existence and non existence of nontrivial solutions for schrodinger systems via nehari pohozaev manifold abstract this paper is concerned with existence of bound states for a coupled gradient system of nonautonomous schrodinger equations which arises from studies of nonlinear optics and bose einstein condensates by using variational methods that are constrained to a nehari pohozaev manifold we obtain existence of nonnegative and positive bound states solutions in particular we show non existence result for a minimizing problem

dynamic scaling of disordered ising systems the critical dynamics of site disordered three dimensional ising systems has been studied by conventional local dynamics simulations investing 1015 single spin flips the author has verified that the correlation functions of disordered ising systems obey dynamic scaling behaviour the dynamic scaling functions have been calculated the critical exponent z appears to be strongly dependent on the degree of disorder the author has shown that this dependence arises from a crossover phenomenon which has been detected in the static critical behaviour the dynamical exponent has been estimated to be z 2 4 or 0 1 which is surprisingly near to the renormalization group result in o in 1 2

the three dimensional dilute ising magnet the dilute ising model with a p 0 8 fraction of the sites occupied by spins is simulated on l3 systems for l up to 300 using a single cluster algorithm of wolff in the range of reduced temperature 0 002 t tc tc 0 03 the susceptibility appears to fit a simple power with an effective exponent eff 1 36

summability of the perturbative expansion for a zero dimensional disordered spin model we show analytically that the perturbative expansion for the free energy of the zero dimensional quenched disordered ising model is borel summable in a certain range of parameters provided that the summation is carried out in two steps first in the strength of the original coupling of the ising model and subsequently in the variance of the quenched disorder this result is illustrated by some high precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method

the evolutionary minority game with local coordination abstract we discuss a modification of the evolutionary minority game emg in which agents are placed in the nodes of a regular or a random graph a neighborhood for each agent can thus be defined and a modification of the usual relaxation dynamics can be made in which each agent updates her decision depending upon her neighborhood we report numerical results for the topologies of a ring a torus and a random graph changing the size of the neighborhood we find the surprising result that in the emg a better coordination a lower frustration can be achieved if agents base their actions on local information disregarding the global trend in the self segregation process

multiplicity of solutions for a fourth order problem with exponential nonlinearity abstract let b be the unit ball in r n n 5 and n be the exterior unit normal vector on the boundary we consider radial solutions to 2 u e u in b u 0 and u n 0 on b where 0 we show that there exists a unique s 0 such that if s there is a radial singular solution if 5 n 12 then for s there exist infinitely many regular radial solutions and as s the number of such solutions goes to infinity if n 13 we prove uniqueness of smooth radial solutions we derive similar results for the same equation with navier boundary conditions

bifurcation diagrams of coupled schrodinger equations radially symmetric solutions of many important systems of partial differential equations can be reduced to systems of special ordinary differential equations a numerical solver for initial value problems for such systems is developed based on matlab and numerical bifurcation diagrams are obtained according to the behavior of the solutions various bifurcation diagrams of coupled schrodinger equations from nonlinear physics are obtained which suggests the uniqueness of the ground state solution

partial regularity of stable solutions to the supercritical equations and its applications abstract we prove the partial regularity of stable solutions of supercritical elliptic equations as an application we prove that any smooth stable entire solution to supercritical equations with p in a suitable range is radially symmetric

existence and stability of entire solutions to a semilinear fourth order elliptic problem for a semilinear biharmonic equation with exponential nonlinearity we study the existence and the asymptotic behavior of entire solutions furthermore their stability and stability outside a compact set of rn n 2 is discussed in any space dimension n

critical behavior of the specific heat for pure and site diluted simple cubic ising systems the exponent of the specific heatc is determined for the pure and the site diluted simple cubic ising model concentrationx 0 0 2 0 4 of nonmagnetic sites by a finite size scaling analysis of the peak value cmax l for systems of linear dimensionsl 8 16 32 and 64 the cmax values are obtained by the ferrenberg swendsen algorithm using monte carlo data from a fully vectorized multi spin coding program we obtain 0 11 for x 0 and a crossover to a negative value upon dilution with 0 029 4 both forx 0 2 andx 0 4

on the minority game analytical and numerical studies abstract we investigate further several properties of the minority game we have recently introduced we explain the origin of the phase transition and give an analytical expression of 2 n in the n 2 m region the ability of the players to learn a given payoff is also analyzed and we show that the darwinian evolution process tends to a self organized state in particular the lifetime distribution is a power law with exponent 2 furthermore we study the influence of identical players on their gain and on the systems performance finally we show that large brains always take advantage of small brains

stable and finite morse index solutions of toda system abstract we prove a liouville type theorem and a partial regularity result for stable and finite morse index solutions of toda system the main tools are integral estimates a monotonicity formula and blowing down analysis for such systems they may be split into two sub systems during the blowing down process some e regularity theorems are developed to deal with this problem

positive solutions of an elliptic equation with negative exponent stability and critical power abstract we study positive solutions of the equation u x u p in r n n 2 where p 0 2 and is a bounded or unbounded domain we show that there is a critical power p p c such that this equation with r n has no stable positive solution for p p c but it admits a family of stable positive solutions when 0 p p c if p p c min 0 we further show that this equation with b r 0 has no positive solution with finite morse index that has an isolated rupture at 0 and analogously it has no positive solution with finite morse index when r n b r among other results we also classify the positive solutions over b r 0 which are not bounded near 0

classification and sharp range of flux pairs for radial solutions to a coupled system abstract in this paper we study a coupled system of two nonlinear partial differential equations in the plane which is related to liouville equations non abelian higgs bps vortex equations or two higgs electroweak model with singularities at the origin in addition to deriving the uniqueness of the so called topological solutions we also clarify the structure of all types of solutions including the blow up ones under various conditions on coefficients and parameters appearing in the system furthermore the sharp range of flux pairs associated with specific types of solutions is considered as well

on the solutions of liouville systems for some prescribed m 0 together with the dirichlet boundary condition u 0 on 0 the liouville equation finds applications in various fields of physics and mathematics to name a few it represents the newtonian potential of a cluster of self gravitating mass distribution where a 0 1 6 36 37 the electric potential induced by charge carriers in the theory of electrolytes where a 0 31 and maximal entropy solutions of the incompressible euler equation 23 9 in the field of differential geometry it stands for the problem of finding a metric corresponding to a prescribed gaussian curvature 3 10 the system analog of l takes the form

critical crossover phenomena in disordered ising systems the author has investigated the critical behaviour of site disordered ising systems over a large range of dilution 0 6 or p or 1 0 investing about 1015 single spin flips with conventional local dynamics critical temperatures have been determined with high precision using the cumulant method the finite size simulations lead to concentration dependent exponents which seem to violate universality the author shows that the concentration dependence is induced by a crossover phenomenon which governs a large interval of the critical region the author finds that the scaling functions of systems with different disorder converge asymptotically to universal behaviour consistent with the fixed point of weak disorder

some remarks on embedding of weighted sobolev spaces abstract in this paper we generalize the well known caffarelli kohn nirenberg inequality to the fourth order case then by using such embeddings we obtain the existence of positive solutions of navier boundary value problems of a weighted fourth order elliptic equation

order and disorder in the local evolutionary minority game abstract we study a modification of the evolutionary minority game emg in which agents are placed in the nodes of a regular or a random graph a neighborhood for each agent can thus be defined and a modification of the usual relaxation dynamics can be made in which each agent updates her decision scheme depending upon the options made in her immediate neighborhood we name this model the local evolutionary minority game lemg we report numerical results for the topologies of a ring a torus and a random graph changing the size of the neighborhood we focus our discussion in a one dimensional system and perform a detailed comparison of the results obtained from the random relaxation dynamics of the lemg and from a linear chain of interacting spin like variables with temperature we provide a physical interpretation of the surprising result that in the lemg a better coordination a lower frustration is achieved if agents base their actions on local information we show how the lemg can be regarded as a model that gradually interpolates between a fully ordered antiferromagnetic like system and a fully disordered system that can be assimilated to a spin glass

entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity we investigate entire radial solutions of the semilinear biharmonic equation 2 u exp u in r n n 5 0 being a parameter we show that singular radial solutions of the corresponding dirichlet problem in the unit ball cannot be extended as solutions of the equation to the whole of r n in particular they cannot be expanded as power series in the natural variable s log x next we prove the existence of infinitely many entire regular radial solutions they all diverge to as x and we specify their asymptotic behaviour as in the case with power type nonlinearities f gazzola h ch grunau radial entire solutions for supercritical biharmonic equations math ann 334 2006 905 936 the entire singular solution x 4l og x plays the role of a separatrix in the bifurcation picture finally a technique for the computer assisted study of a broad class of equations is developed it is applied to obtain a computer assisted proof of the underlying dynamical behaviour for the bifurcation diagram of a corresponding autonomous system of odes in the case n 5

radial symmetry results for fractional laplacian systems abstract in this paper we generalize the direct method of moving planes for the fractional laplacian to the system case considering a coupled nonlinear system with fractional laplacian we first establish a decay at infinity principle and a narrow region principle using these principles we then obtain two radial symmetry results for the decaying solutions of the fractional laplacian systems finally we apply our method to fractional schrodinger systems and fractional henon systems

perturbative solution for the generalised anharmonic oscillators serious difficulties have been encountered in the past when attempting the straightforward application of the borel method to the summation of perturbation series in quantum mechanics and quantum field theory because of an analytic continuation of the borel transform series which is usually performed by means of conformal mapping techniques the author shows that this continuation may be accomplished by combining the borel method with the first confluent form of the epsilon algorithm of wynn 1960 1968 for the calculation of the ground state energy eigenvalue of the generalised anharmonic oscillators two different approaches are presented both of which lead to accurate results

solutions of superlinear elliptic equations and their morse indices we consider here solutions of semilinear second order elliptic equations with superlinear nonlinearities and we present some relationships between their morse indices and some qualitative properties in particular we show that for uo subcritical nonlinearities bounds on solutions are equivalent to bounds on their morse indices

thermal treatment of the minority game we study a cost function for the aggregate behavior of all the agents involved in the minority game mg or the bar attendance model bam the cost function allows us to define a deterministic synchronous dynamic that yields results that have the main relevant features than those of the probabilistic sequential dynamics used for the mg or the bam we define a temperature through a langevin approach in terms of the fluctuations of the average attendance we prove that the cost function is an extensive quantity that can play the role of an internal energy of the many agent system while the temperature so defined is an intensive parameter we compare the results of the thermal perturbation to the deterministic dynamics and prove that they agree with those obtained with the mg or bam in the limit of very low temperature

solutions with high dimensional singular set to a conformally invariant elliptic equation in bf r 4 and in bf r 6 we construct positive weak solutions to the equation delta 0 v v frac n 2 n 2 where 0 denotes the conformal laplacian on then sphere n 4 6 having singular sets of hausdorff dimension greater than or equal to frac n 2 2

on the crossover to universal criticality in dilute ising systems monte carlo simulations of the critical behaviour of disordered ising systems have led to concentration dependent critical exponents which seem to violate universality we apply the renormalization group to investigate the crossover effects which cause the observed behaviour we improve the three loop expansion of the callan symanzik and wilson functions by a pade borel approximation and solve the flow equations for various initial points the exponents found in the simulations can be related to regions in the space of coupling coefficients away from the fixed point

a monotonicity formula and a liouville type theorem for a fourth order supercritical problem we consider liouville type and partial regularity results for the nonlinear fourth order problem

critical behaviour of 3d systems with long range correlated quenched defects a field theoretic description of the critical behaviour of systems with quenched defects obeying power law correlations x a for large separations x is given directly for three dimensional systems and for different values of the correlation parameter 2 a3 a renormalization analysis of the scaling function in the two loop approximation is carried out and the fixed points corresponding to the stability of various types of critical behaviour are identified the obtained results essentially differ from results evaluated by a double expansion the critical exponents in the two loop approximation are calculated with the use of the pade borel summation technique

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

entire solutions of semilinear elliptic equations in r 3 and a conjecture of de giorgi this paper is concerned with the study of bounded solutions of semilinear elliptic equations u f u in the whole space r under the assumption that u is monotone in one direction say nu in r n the goal is to establish the one dimensional character or symmetry of u namely that u only depends on one variable or equivalently that the level sets of u are hyperplanes this type of symmetry question was raised by de giorgi in who made the following conjecture we quote literally page of dg

some liouville theorems for henon type elliptic equations abstract we investigate here the nonlinear elliptic equations u x e u and u x u p 1 u with 2 p 1 and n 2 in particular we prove some liouville type theorems for weak solutions with finite morse index in the low dimensional euclidean spaces or half spaces

uniqueness of topological multi vortex solutions for a skew symmetric chern simons system in this paper we consider a skew symmetric chern simons system problem with a coupling parameter our main goal is that when the coupling parameter is small the topological type solutions to this system problem are uniquely determined by the location of their vortex points this result follows by the bubbling analysis and the non degeneracy of linearized equations

critical exponents of the dilute ising model from four loop expansions four loop expansions of the coefficients of the callan symanzik equation for 3d and 2d dilute ising models are calculated fixed point coordinates and critical exponents are estimated by two methods of summation of double series a generalisation of the pade borel approximation and the first confluent form of the e algorithm of wynn summation of the double series for the 2d dilute ising model gives exponents very close to exponents of the pure ising model in accordance with the exact solution

the singular set of stationary solution for semilinear elliptic equations with supercritical growth abstract in this paper we are concerned with the partial regularity of the stationary solution to semilinear elliptic equations for almost all supercritical exponents we improve the upper bounds of the hausdorff dimension of the singular set which are derived by pacard to the optimal ones

new existence and symmetry results for least energy positive solutions of schrodinger systems with mixed competition and cooperation terms abstract in this paper we focus on existence and symmetry properties of solutions to the cubic schrodinger system u i i u i j 1 d i j u j 2 u i in r n i 1 d where d 2 i i i 0 i j j i r for j i n 2 3 the underlying domain is either bounded or the whole space and u i h 0 1 or u i h rad 1 r n respectively we establish new existence and symmetry results for least energy positive solutions in the case of mixed cooperation and competition coefficients as well as in the purely cooperative case

existence and uniqueness of solutions for a singular semilinear elliptic system abstract in this paper we study the existence and the uniqueness of solutions for the singular semilinear elliptic system u f x u 2 g x u 1 p 2 p q a x u p v 1 q x r n v f x v 2 g x v 1 q 2 p q a x u 1 p v q x r n where 0 p 1 and 0 q 1 we show the existence of a solution for an approximated system by using a perturbation method which eliminates the singularity and via variational methods the limit of the approximated solutions is a positive solution in the case g 0 p q and 1 2 p 1 we prove the uniqueness of solution the proofs rely on the concentration compactness principle

radial symmetry of entire solutions of a bi harmonic equation with exponential nonlinearity abstract we obtain necessary and sufficient conditions for an entire solution u of a bi harmonic equation with exponential nonlinearity e u to be a radially symmetric solution the standard tool to obtain the radial symmetry for a system of equations is the moving plane method mpm in order to apply the mpm we need to know the asymptotic expansions of u and u at we overcome the difficulties due to the fact that e u is supercritical for n 5 e u l n 4 r n and get the right decay rate of u and u at in order to start the moving plane procedure

existence and convergence of solutions for nonlinear biharmonic equations on graphs abstract in this paper we first prove some propositions of sobolev spaces defined on a locally finite graph g v e which are fundamental when dealing with equations on graphs under the variational framework then we consider a nonlinear biharmonic equation 2 u u a 1 u u p 2 u on g v e under some suitable assumptions we prove that for any 1 and p 2 the equation admits a ground state solution u moreover we prove that as the solutions u converge to a solution of the equation 2 u u u u p 2 u in u 0 on where x v a x 0 is the potential well and denotes the boundary of

decay symmetry and existence of solutions of semilinear elliptic systems our utmost aim was originally to establish the existence of solutions of system however in this effort we got sidetracked to consider other questions in this way we come to interesting results on asymptotic behavior of solutions on symmetry properties of such solutions and the existence of ground states

symmetry results for elliptic schrodinger systems on half spaces abstract in this paper we prove some symmetry and monotonicity results for classical positive solutions for elliptic schrodinger systems on half spaces with the neumann type condition our methods employ the alexandrov serrin method of moving planes combined with hopf s lemma at a corner

temporal oscillations and phase transitions in the evolutionary minority game the study of societies of adaptive agents seeking minority status is an active area of research recently it has been demonstrated that such systems display an intriguing phase transition agents tend to self segregate or to cluster according to the value of the prize to fine ratio r we show that such systems do not establish a true stationary distribution the winning probabilities of the agents display temporal oscillations the amplitude and frequency of the oscillations depend on the value of r the temporal oscillations that characterize the system explain the transition in the global behavior from self segregation to clustering in the r 1 case

ground states for a system of schrodinger equations with critical exponent abstract we study the following system of nonlinear schrodinger equations u u u p 1 u v x r n v v v 2 2 v u x r n where n 3 2 2 n n 2 1 p 2 1 and are positive parameters satisfying 0 we show that there is some critical value 0 0 1 such that this system has a positive ground state solution if 0 0 in the case 0 there exists 0 such that this system has no ground state solutions if while this system has a positive ground state solution if in particular if p 2 1 the system has no nontrivial solutions some further properties of the ground state solutions are also studied this seems to be the first result for such a critical schrodinger system

critical dynamics of cluster algorithms in the dilute ising model autocorrelation times for thermodynamic quantities att c are calculated from monte carlo simulations of the site diluted simple cubic ising model using the swendsen wang and wolff cluster algorithms our results show that for these algorithms the autocorrelation timesdecrease when reducing the concentration of magnetic sites from 100 down to 40 this is of crucial importance when estimating static properties of the model since the variances of these estimators increase with autocorrelation time the dynamical critical exponents are calculated for both algorithms observing pronounced finite size effects in the energy autocorrelation data for the algorithm of wolff we conclude that when applied to the dilute ising model cluster algorithms become even more effective than local algorithms for whichincreasing autocorrelation times are expected

boolean game on scale free networks abstract inspired by the local minority game we propose a network boolean game and investigate its dynamical properties on scale free networks the system can self organize to a stable state with better performance than the random choice game although only the local information is available to each agent by introducing the heterogeneity of local interactions we find that the system will achieve the best performance when each agent s interaction frequency is linearly correlated with its information capacity generally the agents with more information gain more than those with less information while in the optimal case each agent almost has the same average profit in addition we investigate the role of irrational factor and find an interesting symmetrical behavior

symmetry of minimizers for some nonlocal variational problems abstract we present a new approach to study the symmetry of minimizers for a large class of nonlocal variational problems this approach which generalizes the reflection method is based on the existence of some integral identities we study the identities that lead to symmetry results the functionals that can be considered and the function spaces that can be used then we use our method to prove the symmetry of minimizers for a class of variational problems involving the fractional powers of laplacian for the generalized choquard functional and for the standing waves of the davey stewartson equation

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

static and dynamic critical properties of 3d systems with long range correlated quenched defects a field theoretic description of static and purely relaxational dynamic critical behaviour of systems with quenched defects obeying power law correlations x a for large separations x is given directly for three dimensional systems and for different values of the correlation parameter 2 a3 a renormalization analysis of the scaling functions in the two loop approximation is carried out and the fixed points corresponding to the stability of various types of critical behaviour are identified the obtained results essentially differ from results evaluated by a double expansion the static and dynamic critical exponents in the two loop approximation are calculated with the use of the pade borel summation technique

the dynamic critical exponent of dilute and pure ising systems a massive dynamic field theory is employed to calculate the critical exponent z of the three dimensional dilute ising model to two loop order without expansion in square root 4 d with result z approximately 2 191 applying the same method to the pure ising model at three loop order we find z 2 022 for d 3 and z 2 124 for d 2

symmetry results for semilinear elliptic systems in the whole space in this paper we obtain symmetry results of gidas ni nirenberg type for cooperative nonlinear elliptic systems in the whole space

partial regularity of finite morse index solutions to the lane emden equation we prove regularity and partial regularity results for finite morse index solutions u h1 lp to the lane emden equation u u p 1u in

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

on the critical fluctuations in superconductors the field theoretical gauge model for a superconductor generalized to an n 2 component complex order parameter is considered the question of the order of the phase transition occurring in this model is discussed previous renormalization group calculations suggest that in such a model a fluctuation induced first order phase transition occurs we re examine previously obtained expressions for the renormalization group functions in the two loop approximation in three dimensions special attention is being paid to the fact that the corresponding series might be the asymptotic ones and therefore have zero radius of convergence we discuss the possible ways of analytical continuation of the series obtained comparing results obtained by direct calculations with those obtained by pade analysis and the pade borel resummation technique the conjecture is made that in the model under consideration there still exists a possibility for a second order phase transition

symmetry and non existence of positive solutions for fractional p laplacian systems abstract chen and li 2018 developed maximum principles for the fractional p laplacian which carry out the direct method of moving planes to the fractional p laplacian equation in this paper we generalize their method to the system case and obtain a symmetry result for the fractional p laplacian system on the whole space we also consider the system on the upper half space and obtain a non existence result

statistical mechanics of systems with heterogeneous agents minority games we study analytically a simple game theoretical model of heterogeneous interacting agents we show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz such a stationary state differs from the nash equilibrium where each agent maximizes her own utility the latter turns out to be characterized by a replica symmetry broken structure numerical results fully agree with our analytical findings

nonequilibrium relaxation study on spin glass model ferromagnetic fm transition point and universality class of the j ising model on cubic lattice are studied by computer simulation using the nonequilibrium relaxation ner method at fm bond density p between multicritical one pmc and 1 static exponents take universal values which are different from those of p 1 or p pmc and they are consistent with the values of the random fixed point and of the simulations and experiments for diluted ising systems the dynamical exponent however seems to depend on p and not to be universal although it may be due to finite time correction the estimation of pmc on square lattice is also refined to be 0 8894 9 which is consistent with the nishimori and nemoto s conjecture 0 889972