previous findings of j r graef l kong h wang existence multiplicity and dependence on a parameter for a periodic boundary value problem j differential equations 245 2008 1185 1197 and some other known results

on the number of positive solutions of a nonlinear algebraic system abstract in this paper we study the nonlinear algebraic system of the form e x af x where 0 is a parameter x and f x denote the column vectors col x 1 x 2 x n and col f 1 x 1 f 2 x 2 f n x n respectively with fk r r k 1 2 n 1 n and n is a positive integer a aij n n is an n n matrix and all its entries are positive numbers many problems in various areas such as difference equations boundary value problems dynamical networks stochastic process numerical analysis etc can be converted to system e applying fixed point theorems we prove results on existence uniqueness multiplicity and nonexistence of positive solutions for e

a relationship between the periodic and the dirichlet bvps of singular differential equations in this paper a relationship between the periodic and the dirichlet boundary value problems for second order ordinary differential equations with singularities is established this relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations using this relationship we give in this paper an existence result of positive periodic solutions to singular differential equations when the singular forces satisfy some strong force condition at the singularity 0 and some linear growth condition at infinity

interlacing properties of the eigenvalues of some matrix classes abstract we establish the eigenvalue interlacing property i e the smallest real eigenvalue of a matrix is less than the smallest real eigenvalue of any of its principal submatrices for the class of matrices introduced by kotelyansky all principal and almost principal minors of these matrices are positive we show that certain generalizations of kotelyansky and totally positive matrices possess this property we also prove some interlacing inequalities for the other eigenvalues of kotelyansky matrices

two periodic solutions of second order neutral functional differential equations in this paper we consider a type of second order neutral functional differential equations we obtain some existence results of multiplicity and nonexistence of positive periodic solutions our approach is based on a fixed point theorem in cones

positive periodic solutions of nonautonomous functional differential systems abstract considered is the periodic functional differential system with a parameter x t a t x t x t f t x t using the eigenvalue problems of completely continuous operators we establish some criteria on the existence of positive periodic solutions moreover we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions which are compared with existing ones

periodic solutions for a non monotone family of delayed differential equations with applications to nicholson systems for a family of n dimensional periodic delay differential equations which encompasses a broad set of models used in structured population dynamics the existence of a positive periodic solution is obtained under very mild conditions the proof uses the schauder fixed point theorem and relies on the permanence of the system a general criterion for the existence of a positive periodic solution for nicholson s blowflies periodic systems with both distributed and discrete time varying delays is derived as a simple application of our main result generalizing the few existing results concerning multi dimensional nicholson models in the case of a nicholson system with discrete delays all multiples of the period the global attractivity of the positive periodic solution is further analyzed improving results in recent literature

positive periodic solutions of second order nonlinear differential systems with two parameters by employing the deimling fixed point index theory we consider a class of second order nonlinear differential systems with two parameters l m r 2 0 0 we show that there exist three nonempty subsets of r 2 0 0 c d 1 and d 2 such that r 2 0 0 c d 1 d 2 and the system has at least two positive periodic solutions for l m d 1 one positive periodic solution for l m c and no positive periodic solutions for l m d 2 meanwhile we find two straight lines l 1 and l 2 such that c lies between l 1 and l 2

positive periodic solutions of functional differential equations abstract we consider the existence multiplicity and nonexistence of positive periodic solutions for the periodic equation x t a t g x x t b t f x t t where a b c r 0 are periodic 0 a t dt 0 0 b t dt 0 f g c 0 0 and f u 0 for u 0 g x is bounded t is a continuous periodic function define f 0 lim u 0 f u u f lim u f u u i0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f we show that the equation has i0 or i positive periodic solution s for sufficiently large or small 0 respectively

positive solutions to nonlinear first order pbvps with parameter on time scales abstract in this paper we consider the following nonlinear first order periodic boundary value problem with parameter on a time scale t x t p t x t f x t t 0 t t x 0 x t where 0 is a parameter for suitable 0 some existence multiplicity and nonexistence criteria of positive solutions are established by using well known results from the fixed point index

on the number of positive solutions of systems of nonlinear dynamic equations on time scales in this paper we consider the following n dimensional second order nonlinear system on time scalesu d d t email protected t f u s t 0 email protected a b twith the sturm liouville boundary email protected a email protected d a 0 cu s b email protected d s b 0 where u u 1 u n a diag a 1 a n b diag b 1 b n c diag c 1 c n d diag d 1 d n let f email protected i 1 nlim u 0f i u email protected and f email protected i 1 email protected email protected f i u email protected define i 0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f by using fixed point index theory we show that i if i 0 1 or 2 then there exist l 0 0 such that the system has i 0 positive solution s for l l 0 ii if i 1 or 2 then there exist l 0 0 such that the system has i 0 positive solution s for 0 0 respectively

positive solutions for nonlinear discrete periodic boundary value problems we are concerned with the nonlinear discrete periodic boundary value problem p d p t 1 du t 1 q t u t rg t f u t t 1 t z u 0 u t p 0 du 0 p t du t where r is a positive parameter optimal interval will be given to the parameter r to ensure that p has at least one positive solution

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

foundations of intrinsic habit formation we provide theoretical foundations for several common nested representations of intrinsic linear habit formation our axiomatization introduces an intertemporal theory of weaning a decision maker from her habits using the device of compensation we clarify differences across specifications of the model provide measures of habit forming tendencies and suggest methods for axiomatizing time nonseparable preferences

on the positive stability of p2 matrices abstract in this paper we study the positive stability of p matrices we prove that a matrix a is positive stable if a is a p 2 matrix and there is at least one nested sequence of principal submatrices of a each of which is also a p 2 matrix this result generalizes the result by carlson which shows the positive stability of sign symmetric p matrices and the result by tang simsek ozdaglar and acemoglu which shows the positive stability of strictly row column square diagonally dominant for every order of minors p matrices

on the existence and global bifurcation of periodic solutions to planar differential delay equations abstract this paper is concerned with periodic solutions to one parameter families of planar differential delay equations the concept of slowly oscillating periodic solution is extended to this setting and we state the existence of an unbounded continuum of such solutions

sequentially continuous non monotonic choquet integrals schmeidler proc amer math soc 97 2 1986 255 261 established an integral representation theorem through the choquet integral for functionals satisfying monotonicity and a weaker condition than additivity namely comonotonic additivity murofushi sugeno machida fuzzy sets and systems 64 1994 73 86 generalize this representation to the case of bounded variation functionals omitting the monotonicity condition we give an alternative approach which is based on sequential continuity and tolerates non monotonicity this later condition is equivalent to s additivity in measure theory

existence nonexistence and multiplicity of periodic solutions for a kind of functional differential equation with parameter abstract in this paper we study the existence multiplicity and nonexistence of positive periodic solutions for a kind of second order delay functional differential equation with parameter u t a t u t f t u t 0 t u t 1 t u t n t by employing the krasnoselskii fixed point theorem for a cone map where 0 is a parameter some new results are obtained as an application of our results we discuss an example

existence of positive periodic solutions of nonlinear first order delayed differential equations abstract we consider the existence of positive periodic solutions for the equation u t a t g u t u t b t f u t t where a b c r 0 are periodic functions with 0 a t d t 0 0 b t d t 0 f g c 0 0 and f s 0 for s 0 is a continuous periodic function 0 is a parameter the proofs of our main results are based upon fixed point index theory

positive periodic solutions of first order functional differential equations with parameter we prove the existence and multiplicity of positive t periodic solution s for t periodic equation x t h t x lb t f x t t t by krasnoselskii fixed point theorem where f x may be singular at x 0 our results improve some recent results in previous literature

on pairs of vectors achieving the maximal angle of a convex cone in this paper we explore the concept of antipodality relative to a closed convex cone the problem under consideration is that of finding a pair of unit vectors in k achieving the maximal angle of the cone we mention also a few words on the attainability of critical angles by way of application of the general theory we briefly discuss the problem of estimating the radius of pointedness of a cone

existence and global attractivity of unique positive periodic solution for a lasota wazewska model abstract in this paper we consider the lasota wazewska model x t a t x t i 1 m p i t e q i t x t i t by using a fixed point theorem some criteria are established for the existence of the unique positive periodic solution x of the above equation in particular we not only give the conclusion of convergence of x n to x where x n is a successive sequence but also show that x is a global attractor of all other positive solutions

existence and global attractivity of unique positive periodic solution for a model of hematopoiesis sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis then some criteria are established for the existence uniqueness and global attractivity of almost periodic solutions of almost periodic system

higher order functional differential systems with parameter dependence abstract in this paper we consider a class of high order functional differential systems depending on a parameter by using the fixed point index theory we prove that there exists a positive number separating 0 into two disjoint subintervals 1 and 2 such that the system has at least two positive periodic solutions for 1 one positive periodic solution for and no positive periodic solution for 2 our results extend and improve some results in the literature as an application an example is given to demonstrate our main results

on the number of positive solutions of nonlinear systems abstract we prove that appropriate combinations of superlinearity and sublinearity of f u with respect to at zero and infinity guarantee the existence multiplicity and nonexistence of positive solutions to boundary value problems for the n dimensional system u h t f u 0 0 is defined by u u 1 u n where u u 1 u n and covers the two important cases u u and u u p 2 u p 1 our methods employ fixed point theorems in a cone

three periodic solutions for a nonlinear first order functional differential equation this paper is concerned with the existence of three positive t periodic solutions of the first order functional differential equations of the formx t a t x t email protected t f t x h t where a t b t and t t are positive t periodic functions and l is a positive parameter leggett williams multiple fixed point theorem has been used to prove our results our results extend and improve some results in the literature

existence theory for positive solutions to one dimensional p laplacian boundary value problems on time scales abstract in this paper we consider the one dimensional p laplacian boundary value problem on time scales p u t h t f u t 0 t a b u a b 0 u a 0 u b 0 where p u is p laplacian operator i e p u u p 2 u p 1 some new results are obtained for the existence of at least single twin or triple positive solutions of the above problem by using krasnosel skii s fixed point theorem new fixed point theorem due to avery and henderson and leggett williams fixed point theorem this is probably the first time the existence of positive solutions of one dimensional p laplacian boundary value problems on time scales has been studied

existence of nonnegative and nonpositive solutions for second order periodic boundary value problems we are interested in nonnegative and nonpositive solutions of the boundary value problem u f t u u 0 u 1 u 0 u 1 where f fulfils the caratheodory conditions on 0 1 r we generalize the results reached by m n nkashama j santanilla and l sanchez and present estimates for solutions in addition we apply our existence theorems to periodic boundary value problems for nonlinear duffing equations whose right hand sides have a repulsive or attractive singularity at the origin we extend or generalize existence results by a c lazer and s solimini and other authors moreover we get some multiplicity results and in the case of a repulsive singularity we also admit a weak singularity in constrast to the previous papers on this subject our proofs are based on the method of lower and upper functions and topological degree arguments and the results are tested on examples

the existence of multiple positive periodic solutions for functional differential equations abstract the existence of multiple positive solutions for the integral equation x t t t g t s b s f s x s 1 s x s n s ds is studied by using fixed point index theory using these results we obtain new results on the existence of multiple positive periodic solutions for some first order periodic functional differential equations

two periodic solutions of n dimensional neutral functional difference systems in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order n dimensional neutral functional difference systems our approach requires the krasnoselskii fixed point theorem in cones

periodicity and stability for a lotka volterra type competition system with feedback controls and deviating arguments abstract this paper deals with the general periodic lotka volterra type competition systems with feedback controls and deviating arguments by employing fixed point index theory on cone an explicit necessary and sufficient condition for the global existence of the positive periodic solution of the systems is proved by constructing a suitable lyapunov functional a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution of the systems is given

existence of positive periodic solutions of impulsive functional differential equations with two parameters in this paper we employ a well known fixed point index theorem to study the existence and non existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters several existence and non existence results are established

positive solutions for boundary value problems of functional differential equations abstract we study the existence of positive solutions of the second order boundary values problems of functional differential equations x t f t x t 0 0 t t x 0 x t a where f 0 t c r r is a continuous function c r c r 0 and a r the proof of our main result is based upon the fixed point theorem in cones

expectation and variation in multi period decisions multi period decisions are decisions which determine an individual s payoffs in several periods in the future this paper examines the theoretical foundations of the prevalent weighted average assumption more specifically we use a multi period interpretation of the famous ellsberg paradox in decision under uncertainty to show that in many cases of interest additively separable functionals in general and weighted average ones in particular do not seem appropriate for the representation of the decision maker s preferences we then suggest replacing the sure thing principle which may be used to axiomatize a weighted average functional by a weaker version of it using the weakened axiom in schmeidler s nonadditive measure model reinterpreted for the multi period context yields an axiomatization of a larger class of decision rules which are representable by a weighted average of the utility in each period und the utility variation between each two consecutive periods the weighted average assumption is a special case of the generalized model a case in which the decision maker is variation neutral similarly we define and characterize variation aversion and variation liking and show an example of the economic implications of these properties

time continuity and nonadditive expected utility information consisting of probabilities of some but possibly not all events induces an integral with respect to a probability specified on a subalgebra a decision maker evaluates the alternatives using only the available information and completely ignoring unavailable information assume now that the decision maker assesses the worth of a different lottery at each point in a discrete time assume also that each such lottery is preferred to some fixed alternative lottery now consider the situation where the sequence of lotteries converges in some sense if the limiting lottery is preferred to the fixed alternative then the preference order is referred to as time continuous this paper studies time continuity for two preference functionals the choquet integral and the integral with respect to a probability specified on a subalgebra the integral with respect to probability specified on a subalgebra is determined by the structure of the available information by relating it to the choquet integral we characterize the structure of available information that would yield time continuity

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

periodic solutions for scalar functional differential equations suf ficient criteria are established f or the existence ofpositive periodic solutions ofscalar f tional differential equations which improve and generalize some related results in the literature the approach is based on the krasnoselskii s fixed point theorem numerical simulations are presented to support the analytical analysis 2005 elsevier ltd all rights reserved msc 34k13 92d25

on positive solutions for second order boundary value problems of functional differential equations in this paper by using krasnoselskii fixed point theorem we obtain sufficient conditions for the existence of at least one or two positive solutions of a second order boundary value problem for a class of nonlinear functional differential equations examples are also included to illustrate our results

periodic solutions of second order non autonomous singular dynamical systems abstract in this paper we establish two different existence results of positive periodic solutions for second order non autonomous singular dynamical systems the first one is based on a nonlinear alternative principle of leray schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity the second one is based on schauder s fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions recent results in the literature are generalized and significantly improved