uniqueness of positive radial solutions for infinite semipositone p laplacian problems in exterior domains abstract we prove uniqueness and asymptotic behavior of positive radial solutions to the p laplacian problem p u k x f u in x r 0 u 0 on x r 0 u x 0 as x where x r n x r 0 0 n p f 0 r is continuous f u u q at for some q 0 p 1 with possible infinite semipositone structure at 0 and is a large parameter

finite size scaling and damage spreading in ising systems with multispin interactions abstract we investigate two dimensional ising systems with multispin interactions of three m 3 and four body terms m 4 the application of a new type of finite size algorithm of de oliveira allow us to clearly distinguish a first order transition in the m 4 case from a continuous one in the m 3 one we also study the damage spreading in these systems in this study a dynamical phenomenon is observed to occur at a critical point separating a chaotic phase from a frozen one however the width of the interval where this transition happens does not yield a conclusive evidence about the order of the phase transition

existence and multiplicity results for generalized logistic equations abstract we consider elliptic dirichlet problem p u f x u u g x u in u 0 on assume that the nonlinearity f satisfies certain growth condition using the fixed point index the leggett williams theorem on fixed point and the arguments on monotone minorant we prove the existence and multiplicity results for the equation this extends some known results

generalized quasilinearization and semilinear elliptic boundary value problems the method of generalized quasilinearization is extended to semilinear elliptic problems employing both the classical and variational approaches the results discussed are very general and include several special cases of interest

on a class of quasilinear systems with sign changing nonlinearities abstract we prove existence and nonexistence of positive solutions for the quasilinear system p u a x f u v in q v b x g u v in u v 0 on where p u div u p 2 u q v div v q 2 v p q 1 is a bounded domain in r n and the coefficients a x and b x are allowed to change sign

positive solutions of generalized nonlinear logistic equations via sub super solutions abstract let be a smooth bounded domain in r n n 1 let m n be two nonnegative functions defined in and let r n r n be a continuous and strictly monotone mapping we consider the existence and nonexistence of positive solutions for nonlinear problems involving the laplacian of the form div u m x f u n x g u in u 0 on where 0 is a real parameter and f g 0 0 are continuous functions modeled by f t t q and g t t r with 0 q r the subdiffusive equidiffusive and superdiffusive cases are all treated and some qualitative properties of the solutions are also given as a byproduct we obtain results in the case of a roughly speaking sublinear nonlinearity f and n 0 we point out that some of our results are new even for the usual p laplacian our main tool is the sub supersolutions method combined with some estimates on related nonlinear problems

on the equivalence of finite size scaling renormalization group and phenomenological renormalization abstract it is shown that the recently proposed finite size scaling renormalization group when using systems infinite in one dimension and finite in the others is equivalent to the nightingale correlation length phenomenological renormalization the equivalence however is concerned only with the critical coupling and thermal critical exponent the finite size scaling renormalization group approach provides other exponents in a more precise and elegant fashion through the flux diagram of the recursion relations in the space spanned by the parameters of the hamiltonian in addition a new set of magnetic exponents which are so accurate as the thermal ones can now be obtained in an easier way

positive solutions of logistic equations with dependence on gradient and nonhomogeneous kirchhoff term abstract consider the equation m x u p u f x u u g x u u in u 0 on the main aim of this paper is to prove existence results for both non degenerate and degenerate cases of the function m our approach relies on the fixed point index and the cone theoretic argument

on the structure of unbounded positive solutions to the quasilinear logistic equation abstract for the quasilinear logistic equation p u m x u u in u 0 on with p 1 m x l q we obtain the existence of the maximal unbounded positive solutions their asymptotic behavior and global bifurcation from the trivial solution

positive solutions for a class of p laplacian systems with multiple parameters abstract consider the system p u 1 f v 1 h u in q v 2 g u 2 v in u 0 v on where s z div z s 2 z s 1 1 2 1 and 2 are nonnegative parameters and is a bounded domain in r n with smooth boundary we prove the existence of a large positive solution for 1 1 and 2 2 large when lim x f m g x 1 q 1 x p 1 0 for every m 0 lim x h x x p 1 0 and lim x x x q 1 0 in particular we do not assume any sign conditions on f 0 g 0 h 0 or 0 we also discuss a multiplicity results when f 0 g 0 h 0 0 0

nontrivial solutions for p laplacian systems abstract the paper deals with the existence and nonexistence of nontrivial nonnegative solutions for the sublinear quasilinear system div u i p 2 u i f i u 1 u n 0 in u i 0 on i 1 n where p 1 is a bounded domain in r n n 2 with smooth boundary and f i i 1 n are continuous nonnegative functions let u u 1 u n u i 1 n u i we prove that the problem has a nontrivial nonnegative solution for small 0 if one of lim u 0 f i u u p 1 is infinity if in addition all lim u f i u u p 1 is zero we show that the problem has a nontrivial nonnegative solution for all 0 a nonexistence result is also obtained

a note on the implicit function theorem for quasi linear eigenvalue problems abstract we consider the quasi linear eigenvalue problem p u g u subject to dirichlet boundary conditions on a bounded open set where g is a locally lipschitz continuous function imposing no further conditions on or g we show that for near zero the problem has a bounded solution which is unique in the class of all small solutions moreover this curve of solutions parameterized by depends continuously on the parameter

positive solutions for nonlinear problems involving the one dimensional ϕ laplacian abstract let a b r m l 1 and 0 be a real parameter let l be the differential operator given by l u u r x u where r r is an odd increasing homeomorphism and 0 r l 1 we study the existence of positive solutions for problems of the form l u m x f u in u 0 on where f 0 0 is a continuous function which is roughly speaking sublinear with respect to our approach combines the sub and supersolution method with some estimates on related nonlinear problems we point out that our results are new even in the cases r 0 and or m 0

criticality of the discrete n vector ferromagnet in planar self dual lattices the authors study an extended version of the discrete n vector or cubic ferromagnetic model within a real space renormalisation group approach which preserves the two spin correlation function the n evolution for real values of n of the wheatstone bridge hierarchical lattice phase diagram which presents paramagnetic intermediate nematic like and ferromagnetic phases as well as of the thermal nu and crossover phi critical exponents is presented the self avoiding walk problem is recovered in the n to o limit and the so called corner rule is re obtained in a larger context the ising n and 2n state potts ferromagnets are recovered as particular cases an interchange of stability occurs at n n approximately 6 9 in such a way that the 2n state potts special point where all three existing phases join is multicritical if n n but only critical if n n consistently phi n o for the cubic model nu n presents a maximum at n nmax approximately 1 5 the results are exact for all n for the wheatstone bridge hierarchical lattice and approximate for n or 2 for the square lattice last but not least they discuss the connection between the present approach and the phenomenological renormalisation group

multiplicity and asymptotic behavior of nonnegative solutions for elliptic problems involving nonlinearities indefinite in sign abstract let p r s be positive numbers with 1 r s p the multiplicity of nonnegative solutions for the problem p u u s 1 u r 1 in u 0 is investigated we prove that there exist two positive constants 2 r s r s with 2 r s r s such that the above problem has at least two solutions at least one solution or no solutions according to whether p r p s 2 r s p r p s 2 r s r s or p r p s r s we also study the asymptotic behavior of the solutions as 0

remarks on eigenvalue problems involving the p x laplacian abstract this paper deals with the eigenvalue problem involving the p x laplacian of the form div u p x 2 u u q x 2 u in u 0 on where is a bounded domain in r n p c 0 inf x p x 1 q l 1 q x q x e p x for x e is a positive constant p x is the sobolev critical exponent it is shown that for every t 0 the problem has at least one sequence of solutions u n t n t such that 1 p x u n t p x t and n t as n the principal eigenvalues for the problem in several important cases are discussed especially the similarities and the differences in the eigenvalue problem between the variable exponent case and the constant exponent case are exposed some known results on the eigenvalue problem are extended

on a class of quasilinear problems with sign changing nonlinearities abstract we prove existence and nonexistence of positive solutions for the quasilinear problem p u m p u a x f u in u 0 on where p u div u p 2 u p u u p 2 u p 1 m 0 is a bounded domain in r n and the coefficient a x is allowed to change sign

orlicz sobolev versus holder local minimizer and multiplicity results for quasilinear elliptic equations national natural science foundation of china nsaf 10976026 national natural science foundation of china 11271305

finite size scaling for first order transitions potts model the finite size scaling algorithm based on bulk and surface renormalization of de oliveira is tesed onq state potts models in dimensionsd 2 and 3 our monte carlo data clearly distinguish between first and second order phase transitions continuous q analytic calculations performed for small lattices show a clear tendency of the magnetic exponenty d v to reach a plateau for increasing values ofq which is consistent with the first order transition valuey d monte carlo data confirm this trend

a unified monotone iterative technique for semilinear elliptic boundary value problems a unified approach to monotone iterative techniques is developed for elliptic boundary value problems when the nonlinear term involved admits a splitting of a difference of two monotone functions the results obtained using both the classical and variational methods include several known results as well as some interesting new ones

singular boundary value problems for the p laplacian abstract we prove the existence of a large positive solution for the boundary value problems p u h u g x u in u 0 on where p u div u p 2 u p 1 is a bounded domain in r n is a positive parameter g x is p 1 subhomogeneous at and h is allowed to become at u 0 results for related systems are also discussed

on the sub supersolution method for p x laplacian equations abstract this paper deals with the sub supersolution method for the p x laplacian equations a sub supersolution principle for the dirichlet problems involving the p x laplacian is established it is proved that the local minimizers in the c 1 topology are also local minimizers in the w 1 p x topology for given energy functionals a strong comparison theorem for the p x laplacian equations is presented some applications of the abstract theorems obtained in this paper to the eigenvalue problems for the p x laplacian equations are given

uniqueness of positive solutions for a class of quasilinear problems abstract we prove uniqueness of positive solutions for the quasilinear problems p u f u in u 0 on where p u div u p 2 u p 1 is a bounded domain in r n with smooth boundary f is p sublinear at f u u p 1 is decreasing for large u and is a large positive parameter we also obtain the asymptotic behavior of the solution obtained as

imprimitive matrices of zeros and ones with extremal numbers of ones abstract in x zhan extremal numbers of positive entries of imprimitive nonnegative matrices linear algebra appl 424 2007 132 138 zhan determined the maximum and minimum numbers of positive entries of irreducible nonnegative matrices in this paper we characterize the irreducible 0 1 matrices with the maximum and minimum numbers of positive entries

matrices permutation equivalent to primitive matrices we give a necessary and sufficient condition for an n n 0 1 matrix or more generally an n n nonnegative matrix to be permutation equivalent to a primitive matrix more precisely except for two simple permutation equivalent classes of n n 0 1 matrices each n n 0 1 matrix having no zero row or zero column is permutation equivalent to some primitive matrix as an application we use this result to characterize the subsemigroup of bn bn is the multiplicative semigroup of n n boolean matrices generated by all the primitive matrices and permutation matrices we also consider a more general problem and give a necessary and sufficient condition for an n n nonnegative matrix to be permutation equivalent to an irreducible matrix with given imprimitive index

kth order convergence for semilinear elliptic boundary value problems the method of quasilinearization coupled with the method of upper and lower solutions is applied to the semilinear elliptic boundary value problems at the same time the result of kth convergence for the semilinear boundary value problems is obtained via the idea of taylors approximation

critical behavior of a probabilistic cellular automaton describing a biological system we study nonequilibrium phase transitions occurring in a probabilistic cellular automaton which describes one part of the immune system in this model each site can be occupied by three type of cells and the immune response under parasitic infections is described in terms of two parameters p and r the local rules governing the evolution of this automaton possess up down symmetry similar to ising models performing monte carlo simulations on square and cubic lattices we verify that the model displays continuous kinetic phase transitions with spontaneous symmetry breaking we present detailed simulations and analysis of the critical behavior our results indicate that the model belongs to the ising universality class supporting the up down conjecture c 1998 elsevier science b v all rights reserved

finite size scaling rg detailed description and applications to diluted ising systems the finite size scaling renormalisation group fssrg was introduced in europhysics letters 20 1992 621 based only on the finite size scaling hypothesis with no further assumptions it differs from other real space renormalisation groups rsrgs in the following essential point one does not need to adopt any particular recipe exp h s t sp s s exp h s t relating the spin states s of the original system to the spin states s of a renormalised system the choice of a particular weight function p s s e g the so called majority rule is generally based on plausibility arguments and involves uncontrollable approximations in addition to being free from these drawbacks fssrg shares with rsrg some good features as for instance the possibility of extracting qualitative informations from multi parameter rg flow diagrams including crossovers universality classes universality breakings multicriticalities orders of transitions etc other unpleasant consequences of particular weight functions as the so called proliferation of parameters are also absent in the fssrg using it in three dimensions we were able to find a semi unstable fixed point in the critical frontier concentration p versus exchange coupling j characterizing a universality class crossover when one goes from pure to diluted ising ferromagnets the specific heat exponents we have obtained for the pure and diluted regimes are in agreement with the harris criterion

a remark on the uniqueness of positive solutions for some dirichlet problems abstract in this paper we prove the uniqueness of positive weak solutions to the problem p u g x u x u 0 x by a direct argument here is a bounded domain in r n n 3 with smooth boundary p denotes the p laplacian operator defined by p z div z p 2 z p 1 g x 0 0 for a e x and g x u is a caratheodory function we provide a direct uniqueness proof for this problem under certain conditions

existence result for a class of semilinear totally characteristic hypoelliptic equations with conical degeneration abstract in this article we use the cone sobolev inequality and the poincare inequality to prove the existence theorem for a class of semilinear degenerate hypoelliptic equation on manifolds with conical singularities in this paper we shall find the existence theorem for the problem 1 1 in cone sobolev space h 2 0 1 n 2 b finally we obtain existence result of global solutions with exponential decay and show the blow up in finite time of solutions

on positive weak solutions for a class of quasilinear elliptic systems abstract in this paper we study the existence and nonexistence of positive weak solution for the quasilinear elliptic system p u u v q v u v with zero dirichlet boundary condition in bounded domain r n a critical exponent is obtained for existence and nonexistence of positive weak solution

an existence result on positive solutions for a class of p laplacian systems abstract consider the system p u f v in p v g u in u v 0 on where pz div z p 2 z p 1 is a positive parameter and is a bounded domain in rn with smooth boundary we prove the existence of a large positive solution for large when lim x f m g x 1 p 1 x p 1 0 for every m 0 in particular we do not assume any sign conditions on f 0 or g 0

multiple positive solutions of the one dimensional p laplacian in this work we investigate the existence of positive solutions of the p laplacian using the quadrature method we prove the existence of multiple solutions of the one dimensional p laplacian for 0 and determine their exact number for 0 2005 elsevier inc all rights reserved

extremal numbers of positive entries of imprimitive nonnegative matrices we determine the maximum and minimum numbers of positive entries of imprimitive nonnegative matrices with a given imprimitivity index one application of the results is to estimate the imprimitivity index by the number of positive entries the proofs involve the study of a cyclic quadratic form this completes a research initiated by lewin in 1990

on the numbers of positive entries of reducible nonnegative matrices abstract let rm n d be the class a a is an n n reducible nonnegative matrix and the greatest common divisor of the lengths of all cycles in d a is d where d a is the associated digraph of a in this paper we determine the set of numbers of positive entries of a for a rm n d we also characterize the reducible nonnegative matrices with the maximum and minimum numbers of positive entries