the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

conditional gauge and potential theory for the schrodinger operator on etend le theoreme de jauge conditionnelle a des operateurs plus generaux et a des domaines moins reguliers on obtient des resultats de theorie du potentiel pour l equation de schrodinger

long time behavior of a cooperative periodic parabolic system in a spatiotemporally degenerate environment this paper is the continuation of our work 1 41 on the study of the cooperative periodic parabolic system tu u u x t v a x t up tv v v x t u b x t vqin 0 u v 0 0 on 0 u x 0 v x 0 u0 x v0 x 0 0 in where p q 1 rn n 2 is a bounded smooth domain 0 and a b 0 are smooth functions that are t periodic in t and is a varying parameter the unknown functions u x t and v x t stand for the densities of two cooperative species at location x and time t the aim of our work is to establish the long time behavior of u v when the species are exposed to a spatiotemporally degenerate environment in 1 and 41 we dealt with the three cases that a and b have simultaneous spatiotemporal degeneracy simultaneous spatial degeneracy and simultaneous temporal degeneracy in this paper we consider some other natural situations of degeneracies our results reveal further interesting effects of spatial and temporal degeneracies on the dynamics of such a cooperative system in addition we provide a sharp improvement of the results in 41 when simultaneous temporal degeneracy occurs

optimal control of harvesting in a nonlinear elliptic system arising from population dynamics the aim of this article is to study an optimal control problem for a system of nonlinear elliptic equations with dirichlet boundary conditions u x a x x c x u x eu x u x x x 1 1 x b x u x d x x f x u x x x u x x 0 on 1 2 the authors were supported in part by cicyt ministry of education and culture spain under grant pb98 1343 by junta de andalucia fqm116 and by eec contract human capital and mobility program erbchrxct 940494 also they thank o arino for suggesting the study of this control problem

statistical mechanics in the extended gaussian ensemble the extended gaussian ensemble ege is introduced as a generalization of the canonical ensemble this ensemble is a further extension of the gaussian ensemble introduced by hetherington j low temp phys 66 145 1987 the statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the maximum statistical entropy principle the probability of each microstate depends on two parameters b and g which allow one to fix independently the mean energy of the system and the energy fluctuations respectively we establish the legendre transform structure for the generalized ther modynamic potential and propose a stability criterion we also compare the ege probability distribution with the q exponential distribution as an example an application to a system with few independent spins is presented the development of statistical mechanics based on en semble theory is founded on the postulate of equal a priori probabilities which is assumed to apply to all microstates consistent with the given macrostate of an isolated system 1 the corresponding statistical ensemble is the so called microcanonical ensemble a representative system in this en semble has all mechanical variables such as energy e volume v magnetization m etc fixed for convenience in calculations other ensembles are used which invariably sup pose the existence of a subsidiary system or reservoir in con tact with the actual system for instance in the canonical ensemble the walls of the system permit an exchange of en ergy with the reservoir while in the grand canonical en semble both energy and matter can be exchanged in gen eral the different ensembles are constructed by allowing one or more mechanical variables to fluctuate the exchange of each of these variables is controlled by a parameter which is a characteristic of the reservoir for instance in the case of the canonical ensemble this parameter is precisely the tem perature of the reservoir and determines the mean energy of the system actually this is adequate when the reservoir is a very large system that can exchange arbitrary amounts of energy without modification of its intensive properties in practical situations this is not always the case however very few studies have been devoted to analyze the conse quences of possible deviations from these ideal reservoir properties in this paper we develop the statistical mechanics of a system that can exchange energy with a finite reservoir char acterized by two parameters b and g these parameters con trol independently the mean energy of the system and its energy fluctuations respectively the corresponding statisti cal ensemble represents a generalization of the canonical en semble and will be called the extended gaussian ensemble ege a similar ensemble was already developed in a more restricted framework by hetherington 2 the author con sidered that the sample system was in contact with a finite reservoir with size dependent properties the so called gaussian ensemble was introduced so that it is equivalent to the canonical ensemble in the limit of large systems except in the energy range of a first order transition interestingly it enables a smooth interpolation between the microcanonical and the canonical ensembles taking into account these fea tures challa and hetherington 3 4 showed the interest of this ensemble for monte carlo simulation studies of phase transitions they demonstrated a significant reduction in computer time compared to standard simulations in the ca nonical ensemble and its adequacy for distinguishing second order from first order transitions compared to the ege introduced in the present paper the main difference arises from the fact that in the gaussian ensemble the sample and the reservoir are assumed to be statistically independent which implies the additivity of the corresponding entropies this is not assumed in our formalism the consequences are important and will be discussed in depth in this work the present formalism can be considered as an alternative to the statistical mechanics based on nonadditive generalized entropies actually the study of such generalized entropies has generated a lot of interest in the past 15 years the mo tivation for the so called tsallis statistical mechanics has been to extend the standard boltzmann gibbs framework to include nonextensive systems 5 among different interpre tations it has been suggested that tsallis formalism corre sponds to an ensemble describing a system attached to a finite reservoir 6 7 although a large number of papers have been published the physical meaning of many related issues is still open to discussion 8 9 the ege formalism that we propose in this paper provides a clear and consistent frame work for the statistical mechanics with a finite reservoir the paper is organized as follows in secs ii and iii the ege is founded from the analysis of a contact with a finite reservoir and from the maximum statistical entropy prin ciple respectively in sec iv the main thermodynamic rela tions are derived in sec v we highlight the nonadditive nature of the thermodynamic formalism in sec vi a stabil

nonlinear quantum dynamical system based on the kadomtsev petviashvili ii equation the structure of soliton solutions of classical integrable nonlinear evolution equations which can be solved through the hirota transformation suggests a new way for the construction of nonlinear quantum dynamical systems that are based on the classical equations in the new approach the classical soliton solution is mapped into an operator u which is a nonlinear functional of the particle number operators over a fock space of quantum particles u obeys the evolution equation the classical soliton solutions are the eigenvalues of u in multi particle states in the fock space the construction easily allows for the incorporation of particle interactions which generate soliton effects that do not have a classical analog in this paper this new approach is applied to the case of the kadomtsev petviashvili ii equation the nonlinear quantum dynamical system describes a set of m 2s 1 particles with intrinsic spin s which interact in clusters of 1 n m 1 particles

diffraction problems for quasilinear reaction diffusion systems abstract the aim of this paper is to investigate existence uniqueness and qualitative properties of the weak and piecewise classical solutions of the diffraction problem for weakly coupled reaction diffusion systems monotony and stability with respect to the time variable of the weak solutions is proved as an application is considered a model reaction diffusion system describing an enzyme sensor for concentration of phenol in the chemical industry

asymptotic behaviour of principal eigenvalues for a class of cooperative systems this paper analyzes the asymptotic behaviour as of the principal eigenvalue of the cooperative operator l l1 a x b cl2 d x in a bounded smooth domain of rn n 1 under homogeneous dirichlet boundary conditions on where a 0 d 0 and b x 0 c x 0 for all x precisely our main result establishes that if int a d 1 0 consists of two components 0 1 and 0 2 then lim 1 l mini 1 2 1 l 0 0 i where for any d and r 1 l d stands for the principal eigenvalue of l in d moreover if we denote by the principal eigenfunction associated to l normalized so that 2 2 1 and for instance 1 l 0 0 1 1 l 0 0 2 then the limit lim is well defined in h01 h01 0 in 0 1 and 0 1 provides us with the principal eigenfunction of l 0 0 1 this is a rather striking result for as according to it the principal eigenfunction must approximate zero as if a d 0 in spite of the cooperative structure of the operator

existence results for the positive solutions of nonlinear elliptic systems in this paper we discuss the existence of solutions for nonlinear elliptic systems the positive weak solution is sought by the leray schauder degree

positivity for equations involving polyharmonic operators with dirichlet boundary conditions cranston fabes and zhao 26 5 established the uniform bound sup x y 2 x 6 y r g1 n x z g1 n z y dz g1 n x y m 1 1 where g1 n x y is the green function for the laplacian with dirichlet boundary conditions on a lipschitz domain rn with n 3 see 27 for n 2 this estimate was used in 23 and 18 to obtain positivity uniformly with respect to f 0 for noncooperative elliptic systems as

quantized representation of some nonlinear integrable evolution equations on the soliton sector the hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple construction of a quantized representation of these equations and their soliton solutions over a fock space of bosons or of fermions the classical nonlinear wave equation becomes a nonlinear equation for an operator the solution of this equation is constructed through an operator analog of the hirota transformation the classical n soliton solution is the expectation value of the solution operator in an n particle state in the fock space the effect of perturbations that modify soliton identity is demonstrated

the sine gordon equations complete and partial integrability the sine gordon equation in one space one time dimension is known to possess the painleve property and to be completely integrable it is shown how the method of singular manifold analysis obtains the backlund transform and the lax pair for this equation a connection with the sequence of higher order kdv equations is found the modified sine gordon equations are defined in terms of the singular manifold these equations are shown to be identically painleve also certain rational solutions are constructed iteratively the double sine gordon equation is shown not to possess the painleve property however if the singular manifold defines an affine minimal surface then the equation has integrable solutions this restriction is termed partial integrability the sine gordon equation in n 1 variables n space 1 time where n is greater than one is shown not to possess the painleve property the condition of partial integrability requires the singular manifold to be an einstein space with null scalar curvature the known integrable solutions satisfy this constraint in a trivial manner finally the coupled kdv or hirota satsuma equations possess the painleve property the associated modified equations are derived and from these the lax pair is found

nonlinear quantum mechanical system associated with sine gordon equation in 1 2 dimensions despite the fact that it is not integrable the 1 2 dimensional sine gordon equation has n soliton solutions whose velocities are lower than the speed of light c 1 for all n 1 based on these solutions a quantum mechanical system is constructed over a fock space of particles the coordinate of each particle is an angle around the unit circle u a nonlinear functional of the particle number operators which obeys the sine gordon equation in 1 2 dimensions is constructed its eigenvalues on n particle states in the fock space are the slower than light n soliton solutions of the equation a projection operator a nonlinear functional of u which vanishes on the single particle subspace is a mass density generator its eigenvalues on multi particle states play the role of the mass density of structures that emulate free spatially extended relativistic particles the simplicity of the quantum mechanical system allows for the incorporation of perturbations with particle interactions which have the capacity to annihilate and create solitons an effect that does not have an analog in perturbed classical nonlinear evolution equations

harnack principle for weakly coupled elliptic systems abstract we prove the harnack inequality for the weakly coupled elliptic system s where su big begin align l 1 cdots l n end align big u qu and u big begin align u 1 cdot cdot cdot u n end align big l k k 1 n are second order elliptic operators with holder continuous coefficients and q is a matrix valued function with singular entries in the case that q is irreducible a full harnack principle is proved

superstatistics thermodynamics and fluctuations a thermodynamiclike formalism is developed for superstatistical systems based on conditional entropies this theory takes into account large scale variations of intensive variables of systems in nonequilibrium stationary states ordinary thermodynamics is recovered as a special case of the present theory and corrections to it can systematically be evaluated a generalization of einstein s relation for fluctuations is presented using a maximum entropy condition

on the least point of the spectrum of certain cooperative linear systems with a large parameter abstract we obtain the asymptotic limit of the principal eigenvalue of a cooperative system of linear elliptic equations as a parameter tends to infinity our results are much more general than those in the work of caudevilla and lopez gomez 2008 2 we obtain an unusual limit problem

sign definite solutions in some linear elliptic systems on considere un ensemble faiblement couple de deux equations aux derivees partielles ou la matrice de couplage a des elements variables et la partie principale de chaque equation est le meme operateur uniformement elliptique on obtient des conditions necessaires pour le decouplage on determine le signe algebrique des composantes de solution

superstatistics and the quest of generalized ensembles equivalence in a system with long range interactions abstract the so called 2 superstatistics of beck and cohen bc is employed to investigate the infinite range blume capel model a well known representative system displaying inequivalence of canonical and microcanonical phase diagrams while not being restricted to any of those particular thermodynamic limits our analytical result can smoothly recover both canonical and microcanonical ensemble solutions as its nonextensive parameter q is properly tuned additionally we compare our findings to ones previously obtained from a generalized canonical framework named extended gaussian ensemble ege finally we show that both ege and bc solutions are equivalent at the thermodynamic level

static solitons lorentz invariance and a new perspective on the integrability of the sine gordon equation in 1 2 dimensions contrary to the common understanding the sine gordon equation in 1 2 dimensions does have n soliton solutions for any n the hirota algorithm allows for the construction of static n soliton solutions i e solutions that do not depend on time of that equation for any n lorentz transforming the static solutions yields n soliton solutions in any moving frame they are scalar functions under lorentz transformations in an n soliton solution in a moving frame n 2 of the 1 2 dimensional momentum vectors of the solitons are linear combinations of the two remaining vectors

global attractivity and singular perturbation for a class of nonlinear cooperative systems abstract in the first part of this paper it is proved a general principle for reaction diffusion cooperative systems with concave nonlinearities it is proved that there exists a unique coexistence state u v if and only if the trivial solution is linearly unstable in this case u v is globally asymptotically stable with respect to positive initial data moreover if the trivial solution is linearly stable it is globally asymptotically stable with respect to non negative initial data in the second part it is investigated the singular perturbation problem it is shown that the positive solution of the diffusion model tends to the positive equilibrium of the purely kinetic model as the diffusion coefficients tend to zero uniformly in compact subsets of the domain

on invariant probability measures of regime switching diffusion processes with singular drifts abstract under integrability conditions of the coefficients the existence uniqueness and regularity estimates are derived for the invariant probability measure of regime switching diffusion processes moreover we study the l 1 uniqueness of the semigroup generated by regime switching diffusion processes as an application the l 1 uniqueness of the extension of weakly coupled elliptic systems is obtained

modelling train delays with q exponential functions we demonstrate that the distribution of train delays on the british railway network is accurately described by q exponential functions we explain this by constructing an underlying superstatistical model

uniqueness of large positive solutions for a class of radially symmetric cooperative systems abstract this paper shows the uniqueness of the large solution of a class of radially symmetric sublinear elliptic systems of cooperative type this result is based on the strong maximum principle rather than on the blow up rates of the large solutions as it is common in most the available results for single equations

application of the beck model to stock markets value at risk and portfolio risk assessment abstract we apply the beck model developed for turbulent systems that exhibit scaling properties to stock markets our study reveals that the beck model elucidates the properties of stock market returns and is applicable to practical use such as the value at risk estimation and the portfolio analysis we perform empirical analysis with daily intraday data of the s p500 index return and find that the volatility fluctuation of real markets is well consistent with the assumptions of the beck model the volatility fluctuates at a much larger time scale than the return itself and the inverse of variance or inverse temperature obeys distribution as predicted by the beck model the distribution of returns is well fitted by q gaussian distribution of tsallis statistics the evaluation method of value at risk var one of the most significant indicators in risk management is studied for q gaussian distribution our proposed method enables the var evaluation in consideration of tail risk which is underestimated by the variance covariance method a framework of portfolio risk assessment under the existence of tail risk is considered we propose a multi asset model with a single volatility fluctuation shared by all assets named the single model and empirically examine the agreement between the model and an imaginary portfolio with dow jones indices it turns out that the single model gives good approximation to portfolios composed of the assets with non gaussian and correlated returns

large deviation techniques applied to systems with long range interactions we discuss a method to solve models with long range interactions in the microcanonical and canonical ensemble the method closely follows the one introduced by r s ellis physica d 133 106 1999 which uses large deviation techniques we show how it can be adapted to obtain the solution of a large class of simple models which can show ensemble inequivalence the model hamiltonian can have both discrete ising potts and continuous hmf free electron laser state variables this latter extension gives access to the comparison with dynamics and to the study of non equilibrium effects we treat both infinite range and slowly decreasing interactions and in particular we present the solution of the ising model in one dimension with 0 1

green function for schrodinger operator and conditioned feynman kac gauge consider the schrodinger operator h 2 q in a bounded c1 1 domain d with q klocd d q satisfies the condition sup spec 2 q d v x y g x y e y x exp 0 t q x t d t x y d where xt is the conditioned brownian motion starting at x and ending at y with the life time t and v g can be extended to a continuous and positive function on d d specifically we give the comparison theorem there exists a constant c c d q 0 such that 1 c g x y v x y c g x y x y d another result is that v nz x z x d z d exists and represents the poisson kernel for the dirichlet problem corresponding to schrodinger operator h

partial equivalence of statistical ensembles and kinetic energy abstract the phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples the mean field xy and the mean field spherical model the configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble furthermore the configurational microcanonical entropy is a smooth function whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble in the presence of a standard kinetic energy contribution partial equivalence is removed and a nonanalyticity arises also microcanonically hence in contrast to the common belief kinetic energy even though a quadratic form in the momenta has a nontrivial effect on the thermodynamic behaviour as a by product we present the microcanonical solution of the mean field spherical model with kinetic energy for finite and infinite system sizes

on the ambrosetti prodi problem for non variational elliptic systems we study the ambrosetti prodi problem for nonlinear elliptic equations and systems with uniformly elliptic operators in non divergence form and non smooth coefficients and with non linearities with linear or power growth

bifurcation for an elliptic system coupled in the linear part we study linearly coupled elliptic systems without any assumption on the signs of the coefficients of the linear part we derive first the leray schauder degree of the associated linear system then we obtain sufficient conditions on the nonlinear terms for having bifurcation to coexistence states our results include the sublinear case keys words linearly coupled elliptic systems bifurcation to positive solutions coexistence states leray schauder degree email jfleck cict fr rpardo sunma4 mat ucm es

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

feynman kac functionals and positive solutions of 1 2δu qu 0 let d be a bounded c 2 domain in d and let q be a bounded borel function in d for x d and z d suppose x t under the law p x z is brownian motion in d starting at x and conditioned to converge to z let be the lifetime of x t we show that if the quantity e x z left exp left int limits 0 t q x s ds right right is finite for one x d and one z d then this quantity remains bounded as x varies over d and z varies over d this may be considered one quantitative expression of the qualitative statement that no matter where brownian motion in d eventually hits d it goes all over d before it gets there we apply this result to show that if the equation 1 2 u qu 0 admits a non negative solution in d which is strictly positive on a subset of d of positive harmonic measure then for any non negative bounded borel function f on d it admits a unique bounded solution u satisfying u f on d and this solution u is non negative

global dynamics of a classical lotka volterra competition diffusion advection system abstract in this paper we study a classical two species lotka volterra competition diffusion advection system where the diffusion and advection rates of two competitors are supposed to be proportional by employing the principal spectral theory we first establish a key a priori estimate on the co existence positive steady state which is a powerful tool to link the local and global dynamics we then further present a complete classification on all possible long time dynamical behaviors by appealing to the theory of monotone dynamical systems lastly we apply these results to a special situation where two species are competing for the same resources and obtain a sharp criteria in term of certain variable parameters for all kinds of global dynamics this work gives a positive answer to the conjecture proposed by lou et al in 34 by considering a more general model under certain conditions and also can be seen as a further development of he and ni 19 for competition diffusion system where we bring new ingredients in the arguments to overcome the difficulty caused by the involvement of advection

coexistence states of an elliptic system modeling a population with two age groups in this work an elliptic system with nonlinear boundary conditions describing two subpopulations of the same species competing for resources is studied under some natural assumptions we find the sufficient conditions for the existence of positive solutions of the system by using bifurcation techniques

maximum and antimaximum principles for some nonlocal diffusion operators abstract in this work we consider the maximum and antimaximum principles for the nonlocal dirichlet problem j u u u h r n j x y u y d y u x u x h x 0 in a bounded domain with u x 0 in r n the kernel j in the convolution is assumed to be a continuous compactly supported nonnegative function with unit integral we prove that for 1 the solution verifies u 0 in if h l 2 h 0 while for 1 and close to 1 the solution verifies u 0 in provided h x x d x 0 h l this last assumption is also shown to be optimal the neumann version of the problem is also analyzed

maximum principles for a coupled system of second and fourth order elliptic equations and an application in this paper we obtain a maximum principle for the coupled system of second and fourth order elliptic equations using an abstract result in a recent paper by correa and souto nonlinear anal 26 1996 and an application of the maximum principle is given

on the existence of coexistence states for an advection cooperative system with spatial heterogeneities abstract this paper is devoted to the analysis of the existence of coexistence states for cooperative systems under homogeneous dirichlet boundary conditions we assume rather general spatial heterogeneities for the coefficients of the non linearities and the cooperative terms in order to obtain sharp existence results we add advection terms related to the cooperative terms so that the system can be transformed into a variational one applying then several variational methods and bifurcation theory we arrive at necessary and sufficient condition on the parameter for the existence and the uniqueness of coexistence states we also compare the conditions for the heterogeneous case and the constant case

comparison principle for non cooperative elliptic systems this paper presents some sufficient conditions for the validity of the comparison principle for weak and classical solutions of non cooperative weakly coupled systems of elliptic second order pde

existence uniqueness and stability of positive solutions to sublinear elliptic systems reaction diffusion systems are used to model many chemical and biological phenomena in the natural world 25 26 and systems of coupled partial differential equations are also used in other physical models such as nonlinear schrodinger systems in multi component bose einstein condensates and nonlinear optics 19 23 the steady state solutions or standing wave solutions of such systems of nonlinear partial differential equations satisfy a nonlinear elliptic system with more than one equation much effort has been devoted to the existence of solutions of such systems see for example 4 8 10 11 13 15 17 24 30 33 34 but it is usually difficult to determine whether or not the solution is unique we consider the positive solutions of a semilinear elliptic system of the form

existence results for some nonlinear elliptic systems abstract the paper is concerned with some nonlinear elliptic systems by using variational methods we obtain the existence of weak solutions for the semilinear elliptic system and the quasilinear elliptic system

switched diffusion processes and systems of elliptic equations a dirichlet space approach the switched diffusion process associated with a weakly coupled system of elliptic equations is studied via a dirichlet space approach and is applied to prove the existence theorem of the cauchy initial problem for the system a representation theorem for the solution of the dirichlet boundary value problem and a generalised skorohod decomposition for the reflecting switched diffusion process are obtained

on a system of reaction diffusion equations describing a population with two age groups abstract a system of reaction diffusion equations modelling a population divided into juvenile and adult age groups is studied the system is not co operative but its linear part is and this makes it possible to establish existence non existence and stability results for non negative solutions of the system in terms of the principal eigenvalue of the corresponding linearized system

irreducible compact operators the purpose of the present paper is to show that a positive compact ideal irreducible operator t in a banach lattice of dimension greater than one has spectral radius r t 0 i e t is not quasi nilpotent it was shown in 6 that there exist positive irreducible operators which are quasi nilpotent and the question under what conditions a positive irreducible operator t satisfies r t 0 has been studied extensively see e g 6 and 7 sect v 6 in particular we mention the ando krieger theorem see e g 9 theorem 136 9 which states that a positive irreducible kernel operator t in a banach function space has r t 0 recently in 8 some special situations are discussed in which a compact positive irreducible operator has a strictly positive spectral radius let l be a real or complex banach lattice by 2 we denote the banach space of all bounded linear operators in l as usual we write s t in l whenever su tu for all o uel given 0 t l the closed ideal j in l is called t invariant if t j j and t is called ideal irreducible if the only closed t invariant ideals are 0 and l see 7 iii 8 for the general theory of banach lattices and positive operators we refer to the books 7 and 9 in the proof of the main result of the paper we will use some properties of the center of a banach lattice we recall some elementary facts let l be a real banach lattice the center z l of l is the subspace of 5 l consisting of all operators z for which there exists 0 2 ir such that f l 2 f for all f l the center has the structure of a vector lattice with nl v n2 u n l u v n2u and ozla zz u lu a nzu for all o u l and all l n2ez l moreover z l is a commutative algebra with respect to composition as multiplication and the identity operator i in l is a strong unit i e for any rc z l there exists 0 2eir such that zi 2i see 9 chap 20 note that if l c k for some compact hausdorff space k then z l can be identified with c k acting on itself by multiplication if l is a dedekind complete banach lattice and 0 u v in l then it is an easy consequence of the freudenthal spectral theorem 4 theorem 40 2 that there exists n z l such that zcv u and o n i however in an arbitrary banach lattice such a 7z need not exist as is shown by the banach lattice l c 0 1 the next lemma shows that under rather mild conditions we can

variational approach for a class of cooperative systems abstract the aim of this work is to ascertain the characterization of the existence of coexistence states for a class of cooperative systems supported by the study of an associated non local equation through classical variational methods thanks to those results we are able to obtain the blow up behavior of the solutions in the whole domain for certain values of the main continuation parameter

ground state positivity negativity and compactness for a schrodinger operator in rn abstract we treat the schrodinger operator a q x on l 2 r n with the potential q r n q 0 bounded below and satisfying some reasonable hypotheses on the growth at infinity faster than x 2 as x we are concerned primarily with the compactness of the resolvent a i 1 of a as an operator on the banach space x x f l 2 r n f l r n f x ess sup r n f where denotes the ground state for a if is the ground state energy for a we show that the restricted operator a i 1 x x is not only bounded but also compact for in particular the spectra of a in l 2 r n and x coincide each eigenfunction belongs to x as another consequence we obtain a maximum and an anti maximum principles

multiparameter generalization of nonextensive statistical mechanics we show that the stochastic interpretation of tsallis s thermostatistics given recently by beck phys rev lett 87 180601 2001 leads naturally to a multiparameter generalization the resulting class of distributions is able to fit experimental results which cannot be reproduced within boltzmann s or tsallis s formalism

a spatial seirs reaction diffusion model in heterogeneous environment abstract we propose a susceptible exposed infected recovered susceptible seirs reaction diffusion model where the disease transmission and recovery rates can be spatially heterogeneous the basic reproduction number r 0 is connected with the principal eigenvalue of a linear cooperative elliptic system threshold type results on the global dynamics in terms of r 0 are established the monotonicity of r 0 with respect to the diffusion rates of the exposed and infected individuals which does not hold in general is established in several cases finally the asymptotic profile of the endemic equilibrium is investigated when the diffusion rate of the susceptible individuals is small our results reveal the importance of the movement of the exposed and recovered individuals in disease dynamics as opposed to most of previous works which solely focused on the movement of the susceptible and infected individuals

an extension of maximum and anti maximum principles to a schrodinger equation in r2 abstract strong maximum and anti maximum principles are extended to weak l2 r 2 solutions u of the schrodinger equation u q x u u f x in l2 r 2 in the following form let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the schrodinger operator a q x in l2 r 2 assume that q x q x f is a sufficiently smooth perturbation of a radially symmetric function f 0 and 0 f 1 c const a e in r 2 then there exists a positive number depending upon f such that for every 1 with 1 the inequality 1 u c 1 holds a e in r 2 where c is a positive constant depending upon f and it is shown that such an inequality is valid if and only if the potential q x which is assumed to be strictly positive and locally bounded has a superquadratic growth as x this result is applied to linear and nonlinear elliptic boundary value problems in strongly ordered banach spaces whose positive cone is generated by the eigenfunction 1 in particular problems of existence and uniqueness are addressed

liouville type theorems monotonicity results and a priori bounds for positive solutions of elliptic systems this paper is a contribution to the study of boundary value problems for systems of elliptic partial differential equations

principal eigenvalue and maximum principle for cooperative periodic parabolic systems abstract this paper classifies the set of supersolutions of a general class of periodic parabolic problems in the presence of a positive supersolution from this result we characterize the positivity of the underlying resolvent operator through the positivity of the associated principal eigenvalue and the existence of a positive strict supersolution lastly this scalar characterization is used to characterize the strong maximum principle for a class of periodic parabolic systems of cooperative type under arbitrary boundary conditions of mixed type

quantization of solitons and the restricted sine gordon model we show how to compute form factors matrix elements of local fields in the restricted sine gordon model at the reflectionless points by quantizing solitons we introduce quantum separated variables in which the hamiltonians are expressed in terms of quantum functions we explicitly describe the soliton wave functions and we explain how the restriction is related to an unusual hermitian structure we also present a semi classical analysis which enlightens the fact that the restricted sine gordon model corresponds to an analytical continuation of the sine gordon model intermediate between sine gordon and kdv

positive solutions of an elliptic system modeling a population with two age groups we study the existence of positive solutions for an elliptic system modeling two subpopulations of the same species competing for resources under some suitable assumptions we find the necessary and sufficient conditions for the existence of positive solutions of the system by using bifurcation techniques moreover an open problem proposed by bouguima et al 2008 is answered

asymptotic behavior of the principal eigenvalue for cooperative periodic parabolic systems and applications abstract the effects of spatial heterogeneity on population dynamics have been studied extensively however the effects of temporal periodicity on the dynamics of general periodic parabolic reaction diffusion systems remain largely unexplored as a first attempt to understand such effects we analyze the asymptotic behavior of the principal eigenvalue for linear cooperative periodic parabolic systems with small diffusion rates as an application we show that if a cooperative system of periodic ordinary differential equations has a unique positive periodic solution which is globally asymptotically stable then the corresponding reaction diffusion system with either the neumann or regular oblique derivative boundary condition also has a unique positive periodic solution which is globally asymptotically stable provided that the diffusion coefficients are sufficiently small the role of temporal periodicity spatial heterogeneity and their combined effects with diffusion will be studied in subsequent papers for further understanding and illustration