nonsymmetric ground states of symmetric variational problems in this paper we study a minimization problem which is invariant by rotation the corresponding euler lagrange equations are semilinear elliptic equations in an exterior domain with neumann boundary conditions we prove that this minimization problem has at least one solution yet all its solutions are shown not to be rotationally invariant furthermore we describe how the radial symmetry is broken

invariants of 3 manifolds via link polynomials and quantum groups the aim of this paper is to construct new topological invariants of compact oriented 3 manifolds and of framed links in such manifolds our invariant of a link in a closed oriented 3 manifold is a sequence of complex numbers parametrized by complex roots of 1 for a framed link in s 3 the terms of the sequence are equale to the values of the suitably parametrized jones polynomial of the link in the corresponding roots of 1 in the case of manifolds with boundary our invariant is a sequence of finite dimensional complex linear operators this produces from each root of unity q a 3 dimensional topological quantum field theory

semilinear elliptic equations on unbounded domains on presente une nouvelle approche variationnelle a l existence des solutions pour le probleme aux valeurs limites u u r x f u x x x h 0 1 sur des domaines non bornes

emden fowler equations involving critical exponents on considere le probleme y t k y 2 y 2k 3 0 t 0 pour t 2 0 0 soit t inf t 0 y 0 sur t alors t 0 0 on etudie comment la position t du premier zero de y t varie avec

representations of the kauffman bracket skein algebra i invariants and miraculous cancellations we study finite dimensional representations of the kauffman bracket skein algebra of a surface s in particular we construct invariants of such irreducible representations when the underlying parameter q mathrm e 2 pi mathrm i hbar is a root of unity the main one of these invariants is a point in the character variety consisting of group homomorphisms from the fundamental group pi 1 s to mathrm sl 2 mathbb c or in a twisted version of this character variety the proof relies on certain miraculous cancellations that occur for the quantum trace homomorphism constructed by the authors these miraculous cancellations also play a fundamental role in subsequent work of the authors where novel examples of representations of the skein algebra are constructed

multiple solutions to a linearly coupled elliptic system with critical exponents abstract we are concerned with the linearly coupled elliptic system with critical exponents u a x u u 2 2 u u p 2 u v x r n v b x v v 2 2 v v q 2 v u x r n u v h 1 r n where n 3 2 p q 2 2 n n 2 and are nonnegative constants and a x b x are positive periodic functions the existence of a positive ground state and a higher energy solution of this system is proved using variational methods additionally the asymptotic behavior of these solutions as 0 is obtained

multiple positive solutions for quasilinear problems with indefinite sublinear nonlinearity abstract we have established multiplicity of nontrivial solutions for the quasilinear elliptic problem p u h x u 1 g x u in u 0 in u 0 on where r n is a smooth bounded domain p 1 1 p h is a measurable function and g r r is a caratheodory function such that g x 0 0 which is asymptotically linear we also prove existence and nonexistence results when g x t k x t p 1

the multigrid method in solid mechanics part i algorithm description and behaviour a multigrid algorithm is described that can be used to obtain the finite element solution of linear elastic solid mechanics problems the method is applied to some two dimensional problems to evaluate its strengths and weaknesses extensive studies are made to determine the convergence behaviour of the method in general this depends on many factors the number of degrees of freedom in the discretization characteristics of the algorithm poisson s ratio when it is close to 0 5 the amount of bending deformation in the problem under consideration and the degree of non uniformity in the mesh only certain values of the multigrid parameters allow a converged solution to be obtained with a computational effort proportional to the number of degrees of freedom these values include the optimum ones i e those that lead to convergence with the least computational effort the constant of proportionality is only independent of the number of degrees of freedom and still depends on the other factors listed above

multilevel aggregation method for solving large scale generalized eigenvalue problems in structural dynamics in this paper a novel iterative method of multilevel type for solving large scale generalized eigenvalue problems encountered in structural dynamics is presented a preconditioned iterative technique which can be viewed as a modification of the subspace iteration method is used for simultaneous calculation of a group of lowest modes and frequencies the paper demonstrates that a coarse aggregation model can be employed in the hierarchical structure of the preconditioner in order to provide a good resemblance of the latter to the stiffness matrix of the finite element approximation with respect to low frequency modes this leads to a fast convergent procedure of subspace iterations as opposed to the coarse grid used in methods of multigrid type this model allows for solving problems with different finite elements including reticulated structures in the framework of large comprehensive finite element software systems numerical experiments performed for three dimensional truss frame and solid structures demonstrate an excellent performance of the method 1997 by john wiley sons ltd

positive ground state solutions for the critical klein gordon maxwell system with potentials abstract this paper deals with the klein gordon maxwell system when the nonlinearity exhibits critical growth we prove the existence of positive ground state solutions for this system when a periodic potential v is introduced the method combines the minimization of the corresponding euler lagrange functional on the nehari manifold with the brezis and nirenberg technique

effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures a paradigm in three dimensions we present a methodology for the efficient numerical solution of eigenvalue problems of full three dimensional elasticity for thin elastic structures such as shells plates and rods of arbitrary geometry discretized by the finite element method such problems are solved by iterative methods which however are known to suffer from slow convergence or even convergence failure when the thickness is small in this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm edra as an example we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters i e the convergence does not deteriorate with diminishing thickness or mesh refinement this robustness is sine qua non for the efficient computation of large scale eigenvalue problems for thin elastic structures

on the classification of irreducible finite dimensional representations of uq so3 algebra in an earlier work m havlicek et al j math phys 40 2135 1999 we defined for any finite dimension five nonequivalent irreducible representations of the nonstandard deformation uq so3 of the lie algebra so3 where q is not a root of unity for each dimension only one of them called classical admits limit q 1 in the first part of this paper we show that any finite dimensional irreducible representation is equivalent to some of these representations in the case qn 1 we derive new casimir elements of uq so3 and show that a dimension of any irreducible representation is not higher than n these elements are casimir elements of uq som for all m and even of uq isom 1 due to inonu wigner contraction according to the spectrum of one of the generators the representations are found to belong to two main disjoint sets we give full classification and explicit formulas for all representations from the first set we call them nonsingular representations if n is odd we have full classificatio

unicity for representations of the kauffman bracket skein algebra this paper resolves the unicity conjecture of bonahon and wong for the kauffman bracket skein algebras of all oriented finite type surfaces at all roots of unity the proof is a consequence of a general unicity theorem that says that the irreducible representations of a prime affine k algebra over an algebraically closed field k that is finitely generated as a module over its center are generically classified by their central characters the center of the kauffman bracket skein algebra of any orientable surface at any root of unity is characterized and it is proved that the skein algebra is finitely generated as a module over its center it is shown that for any orientable surface the center of the skein algebra at any root of unity is the coordinate ring of an affine algebraic variety

existence and asymptotic behavior of vector solutions for coupled nonlinear kirchhoff type systems abstract this paper deals with the following linearly coupled nonlinear kirchhoff type system a 1 b 1 r 3 u 2 d x u 1 u f u v in r 3 a 2 b 2 r 3 v 2 d x v 2 v g v u in r 3 u v h 1 r 3 where a i 0 b i 0 i 0 are constants for i 1 2 0 is a parameter and f g c r r under the general berestycki lions type assumptions on f and g we establish the existence of positive vector solutions and positive vector ground state solutions respectively by using variational methods we also study the asymptotic behavior of these solutions as 0

multiple positive solutions for semilinear dirichlet problems with sign changing weight function in infinite strip domains abstract in this paper existence and multiplicity results to the following dirichlet problem u u f x u q 1 h x u p 1 in u 0 in u 0 on are established where r r n 1 is bounded smooth domain and n 2 here 1 q 2 p 2 2 2 n n 2 if n 3 2 if n 2 is a positive real parameter the function f among other conditions can possibly change sign in and the function h satisfies suitable conditions the study is based on the comparison of energy levels on nehari manifold

multiplicity of solutions for homogeneous elliptic systems with critical growth abstract in this paper we are concerned with the number of nonnegative solutions of the elliptic system u q u u v 1 2 h u u v in v q v u v 1 2 h v u v in u v 0 on where r n is a bounded smooth domain n 4 2 2 n n 2 and q u h u and q v h v are the partial derivatives of the homogeneous functions q h c 1 r 2 r where r 2 0 0 in the proofs we apply variational methods and ljusternik schnirelmann theory

on perturbations of a class of a periodic m laplacian equation with critical growth 1 after the well known results of brezis nirenberg 10 problems involving ellipticequationswithcriticalgrowthinboundeddomainshavebeenstudiedbyseveralauthors see for example 7 15 11 13 17 and the references therein the special features of this class of problems considered in this paper is that it isdened in r

existence and concentration of ground state solutions for critical schrodinger equation with steep potential well abstract in this paper we study the following schrodinger equation u 1 a x u f u u 2 2 u in r n where n 3 and 0 we obtain a ground state solution for the above equation moreover the concentration behavior of the ground state solution is also described as

on a schrodinger kirchhoff type equation involving the p x laplacian abstract in this paper we deal with a schrodinger type equation involving a nonlocal kirchhoff type coefficient and depending on two real parameters working within the framework of variable exponent spaces and using the variational approach we obtain several results of existence and multiplicity of solutions depending on the range of the parameters

bounds for best constants in subcritical sobolev embeddings abstract we establish upper and lower estimates for the embedding constants related to the classical sobolev embeddings h 0 1 l p where r n is a bounded domain or the whole r n and p 2 2 n n 2 n 3 in dimension n 2 we also derive the sharp asymptotic behavior of the embedding constant as p

multiple solutions for p kirchhoff equations in rn abstract in this paper we prove the existence of multiple ground state solutions for the nonhomogeneous p kirchhoff elliptic equation 0 1 m r n u p v x u p d x p u v x u p 2 u f x u g x in r n where v x c r n and v x as x the nonlinear function f x u is continuous and satisfies some conditions the solutions will be obtained by the mountain pass theorem ekeland s variational principle and krasnoselskii s genus theory in struwe 2000 1

skein modules and the noncommutative torus we prove that the kauffman bracket skein algebra of the cylinder over a torus is a canonical subalgebra of the noncommutative torus the proof is based on chebyshev polynomials as an application we describe the structure of the kauffman bracket skein module of a solid torus as a module over the algebra of the cylinder over a torus and recover a result of hoste and przytycki about the skein module of a lens space we establish simple formulas for jones wenzl idempotents in the skein algebra of a cylinder over a torus and give a straightforward computation of the n th colored kauffman bracket of a torus knot evaluated in the plane or in an annulus

multiple positive solutions for linearly coupled nonlinear elliptic systems with critical exponent abstract this paper deals with the following system linearly coupled by nonlinear elliptic equations u 1 u u 2 2 u v x v 2 v v 2 2 v u x u v 0 on here is a smooth bounded domain in r n n 3 1 2 1 are constants 1 is the first eigenvalue of h 0 1 2 2 n n 2 is the sobolev critical exponent and r is a coupling parameter by variational method we prove that this system has a positive ground state solution for some 0 via a perturbation argument we show that this system also admits a positive higher energy solution when is small moreover the asymptotic behaviors of the positive ground state and higher energy solutions as 0 are analyzed

nonlinear perturbations of a periodic elliptic problem with critical growth abstract using the well known mountain pass theorem due to ambrosetti and rabinowitz we establish conditions for the existence of a positive solution for a class of nonlinear elliptic problems in r n with critical growth

revisiting an idea of brezis and nirenberg abstract let n 3 and be a c 1 bounded domain in r n with 0 suppose is c 2 at 0 and the mean curvature of at 0 is negative we prove the existence of positive solutions for the equation 0 1 u u n 2 n 2 u 2 s 1 x s 0 in u 0 on where 0 0 s 2 2 s 2 n s n 2 and n 4 for n 3 the existence result holds for 0 s 1 under the same assumption of the domain for p 2 s 1 we also prove the existence of a positive solution for the following equation 0 2 u u p u 2 s 1 x s 0 in u 0 on where 0 and 1 p n n 2

solutions to semilinear elliptic problems with combined nonlinearities abstract we are concerned with the following nonlinear dirichlet problem u h x u q f x u 0 u h 0 1 0 where is a bounded smooth domain in rn n 1 and h x l f x s is asymptotically linear with respect to s at infinity by a variant version of mountain pass theorem we prove that there exist at least two nonnegative solutions under suitable assumptions on f x s our methods also work for the cases where f x s is superlinear or linear in s

estimates of the conformal scalar curvature equation via the method of moving planes in this paper we derive a local estimate of a positive singular solution u near its singular set z of the conformal equation where k x is a positive continuous function z is a compact subset of and g satisfies that is nonincreasing for t 0 assuming that the order of flatness at critical points of k on z is no less than we prove that through the application of the method of moving planes the inequality holds for any solution of 0 1 with cap z 0 by the same method we also derive a harnack type inequality for smooth positive solutions let u satisfy assume that the order of flatness at critical points of k is no less than n 2 then the inequality holds for r 1 we also show by examples that the assumption about the flatness at critical points is optimal for validity of the inequality 0 4 1997 john wiley sons inc

multiple positive solutions for dirichlet problems involving concave and convex nonlinearities abstract in this paper we study the multiplicity of positive solutions for the following dirichlet problems involving concave and convex nonlinearities u u f x u q 2 u h x u p 2 u in a u h 0 1 a where 1 q 2 p 2 2 2 n n 2 if n 3 2 if n 2 0 a r is an infinite strip in r n is a bounded domain in r n 1 and f x h x satisfy suitable conditions

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

positive solutions for some quasilinear equations with critical and supercritical growth abstract we establish results concerning the existence and multiplicity of positive solutions for the problem div a e x u p 2 u u p 1 f u u p 1 in r n u w 1 p r n where e 0 is a small parameter 2 p n p n p n p a is a positive potential and f is a superlinear function we obtain the existence of a ground state solution and relate the number of positive solutions with the topology of the set where a attains its minimum we also prove a multiplicity result for a supercritical version of the above problem in the proofs we use minimax theorems and ljusternik schnirelmann theory

the multigrid method in solid mechanics part ii practical applications no proportionality is observed between the total number of operations to convergence and the problem size despite such behaviour the multigrid algorithm proves to be an effective matrix equation solver for solid mechanics problems it is orders of magnitude faster than a direct factorization method and yields converged solutions several times faster than the jacobi preconditioned conjugate gradient method

multiple positive solutions for a class of concave convex elliptic problems in rn involving sign changing weight in this paper we study the multiplicity of positive solutions for the following concave convex elliptic equation u u f x uq 1 g x up 1in rn u 0in rn u h1 rn where 1 q 2 p 2 2 2nn 2 if n 3 2 if n 1 2 and the parameters 0 we assume that f x f x f x is sign changing and g x a x b x where the functions f a and b satisfy suitable conditions

a multigrid method for the generalized symmetric eigenvalue problem part i algorithm and implementation a multigrid method is described that can solve the generalized eigenvalue problem encountered in structural dynamics the algorithm combines relaxation on a fine mesh with the solution of a singular equation on a coarse mesh a sequence of coarser meshes may be used to quickly solve this singular equation using another multigrid method the hierarchy of increasingly finer meshes can be further exploited using a nested iteration scheme whereby initial approximations to the fine mesh eigenvectors are computed using interpolated coarse mesh eigenvectors the solution of some simple plate problems on a convex c240 demonstrates the efficiency of a vectorized version of the multigrid algorithm

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

ground state solutions to nonlinear equations with p laplacian abstract we investigate the existence of positive radial solutions for a nonlinear elliptic equation with p laplace operator and sign changing weight both in superlinear and sublinear case we prove the existence of solutions u which are globally defined and positive outside a ball of radius r satisfy fixed initial conditions u r c 0 u r 0 and tend to zero at infinity our method is based on a fixed point result for boundary value problems on noncompact intervals and on asymptotic properties of suitable auxiliary half linear differential equations the results are new also for the classical laplace operator and may be used for proving the existence of ground state solutions and decaying solutions with exactly k zeros which are defined in the whole space some examples illustrate our results

multiplicity of solutions for a class of elliptic problem in r 2 with neumann conditions abstract in this work we study the existence and multiplicity of solutions for a class of elliptic problems in exterior domains of r 2 with neumann boundary conditions and nonlinearity with critical growth

positive ground state solutions for a nonlinearly coupled schrodinger system with critical exponents in r4 abstract consider the following nonlinear schrodinger equations u 1 u 1 u 3 3 u 2 v u v 2 v 3 x v 2 v 2 v 3 3 u v 2 u 2 v u 3 x u 0 v 0 in u v 0 on where r 4 is a smooth bounded domain 1 2 0 1 2 0 0 and is the first eigenvalue of with the dirichlet boundary condition note that all the cubic nonlinearities including the coupling terms are of critical growth the existence of positive ground state solutions for the system is established

a multigrid method for the generalized symmetric eigenvalue problem part ii performance evaluation the behaviour of the multigrid method is studied by solving some simple test problems optimum choices for some of the parameters are discussed together with effective techniques for solving the coarse mesh correction equation the effects of ill conditioning on the performance of the algorithm are examined in particular thin shells and non uniform meshes are observed to slow convergence the solution of practical large scale problems demonstrates the utility and speed of the proposed multigrid method for example the first 10 eigensolutions of a stiffened plate problem with 193 536 degrees of freedom were computed in 1 6 cpu hours using 42 mbytes of memory on a convex c240

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

remarks on sublinear elliptic problems on unbounded cylinders m l where v s o r o r is a bounded smooth domain m l g 0 m w n m q l g 1 v s o if m s 0 and v s r if l s 0 f v 0 a r is a caratheodory function and r v a r is continuous r g 0 there is by now an extensive literature on this kind of problem for w x w x w x w x instance amick and toland 1 stuart 2 esteban 3 burton 4 bona w x w x bose and turner 5 and berestycki and lions 20 where different conditions on r x and f x s as well as several techniques were considered this list is of course far from complete and we would also refer to w x w x schindler 6 costa and miyagaki 7 and their references physical motiva

existence of a ground state solution for an elliptic problem with critical growth in an exterior domain abstract in this work we prove the existence of a radially symmetric ground state solution for an elliptic equation in an exterior of a ball with neumann boundary condition

non semi simple tqfts reidemeister torsion and kashaev s invariants we construct and study a new family of tqfts based on nilpotent highest weight representations of quantum sl 2 at a root of unity indexed by generic complex numbers this extends to cobordisms the non semi simple invariants defined in arxiv 1202 3553 including the kashaev invariant of links here the modular category framework does not apply and we use the universal construction our tqft provides a monoidal functor from a category of surfaces and their cobordisms into the category of graded finite dimensional vector spaces and their degree 0 morphisms and depends on the choice of a root of unity of order 2r the functor is always symmetric monoidal but for even values of r the braiding on grvect has to be the super symmetric one thus our tqft may be considered as a super tqft in the special case r 2 our construction yields a tqft for a canonical normalization of reidemeister torsion and we re prove the classification of lens spaces via the non semi simple quantum invariants defined in arxiv 1202 3553 we prove that the representations of mapping class groups and torelli groups resulting from our constructions are potentially more sensitive than those obtained from the standard reshetikhin turaev functors in particular we prove that the action of the bounding pairs generators of the torelli group has always infinite order

a nonhomogeneous elliptic problem involving critical growth in dimension two abstract in this paper we study a class of nonhomogeneous schrodinger equations u v x u f u h x in the whole two dimension space where v x is a continuous positive potential bounded away from zero and which can be large at the infinity the main difficulty in this paper is the lack of compactness due to the unboundedness of the domain besides the fact that the nonlinear term f s is allowed to enjoy the critical exponential growth by means of the trudinger moser inequality by combining variational arguments and a version of the trudinger moser inequality we establish the existence of two distinct solutions when h is suitably small

a finite set of generators for the kauffman bracket skein algebra if f is a compact orientable surface it is known that the kauffman bracket skein module of f times i has a multiplicative structure our central result is the construction of a finite set of knots which generate the module as an algebra we can then define an integer valued invariant of compact orientable 3 manifolds which characterizes s 3

existence of solutions for a class of elliptic equations in r n with vanishing potentials in this paper we investigate the existence of positive solution for the following class of elliptic equation u v x u f u in rn where f has a subcritical growth and v is a nonnegative potential which can vanish at infinity that is v x 0 as x or shortly v 0

soliton solutions for quasilinear schrodinger equations with critical growth in this paper we establish the existence of standing wave solutions for quasilinear schrodinger equations involving critical growth by using a change of variables the quasilinear equations are reduced to semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle due to p l lions together with some classical arguments used by h brezis and l nirenberg 1983 in 9