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

another runner removal theorem for v decomposition numbers of iwahori hecke algebras and q schur algebras abstract let f denote the fock space representation of the quantum group u v sl e the v decomposition numbers are the coefficients when the canonical basis for this representation is expanded in terms of the basis of partitions and the evaluations at v 1 of these polynomials give the decomposition numbers for iwahori hecke algebras and q schur algebras over c james and mathas have proved a theorem which relates v decomposition numbers for different values of e by adding empty runners to the abacus displays for the labelling partitions here we prove a similar theorem which involves adding full runners to these abacus displays

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

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

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

monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation we consider the problem of identifying an unknown diffusion coefficient in a nonlinear diffusion equation from overspecified data measured on the boundary conditions ensuring compatibility of the data are derived and it is shown that the mapping which carries the diffusion coefficient into the data is isotonic this result is then used to derive a uniqueness result for the inverse problem and for an associated identification problem some results of numerical experiments are presented to illustrate the various results

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

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

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

a variational approach for standing waves of fitzhugh nagumo type systems abstract we study the existence of radially symmetric solutions of fitzhugh nagumo type elliptic systems in r n n 2 u g u v in r n d v v u in r n u x v x 0 0 as x we utilize a truncation technique and apply minimax arguments to the corresponding strongly indefinite functional i u v 1 2 r n u 2 d v 2 d x r n g u 2 v 2 u v d x defined on h r 1 r n h r 1 r n to find positive and possibly sign changing solutions of in particular we overcome difficulty related to palais smale condition via our new scaling argument when g 1 0 1 2 we improve the existence result of reinecke sweers 23

interior peak solutions for an elliptic system of fitzhugh nagumo type abstract we consider the dirichlet problem for an elliptic system of fitzhugh nagumo type we prove that the problem has a solution with a sharp peak inside 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

the γ limit of traveling waves in the fitzhugh nagumo system abstract patterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems a common theme in investigating such systems is to identify the intrinsic factors responsible for such self organization the convergence is a well known technique applicable to variational formulations of concentration phenomena of stable patterns recently a geometric variational functional associated with the limit of standing waves of the fitzhugh nagumo system has been built this article studies the limit of traveling waves to the best of our knowledge this is the first attempt to expand the scope of applicability of convergence to cover non stationary problems

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

application of finite difference method to analysis an ill posed problem abstract in this paper a numerical solution of an inverse non dimensional heat conduction problem will be considered by using a sensor located at a point inside the body and measuring the temperature at a point x x 1 0 x 1

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

stationary wave solutions of a system of reaction diffusion equations derived from the fitzhugh nagumo equations we consider an extension of the fitzhugh nagumo model namely the system u t d 1 u xx f u w qquad w t d 2 w xx varepsilon u gamma w where varepsilon 0 gamma 0 d 1 0 d 2 0 and f u is cubic we allow gamma to be large which implies that there are three constant solutions we show that over an appropriate range of parameters the system has time independent pulse solutions and an infinite number of periodic solutions depending on the particular choice of parameters we show that the pulse solution leads to either the first constant solution or the third constant solution

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

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

a numerical method for solving of a nonlinear inverse diffusion problem in this paper we will first study the existence and uniqueness of the solution for a one dimensional nonlinear inverse diffusion problem via an auxiliary problem and the schauder fixed point theorem furthermore a numerical algorithm based on the finite difference method and the least squares scheme for solving a nonlinear inverse problem is proposed at the beginning of the numerical algorithm taylor s series expansion is employed to linearize nonlinear terms and then the finite difference method is used to discretize the problem domain the present approach is to rearrange the matrix forms of the differential governing equations and estimate the unknown diffusion coefficient the least squares method is adopted to find the solution it is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study and thus it is classified as the function estimation in inverse calculation results show that an excellent estimation on the diffusion coefficient can be obtained within a couple of minutes of cpu time on a pentium iv 2 4ghz pc

standing waves in the fitzhugh nagumo system and a problem in combinatorial geometry we show that there is a close relation between standing wave solutions for the fitzhugh nagumo system

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

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 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

traveling waves for the fitzhugh nagumo system on an infinite channel abstract we are concerned with the traveling wave solutions for the fitzhugh nagumo system on an infinite channel based on a variational formulation in which a non local term depends on a parameter the speed of a traveling wave can be selected out furthermore to show the existence of a traveling wave solution with such a speed we seek a minimizer subject to a constraint in the way of solving the variational problem we apply a truncation technique to the nonlocal term to obtain a minimizer located in a bounded invariant region

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

james s conjecture holds for weight four blocks of iwahori hecke algebras abstract james s conjecture suggests that in certain cases the decomposition numbers for the iwahori hecke algebra of the symmetric group over a field of prime characteristic and in particular the decomposition numbers for the symmetric group itself coincide with the decomposition numbers for a corresponding iwahori hecke algebra defined over c and hence can be computed using the llt algorithm we prove this conjecture for blocks of weight 4

multipeak solutions for an elliptic system of fitzhugh nagumo type we consider the dirichlet problem for an elliptic system of fitzhugh nagumo type we prove that the problem has solutions with arbitrary many sharp peaks near the boundary but not on the boundary

symmetry properties in systems of semilinear elliptic equations abstract we investigate symmetry properties of solutions of systems of semilinear elliptic equations the two main tools we use consist of the maximum principle and the device of moving parallel planes to a critical position and then showing that the solution is symmetric about the limiting plane an application to the belousov zhabotinskii chemical reaction is given

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

quasi solution approach for a two dimensional nonlinear inverse diffusion problem this paper is related to a class of inverse problems for identification of the coefficient in a square porous medium the unknown coefficient depends on the solution and belongs the class of admissible coefficients using continuous dependence of solutions on the coefficient convergence in the corresponding direct problems the existence of the quasi solution of the inverse problem is obtained in the appropriate class of admissible coefficients

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

standing pulse solutions to fitzhugh nagumo equations reaction diffusion systems serve as relevant models for studying complex patterns in several fields of nonlinear sciences a localized pattern is a stable non constant stationary solution usually located far away from neighborhoods of bifurcation induced by turing s instability in the study of fitzhugh nagumo equations we look for a standing pulse with a profile staying close to a trivial background state except in one localized spatial region where the change is substantial this amounts to seeking a homoclinic orbit for a corresponding hamiltonian system and we utilize a variational formulation which involves a nonlocal term such a functional is referred to as helmholtz free energy in modeling microphase separation in diblock copolymers while its global minimizer does not exist in our setting of dealing with standing pulse the homoclinic orbit obtained here is a local minimizer extracted from a suitable topological class of admissible functions in contrast with the known results for positive standing pulses found in the literature a new technique is attempted by seeking a standing pulse solution with a sign change

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

decomposition numbers for weight three blocks of symmetric groups and iwahori hecke algebras let f be a field q a non zero element of f and h n h f q g n the iwahori hecke algebra of the symmetric group g n if b is a block of h n of e weight 3 and the characteristic of f is at least 5 we prove that the decomposition numbers for b are all at most 1 in particular the decomposition numbers for a p block of g n of defect 3 are all at most 1

general runner removal and the mullineux map abstract we prove a new runner removal theorem for q decomposition numbers of the level 1 fock space of type a e 1 1 generalising earlier theorems of james mathas and the author by combining this with another theorem relating to the mullineux map we show that the problem of finding all q decomposition numbers indexed by partitions of a given weight is a finite computation

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

equating decomposition numbers for different primes abstract this paper shows that certain decomposition numbers for the iwahori hecke algebras of the symmetric groups and the q schur algebras at different roots of unity in characteristic zero are equal to prove our results we first establish the corresponding theorem for the canonical basis of the level one fock space and then apply deep results of ariki and varagnolo vasserot

existence and uniqueness of a solution for a two dimensional nonlinear inverse diffusion problem abstract the problem of identifying the coefficient in a square porous medium is considered it is shown that under certain conditions of data f g and for a properly specified class a of admissible coefficients there exists at least one a a such that a u is a solution of the corresponding inverse problem