on mutual information in multipartite quantum states and equality in strong subadditivity of entropy the challenge of equality in the strong subadditivity inequality of entropy is approached via a general additivity of correlation information in terms of nonoverlapping clusters of subsystems in multipartite states density operators a family of tripartite states satisfying equality is derived

existence of solutions and boundary asymptotic behavior of p r laplacian equation multi point boundary value problems abstract this paper investigates the problem p r u r f r u 0 r 0 r u 0 i 1 m i u i e 0 u r as r r where p r u u p r 2 u is called the p r laplacian r is a singular coefficient the existence and nonexistence of solutions are discussed and the exact boundary blow up rate of solutions is given

the existence and nonexistence of entire large solutions for a quasilinear schrodinger elliptic system by dual approach abstract in this paper we establish some new results on the existence and nonexistence of radial large positive solutions for a modified schrodinger system with a nonconvex diffusion term by a successive iteration technique and the dual approach the necessary and sufficient condition for the existence of radial large positive solutions is established our results improve and extend many previous work in this field of research

existence of positive radial solutions for some nonvariational superlinear elliptic systems the system under consideration is u cu g u v up u u x x b rn u b 0 v dv h u v vq v v x v b 0 where c d 0 are constants b is a ball and 1 0 in b

large solutions to semi linear elliptic systems with variable exponents abstract we consider the elliptic system u u a v b v u c v d where the exponents are non negative spherically symmetric functions we study positive solutions on balls of finite and infinite radius r which satisfy lim x r u x lim x r v x we give conditions on the exponents that either ensure existence or nonexistence of these large solutions

on the existence of multiple positive entire solutions for a quasilinear elliptic systems abstract in this paper our main purpose is to establish the existence of infinitely positive bounded entire solutions of second order quasilinear elliptic systems these extend a work of zuodong yang zuodong yang existence of positive bounded entire solutions of quasilinear elliptic equations appl math comput 156 2004 743 754 which considered the single quasilinear elliptic equation these extend also a work of kawano and kusano n kawano t kusano on positive entire solutions of a class of second order semilinear elliptic systems math zeitschrift 186 3 1984 287 297 which studied the semilinear elliptic equation

new results on the existence of bounded positive entire solutions for quasilinear elliptic systems abstract in this paper our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic systems the main results of the present paper are new and extend the previously known results

boundary blow up solutions to elliptic systems of competitive type abstract we consider the elliptic system u u p v q v u r v s in where p s 1 q r 0 and r n is a smooth bounded domain subject to different types of dirichlet boundary conditions f u v i u v and sf u v on where 0 under several hypotheses on the parameters p q r s we show existence and nonexistence of positive solutions uniqueness and nonuniqueness we further provide the exact asymptotic behaviour of the solutions and their normal derivatives near some more general related problems are also studied

entire solutions of quasilinear elliptic equations abstract we consider the existence of entire solutions of a quasilinear elliptic equation div d u p 2 d u k x f u x r n where p 1 n n conditions of the existence of entire solutions have been obtained by different authors we prove an optimality of some of these results and give new sufficient conditions for the nonexistence of entire solutions

effects of a degeneracy in the competition model part i classical and generalized steady state solutions abstract we study the competition model where the coefficient functions are strictly positive over the underlying spatial region except b x which vanishes in a nontrivial subdomain of and is positive in the rest of we show that there exists a critical number such that if then the model behaves similarly to the well studied classical competition model where all the coefficient functions are positive constants but when new phenomena occur our results demonstrate the fact that heterogeneous environmental effects on population models are not only quantitative but can be qualitative as well in part i here we mainly study two kinds of steady state solutions which determine the dynamics of the model one consists of finite functions while the other consists of generalized functions which satisfy u v 0 on the part of the domain that b x vanishes but are positive and finite on the rest of the domain and are determined by certain boundary blow up systems the research is continued in part ii where these two kinds of steady state solutions will be used to determine the dynamics of the model

existence nonexistence and asymptotic behavior of boundary blow up solutions to p x laplacian problems with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u d i v u p x 2 u is called the p x laplacian and x is a singular coefficient the existence and nonexistence of boundary blow up solutions is discussed and the asymptotic behavior of boundary blow up solutions is given in particular we do not assume radial symmetric conditions and the pointwise different exact blow up rate of solutions has been discussed

on hamiltonian elliptic systems with periodic or non periodic potentials abstract this paper is concerned with the following hamiltonian elliptic system u b x u v x u h v x u v v b x v v x v h u x u v for x r n existence and multiplicity of solutions are obtained for the systems with periodic or non periodic potentials v via variational methods

a remark on the existence of entire positive solutions for a class of semilinear elliptic systems abstract under the simple conditions on f and g we show that entire positive radial solutions exist for the semilinear elliptic system u p x f v v q x g u x r n n 3 where the functions p q 0 0 are continuous

existence and boundary blow up rates of solutions for boundary blow up elliptic systems abstract in this paper we study some elliptic systems with boundary blow up conditions in a smooth bounded domain by constructing the suitable upper and lower solutions we discuss the existence and global estimate of the positive solution furthermore the boundary blow up rates of the positive solution are also partly discussed

pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs in this paper we analyze the uniqueness and the pointwise growth of the positive solutions of a nonlinear elliptic boundary value problem of general sublinear type with a weight function multiplying the nonlinearity when this function vanishes on some subdomain the problem exhibits a bifurcation from infinity in this case almost nothing is known about the pointwise growth of the positive solutions as the parameter approaches the critical value where the bifurcation from infinity occurs in this work we show that the positive solutions grow to infinity in the region where the weight function vanishes and that on its support they stabilize to the minimal positive solution of the original equation subject to infinite dirichlet boundary conditions this behavior provides us with the uniqueness of the positive solution near the value of the parameter where the bifurcation from infinity occurs also we solve the problem using spectral collocation methods coupled with path following techniques to show how the main uniqueness result is optimal throughout the paper the mathematical analysis aids the numerical study and the numerical study confirms and illuminates the analysis

on a singular elliptic system with quadratic growth in the gradient abstract in this paper we deal with the following singular elliptic system u u 2 u p p q a x v q u p 2 u f x r n v v 2 v q p q a x u p v q 2 v g x r n where n 3 n 2 4 p q 1 and p q n 2 n 2 we show through the sub and supersolutions method the existence of a nonnegative solution for an approximated system the limit of the approximated solution is a positive solution in the case 0 p q and f g we prove the uniqueness of a solution among others we prove some existence and uniqueness results for some auxiliary problems by using the comparison principle a minimization method and with the help of nehari manifold the proofs rely on the concentration compactness principle

existence and estimate of large solutions for an elliptic system abstract in this paper an elliptic system with boundary blow up is considered in a smooth bounded domain by constructing certain upper solution and subsolution we show the existence of positive solutions and give a global estimate furthermore the boundary behavior of positive solutions is also discussed

sufficient subalgebras and the relative entropy of states of a von neumann algebra a subalgebram 0 of a von neumann algebram is called weakly sufficient with respect to a pair of states if the relative entropy of and coincides with the relative entropy of their restrictions tom 0 the main result says thatm 0 is weakly sufficient for if and only ifm 0 contains the radon nikodym cocycle d d t other conditions are formulated in terms of generalized conditional expectations and the relative hamiltonian

a remark on uniqueness of large solutions for elliptic systems of competitive type abstract we prove that the semilinear system u a x u p v q v b x u r v s in a smooth bounded domain r n has a unique positive solution with the boundary condition u v on provided that p s 1 q r 0 and p 1 s 1 q r 0 the main novelty is imposing a growth on the possibly singular weights a x b x near rather than requiring them to have a precise asymptotic behavior

convergence of the pseudospectral method for the ginzburg landau equation abstract the convergence of the pseudospectral fourier method for the ginzburg landau equation in nonlinear wave theory is proved the rate of convergence depends on the smoothness of the initial data

existence and uniqueness of positive solutions to the boundary blow up problem for an elliptic system abstract an elliptic system is considered in a smooth bounded domain subject to dirichlet boundary conditions of three different types based on the construction of certain upper and sub solutions we obtain some conditions on the parameters a i b i c i i 1 2 and the exponents m n p q to ensure the existence of positive solutions furthermore uniqueness and boundary behavior of positive solutions is also discussed

boundary blow up solutions for a class of elliptic equations on a bounded domain this paper deals with existence of solutions of the quasilinear elliptic equation du f x u u in w satisfying the boundary blow up condition u x x email protected where email protected r n is a bounded domain with smooth boundary email protected our main result applies to the existence of blow up solutions of a class of equations which appear in stochastic control theory namely du a x g u email protected u email protected x in w where a x g u j x are suitable functions and l s are nonnegative constants our approach employs an approximation procedure combined with both a non monotone iteration variant of the method of lower and upper solutions and fixed point arguments

large solutions of semilinear elliptic equations under the keller osserman condition abstract we consider the equation u p x f u where p is a nonnegative nontrivial continuous function and f is continuous and nondecreasing on 0 satisfies f 0 0 f s 0 for s 0 and the keller osserman condition 1 f s 1 2 d s where f s 0 s f t d t we establish conditions on the function p that are necessary and sufficient for the existence of positive solutions bounded and unbounded of the given equation

existence of nonnegative solutions for a class of semilinear elliptic systems with indefinite weight abstract we prove the existence of nonnegative solutions to the system u a x f v in v b x g u in u 0 v on where is a bounded domain in r n with a smooth boundary is a positive parameter by the method of monotone iteration and schauder fixed point theorem we prove the existence of a nonnegative solution to the above system for sufficiently small in this study we do not restrict the sign of a and b

large solutions to non monotone semilinear elliptic systems abstract we present the existence of entire large positive radial solutions for the non monotonic system u p x g v v q x f u on r n where n 3 the functions f and g satisfy a keller osserman type condition while nonnegative functions p and q are required to satisfy the decay conditions 0 t p t d t and 0 t q t d t further p and q are such that min p q does not have compact support

the role of coherence entropy of physical twin observables in entanglement the concept of physical twin observables pto for bipartite quantum states introduced and proved relevant for quantum information theory in recent work is substantially simplified the relation of observable and state is studied in detail from the point of view of coherence entropy properties of this quantity are further explored it is shown that besides for pure states also for a class of mixed states quantum discord measure of entanglement can be expressed through the coherence entropy of a pto complete in relation to the state

the existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term abstract we show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term u u p x f u v v v q x g u v on r n n 3 provided that nonlinearities f and g are positive and continuous the potentials p and q are continuous c positive and satisfy appropriate growth conditions at infinity we find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity while if f and g satisfy some growth conditions at infinity and p q are of slow decay or fast decay at infinity then the system has infinitely many entire solutions which are large or bounded

an elliptic system with bifurcation parameters on the boundary conditions in this paper we consider the elliptic system u a x upvq v b x urvs in a smooth bounded domain with boundary conditions u u v v on here and are regarded as parameters and p s 1 q r 0 verify p 1 s 1 qr we consider the case where a x 0 in and a x is allowed to vanish in an interior subdomain 0 while b x 0 in our main results include existence of nonnegative nontrivial solutions in the range 0 0 where 1 is characterized by means of an eigenvalue problem and the uniqueness of such solutions we also study their asymptotic behavior in all possible cases as both 0 as 1 for fixed respectively for fixed and when both in case 1

entire large solutions to semilinear elliptic systems abstract we consider the problem of existence of positive solutions to the elliptic system u p x v v q x u on r n n 3 which satisfies lim x u x lim x v x the parameters and are positive and the nonnegative functions p and q are continuous and min p r q r does not have compact support we show that if 1 then such a solution exists if and only if the functions p and q satisfy 0 t p t t 2 n 0 t s n 3 q s d s d t 0 t q t t 2 n 0 t s n 3 p s d s d t with p r 0 r p d and q r 0 r q d for 1 we show that a solution exists if either of the above conditions fails to hold i e one of the integrals is finite these extend all known results for the given system

the existence of large solutions of semilinear elliptic equations with negative exponents abstract in this work we consider semilinear elliptic equations with boundary blow up whose nonlinearities involve a negative exponent combining sub and super solution arguments comparison principles and topological degree theory we establish the existence of large solutions furthermore we show the existence of a maximal large positive solution

positive solutions of lane emden systems with negative exponents existence boundary behavior and uniqueness abstract we study the existence boundary behavior and uniqueness of solutions for the singular elliptic system u u p v q v u r v s u 0 v 0 x u v 0 where is a bounded domain with smooth boundary in r n p s 0 and q r 0 our results are obtained in a range of p q r s different from those in m ghergu lane emden systems with negative exponents j funct anal 258 2010 3295 3318

optimal uniqueness theorems and exact blow up rates of large solutions in this paper we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non linearity and combine these results with the localization method introduced in lopez gomez the boundary blow up rate of large solutions j differential equations 195 2003 25 45 to prove that any large solution l of u a x up p 1 a 0 must satisfy limx x0l x fx0 dist x i0 pp 1p 1p 1p 1p 1foreachx0 where fx0 t t 0sfx01p 1 p 1p 1ds i0 limt 0fx0 t fx0 t fx0 t 2 and fx0 is any smooth extension of the boundary normal section of a at x0 i e fx0 t a x0 tnx0 t 0 t 0 subsequently nx0 stands for the outward unit normal at x0 therefore the theory can be extended to cover the general case when fx0 l1p 1

inequalities for quantum entropy a review with conditions for equality this article presents self contained proofs of the strong subadditivity inequality for von neumann s quantum entropy s and some related inequalities for the quantum relative entropy most notably its convexity and its monotonicity under stochastic maps moreover the approach presented here which is based on klein s inequality and lieb s theorem that the function a tr ek log a is concave allows one to obtain conditions for equality in the case of strong subadditivity which states that s 123 s 2 s 12 s 23 where the subscripts denote subsystems of a composite system equality holds if and only if log 123 log 12 log 2 log 23 using the fact that the holevo bound on the accessible information in a quantum ensemble can be obtained as a consequence of the monotonicity of relative entropy we show that equality can be attained for that bound only when the states in the ensemble commute the article concludes with an appendix giving a short description of epstein s elegant proof of lieb s the

existence of boundary blow up solutions for a class of quasilinear elliptic systems with critical case abstract we consider the quasilinear elliptic system div u p 2 u u m 1 v n 1 div v q 2 v u m 2 v n 2 in where m 1 p 1 n 2 q 1 m 2 n 1 0 and r n is a smooth bounded domain subject to three different types of dirichlet boundary conditions u v or u v or u v on where 0 under several hypotheses on the parameters m 1 n 1 m 2 n 2 which is a critical case we show that the existence of positive solutions

a necessary and sufficient condition for the existence of large solutions to sublinear elliptic systems abstract we prove that the elliptic system u p x v v q x u on r n n 3 where 0 1 0 1 and p and q are nonnegative continuous functions has a nonnegative entire radial solution satisfying lim x u x lim x v x if and only if the functions p and q satisfy 0 t p t t 2 n 0 t s n 3 q s d s d t 0 t q t t 2 n 0 t s n 3 p s d s d t with p r 0 r p d and q r 0 r q d this extends previous existence results for both the single equation and systems

large solutions for an elliptic equation with a nonhomogeneous term abstract in this paper we study the elliptic boundary blow up problem u u p 1 u h x in where p 1 is a smooth bounded domain of r n and h c we are concerned with existence and uniqueness of solutions for quite general functions h which may change sign and are not necessarily bounded near

remarks on nonexistence of solutions of mixed sublinear and superlinear elliptic equation in rn abstract in this note we consider the quasilinear elliptic equation p u h x u m h x u n in r n n 3 where 0 m p 1 n we establish conditions sufficient to ensure the nonexistence of nonnegative entire solutions which improves a result of a v lair a v lair large solutions of mixed sublinear superlinear elliptic equations j math anal appl 346 2008 99 106

existence of entire explosive positive solutions of quasi linear elliptic equations in this paper our main purpose is to establish the existence of entire explosive positive radial solutions for quasi linear elliptic equations the main results of the paper extend previously known results both for the super linear and sub linear cases

large solutions of mixed sublinear superlinear elliptic equations abstract we consider the equation u p x u q x u on r n n 3 where p q are nonnegative continuous functions and 0 we establish conditions sufficient to ensure the existence and nonexistence of nonnegative entire large solutions of the equation

entire bounded solutions for a class of sublinear elliptic equations abstract let be an arbitrary domain of r n and let be a nonnegative locally bounded borel function on in this paper necessary and sufficient conditions are obtained for the existence of a nonnegative nontrivial bounded solution to the sublinear elliptic equation u x u in where 0 1 the special case of a radial function is discussed in detail

radial solutions for a quasilinear elliptic system of schrodinger type in this paper we analyze the existence of entire radially symmetric solutions for the schrodinger system d p iu i h i r u i p i 1 a i r f i u 1 u d fori 1 d on r n where p i 1 email protected 1 2 3 h i and a i are nonnegative radial continuous functions and f i are nonnegative non decreasing continuous functions on 0 d in all variables

existence and asymptotic behavior of positive blow up solutions for semilinear elliptic coupled system in this article we study the existence and the boundary behavior of positive blow up solutions for the semilinear elliptic coupled system our arguments are based on the subsupersolution method and the karamata regular variation theory in this article we study the existence and the boundary behavior of positive blow up solutions for the semilinear elliptic coupled system our arguments are based on the subsupersolution method and the karamata regular variation theory

a necessary and sufficient condition for existence of large solutions to semilinear elliptic equations we consider the semilinear equation u p x f u on a domain rn n 3 where f is a nonnegative nondecreasing continuous function which vanishes at the origin and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary for bounded we show that a nonnegative solution u satisfying u x as x exists if and only if the function s s0 f t dt satisfies 1 s 1 2 ds for unbounded including rn we show that a similar result holds where u x as x within and u x as x if p x decays to zero rapidly as x

nondegeneracy and uniqueness for boundary blow up elliptic problems abstract in this paper we use for the first time linearization techniques to deal with boundary blow up elliptic problems after introducing a convenient functional setting we show that the problem u a x u p g x u in with u on has a unique positive solution for large enough and determine its asymptotic behavior as here p 1 a x is a continuous function which can be singular near and g x u is a perturbation term with potential growth near zero and infinity we also consider more general problems obtained by replacing u p by e u or a logistic type function f u

global spatially periodic solutions to the ginzburg landau equation on etudie l existence globale et la non existence de solutions spatialement periodiques pour le probleme aux valeurs initiales de l equation de ginzburg landau

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

a new critical curve for a class of quasilinear elliptic systems abstract we study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms the main model cases are given by the p laplacian operator as well as the mean curvature operator in nonparametric form we prove that if the exponents lie under a certain curve then the system has only the trivial solution these results hold without any restriction provided the possible solutions are more regular the underlying framework is the classical euclidean case as well as the carnot groups setting

entire large solutions for a class of schrodinger systems with a nonlinear random operator abstract in this paper we study the nonexistence and existence of radial large positive solutions for a class of schrodinger systems with a nonlinear random operator under certain growth conditions we also establish the necessary and sufficient conditions for the existence of radial large positive solutions by a successive iteration technique the results of the paper improve and extend many previous work in this field of research

existence of entire large positive solutions of a semilinear elliptic system we show that large positive radial solutions exist for the semilinear elliptic system du p x f v dv q x g u on r n n 3 for nonnegative nondecreasing continuous functions f and g provided the nonnegative functions p and q are continuous c positive and satisfy the decay conditions 0tp t dt and 0tq t dt and f g satisfy 1 s 0f t dt 1 2 ds 1 s 0g t dt 1 2 ds

the existence and uniqueness of positive monotone solutions for a class of nonlinear schrdinger equations on infinite domains in this paper by constructing a new weighted norm method and analysis technique we establish the conditions for the existence and uniqueness of positive monotone solutions to a class of nonlinear schrdinger equations in planar exterior domains some examples are also given to demonstrate the application of our main results

nonradial large solutions of sublinear elliptic problems let p be a nonnegative locally bounded function on rn n 3 and 0 1 assuming that the oscillation sup x rp x inf x rp x tends to zero as r at a specified rate it is shown that the equation u p x u admits a positive solution in rn satisfying lim x u x if and only if rnp x x n 2dx

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

existence of entire large positive solutions of semilinear elliptic systems abstract we show that entire large positive radial solutions exist for the semilinear elliptic system u p x v v q x u on r n n 3 for positive and provided that the nonnegative functions p and q are continuous c positive and satisfy the decay conditions 0 tp t dt 0 tq t dt and greater than unity and 0 tp t dt and 0 tq t dt if neither nor is greater than one

a quantum measure of coherence and incompatibility the well known two slit interference is understood as a special relation between an observable localization at the slits and a state being on both slits the relation between an observable and a quantum state is investigated in the general case it is assumed that the amount of coherence equals that of the incompatibility between an observable and a state on these grounds an argument is presented that leads to a natural quantum measure of coherence called coherence or incompatibility information its properties are studied in detail making use of the mixing property of relative entropy derived in this paper a precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view convexity of the measure is proved and thus the fact that it is an information entity is established a few more detailed properties of the coherence information are derived with a view to investigating the final state entanglement in general repeatable measurement and more importantly general bipartite entanglement in follow ups of this study

existence of entire explosive positive radial solutions for a class of quasilinear elliptic systems abstract we show the existence of entire explosive positive radial solutions for quasilinear elliptic systems div u m 2 u p x g v div v n 2 v q x f u on r n where f and g are positive and non decreasing functions on 0 satisfying the keller osserman condition

boundary behavior for large solutions to elliptic equations with singular weights abstract in this paper we analyze the boundary behavior of large positive solutions to some semilinear elliptic equations which include a singular weight the most important point is that the growth of the solutions can be determined in terms of the solution to a one dimensional first order equation we also consider the questions of existence and uniqueness of positive solutions

on the existence of radial positive entire solutions for polyharmonic systems abstract two dimensional nonlinear polyharmonic systems of the type n u j p j 2 n u j f j x u 1 u 2 u 1 u 2 x r 2 j 1 2 are considered where p j 1 is a constant and f j 0 0 2 0 2 0 is a continuous function for j 1 2 some sufficient conditions are obtained for the existence of infinitely many radial positive entire solutions of the system with the prescribed asymptotic behavior at infinity

existence and nonexistence of entire positive solutions of semilinear elliptic systems abstract we show that entire positive solutions exist for the semilinear elliptic system u p x v v q x u on r n n 3 for positive and provided that the nonnegative functions p and q are continuous and satisfy appropriate decay conditions at infinity we also show that entire solutions fail to exist if the functions p and q are of slow decay

symmetry results of large solutions for semilinear cooperative elliptic systems abstract in this paper we consider symmetry of large solutions of the semilinear cooperative elliptic system u i g i u 1 u m in b r u i on b r where u i c 2 b r g i r m r a c function b r is the open ball of center 0 and radius r 0 in r n n 3 m n i 1 2 m after introducing the weakly coupled fully coupled hypotheses and some assumptions for g we use the moving plane method to prove any large solution of the semilinear cooperative elliptic system is radially symmetric and radially increasing in order to use the moving plane method for our problem a strong maximum principle of the linear cooperative elliptic system is constructed furthermore we also get the symmetry result of large solutions of the semilinear cooperative elliptic system in an annulus

asymptotic behavior of large radial solutions of a polyharmonic equation with superlinear growth this paper concerns the blow up behavior of large radial solutions of polyharmonic equations with power nonlinearities and positive radial weights specifically we consider radially symmetric solutions of mu c x u p on an annulus x rn x with 0 and 0 that diverge to infinity as x here n m n p 1 and c is a positive continuous function on the interval letting r qc r q for r with q 2m p 1 q q q 1 q 2m 1 1 p 1 and c c 1 p 1 we show that as x the ratio u x x remains between positive constants that depend only on m and p extending well known results for the second order problem we prove in the fourth order case that u x x 1 as x and obtain precise asymptotic expansions if c is sufficiently smooth at in certain higher order cases we find solutions for which the ratio u x x does not converge but oscillates about 1 with non vanishing amplitude

effects of a degeneracy in the competition model part ii perturbation and dynamical behaviour this is the second part of our study on the competition model where the coefficient functions are strictly positive over the underlying spatial region except b x which vanishes in a nontrivial subdomain of and is positive in the rest of in part i we mainly discussed the existence of two kinds of steady state solutions of this system namely the classical steady states and the generalized steady states here we use these solutions to determine the dynamics of the model we do this with the help of the perturbed model where b x is replaced by b x e which itself is a classical competition model this approach also reveals the interesting relationship between the steady state solutions both classical and generalized of the above system and that of the perturbed system

positive radial solutions for multiparameter dirichlet systems with mean curvature operator in minkowski space and lane emden type nonlinearities abstract we deal with dirichlet systems involving the mean curvature operator in minkowski space m w div w 1 w 2 in a ball in r n using the fixed point index and the lower and upper solutions method we first obtain the existence of positive solutions for a class of differential systems with a singular laplacian subjected to homogeneous mixed boundary conditions the main application of the general results concerns dirichlet systems with lane emden type nonlinearities in a superlinear case depending on two parameters 1 2 so we prove that for such a system there exists a continuous curve which separates the first quadrant in two disjoint unbounded open sets o 1 and o 2 such that the system has zero at least one or at least two radial positive solutions according to 1 2 o 1 1 2 or 1 2 o 2

existence of positive bounded solutions for some nonlinear elliptic systems abstract we prove some existence results of positive bounded continuous solutions to the semilinear elliptic system u p x g v v q x f u in domains d with compact boundary subject to some dirichlet conditions where and are nonnegative parameters the functions f g are nonnegative continuous monotone on 0 and the potentials p q are nonnegative and satisfy some hypotheses related to the kato class k d

the asymptotic behaviour of solutions with blow up at the boundary for semilinear elliptic problems abstract by constructing the comparison functions and the perturbed method it is showed that any solution u c 2 to the semilinear elliptic problems u k x g u x u satisfies lim d x 0 u x z d x 2 2 2 c 0 2 1 where is a bounded domain with smooth boundary in r n lim d x 0 k x d x c 0 2 c 0 0 2 2 g c 1 0 g 0 and g s s is increasing on 0 there exists 0 such that lim s g s g s 0 z s d t 2 g t s g t 0 t g s d s

large solutions for an elliptic system of competitive type existence uniqueness and asymptotic behavior abstract this paper deals with the existence uniqueness and asymptotic behavior of boundary blow up solutions for an elliptic system of competitive type where the weight functions a x b x vanish on the boundary of the underlying domain at different rates according to the point of the boundary the proof relies on subsolutions and supersolutions and the localization method

periodic solutions of the ginzburg landau equation abstract spatially periodic solutions to the ginzburg landau equation are considered in particular we obtain criteria for primary and secondary bifurcation limit cycle solutions nonlinear dispersion relations relating spatial and temporal frequencies only relatively simple tools appear in the treatment and as a result a wide range of parameter cases are considered finally we briefly treat the case of spatial bifurcations

asymptotic behavior of large solution for boundary blowup problems with non linear gradient terms let email protected r n n 3 be a bounded domain with smooth boundary we show the asymptotic behavior of boundary blowup solutions to non linear elliptic equation du u q b x f u in w subject to the singular boundary condition u x as dist x email protected 0 f is c varying at our analysis is based on the karamata regular variation theory combined with the method of lower and supper solution

existence non existence and asymptotic behavior of blow up entire solutions of semilinear elliptic equations abstract we are mainly concerned with existence non existence and the behavior at infinity of non negative blow up entire solutions of the equation u x f u in r n no monotonicity condition is assumed upon f and in fact we obtain solutions with a prescribed behavior both at infinity and at the origin the method used to get existence is based upon lower and upper solutions techniques while for non existence we explore radial symmetry estimates on an associated integral equation and the keller osserman condition

on the boundary blow up solutions of p x laplacian equations with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u div u p x 2 u is called the p x laplacian x is a singular coefficient the existence and nonexistence of boundary blow up solutions are discussed and the singularity of the boundary blow up solution is given