nontrivial periodic solutions for the asymptotically linear hamiltonian systems with resonance at infinity abstract in this paper we are concerned with the existence of nontrivial periodic solutions of an asymptotically linear hamiltonian systems when a kind of resonance condition is satisfied we prove several new existence results via the morse theory the garlerkin methods and the moslov index theory

the minimal period problem for nonconvex even second order hamiltonian systems abstract in this paper we study the minimal period problem for even autonomous second order hamiltonian systems defined on r nwithout any convexity assumption by using the variational methods we obtain estimates on the minimal period of the corresponding nonconstant periodic solution of the superquadratic and asymptotically linear hamiltonian systems

a discontinuous wave in cell numerical scheme for hyperbolic conservation laws a new riemann solver scheme for hyperbolic systems is introduced the method consists of a discretization of the initial data into an approximate representation by discrete discontinuous waves instead of calculating an intercell flux based on these waves the discontinuous waves are propagated directly since the sum total of all discontinuous waves represents an extension of the linear riemann problem the solution is determined straightforwardly for nonlinear systems each timestep is considered a separate linear riemann problem and the projected waves are weighted to a background grid this method is strikingly similar to the particle in cell approach except that discontinuous waves are pushed around instead of macroparticles the method is applied to maxwell s equations and the equations of inviscid gasdynamics for linear systems exact solutions can be achieved without dissipation and exact transmissive boundary condition treatments are trivial to implement for inviscid gasdynamics the nonlinear method tended to resolve discontinuities more sharply than the roe hll or hllc methods while requiring only between 30 and 50 of the execution time under identical conditions the approach is also extremely robust as it works for any courant number in the limit that the courant number becomes infinite the nonlinear solution approaches the linearized solution

application of the principle of minimizing the derivative to the construction of finite difference schemes for computing discontinuous solutions of gas dynamics progress in computer technology now allows the application of numerical methods to some practical multidimensional steady and unsteady gas flows while selecting a numerical method preference should be given to higher order schemes since they allow the study of the fine features of the solution and the reduction of the computation time in general however solutions of non stationary nonlinear equations of gas dynamics are not smooth and may include strong discontinuities such as shock waves or contact discontinuities this fact is important for choosing an appropriate numerical scheme if the strong discontinuities are extracted from the simulation domain and traced shock fitting while the rest of the flow is smooth it is possible to use numerical schemes with approximation close to the second order 1 3 however if the number of discontinuities increases with time leading to a complicated pattern the application of the shock fitting approach becomes difficult in this case it is preferable to apply shock capturing schemes 4 6 which have a lower order of approximation but allow the integration of the governing equations through the discontinuities without extracting their surfaces shock capturing schemes of a higher order of approximation are currently under development 7 9 in this paper certain aspects of constructing a numerical scheme applicable to discontinuous flows of gas dynamics are discussed using the idea of minimizing the derivatives of the solution a numerical scheme that is second order accurate in space and first order accurate in time is developed for the model equation u t u x 0 the properties of this scheme are analyzed and the conditions for its stability and monotonicity are formulated these results are then used in devising a similar scheme for the non stationary one dimensional equations of gas dynamics the performance of the new scheme is compared to that of other schemes using the break up of an initial discontinuity riemann problem as an example

multiple periodic solutions for discrete hamiltonian systems abstract several existence results of multiple periodic solutions for discrete hamiltonian system are established where the nonlinearity is either asymptotically linear or superlinear at infinity the approach used here is based on morse theory

morse theory and asymptotic linear hamiltonian system on considere l existence de solutions 2 periodiques des systemes hamiltoniens asymptotiquement quadratiques jz h z t ou j 0 i i 0 i in la matrice identite de n n

solutions of asymptotically linear operator equations via morse theory abstract in this paper we use the classical morse theory of critical points to study the existence and multiplicity of solutions of a class of asymptotically linear operator equations as special cases we include multiplicity results for semilinear elliptic bvp s as well as existence and multiplicity of periodic solutions of semilinear wave equation and of hamiltonian systems these results simplify and complement recent work of amann zehnder and castro lazer author

periodic solutions for asymptotically linear hamiltonian system with resonance both at infinity and origin via computation of critical groups abstract in this paper we study the existence of nontrivial periodic solutions for asymptotically linear hamiltonian system which has the same linear term both at infinity and origin by computation of critical groups at origin and infinity associated with maslov type index we establish the existence for nontrivial periodic solution of the system moreover some conditions employed for the computation of critical groups are weakened

an elliptic resonance problem with multiple solutions in this paper we study the existence of multiple nontrivial solutions for a semilinear elliptic equation at resonance by the minimax methods and morse theory

periodic solutions of classical hamiltonian systems without palais smale condition abstract in this paper we study the existence of periodic solutions for classical hamiltonian systems without the palais smale condition we prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions moreover we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function v

on resonant neumann problems multiplicity of solutions abstract we consider a semilinear neumann problem with an asymptotically linear reaction term we assume that resonance occurs at infinity using variational methods based on the critical point theory together with the reduction technique and morse theory we show that the problem has at least four nontrivial smooth solutions

multiple solutions for the coercive semilinear elliptic equations abstract in this paper we study the semilinear elliptic equations u f x u x u 0 x where r n is a smooth bounded domain by using the minimax methods bifurcation methods conley index theory and morse theory we obtain six nontrivial solutions for the equations with coercive nonlinearities

multiple solutions for asymptotically p 1 homogeneous p laplacian equations we consider a nonlinear elliptic equation driven by the p laplacian and with a reaction term which exhibits a p 1 homogeneous growth both near and near zero using critical point theory with truncation techniques the method of upper lower solutions and morse theory we show that the problem has five nontrivial smooth solutions four of which have constant sign two positive and two negative

multiple solutions for semilinear resonance elliptic problems with nonconstant coefficients at infinity in this paper we study a class of semilinear elliptic equations which are completely resonant with nonconstant coefficients at origin and at infinity by applying morse theory and minimax method we obtain the existence of multiple nontrivial solutions for the equations

nonparametric bayes estimators based on beta processes in models for life history data the article studies the problem of finding bayes estimators for cumulative hazard rates and related quantities w r t prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments a particular class of prior processes termed beta processes is introduced and is shown to constitute a conjugate class an important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated for example time inhomogeneous markov chains we find posterior distributions and derive bayes estimators in such models and present a semiparametric bayesian analysis of the cox regression model

existence of three nontrivial solutions for asymptotically p linear noncoercive p laplacian equations abstract we consider a nonlinear elliptic problem driven by the p laplacian where the right hand side nonlinearity exhibits a p linear behavior near infinity and the euler functional of the problem need not be coercive and in fact can be indefinite using a combination of minimax arguments with truncation techniques and morse theory we show that the problem has at least three nontrivial smooth solutions two of which have a constant sign our method of proof uses some results on critical groups and the spectrum of the p laplacian due to perera and dancer perera

solutions to a gradient system with resonance at both zero and infinity in this paper we study the existence and multiplicity of nontrivial solutions for a gradient system with resonance at both zero and infinity via morse theory

on multiple solutions of a nonlinear dirichlet problem we prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues we also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial

multiple solutions of semilinear elliptic problems in a ball in this paper lower bounds for the number of solutions of semilinear elliptic problems in a ball of rn are given its hypotheses are only related to the behavior of the nonlinearities at and at 0 global assumptions are never made for example oddness is never required for the proof of multiplicity results

a cohomological conley index in hilbert spaces and applications to strongly indefinite problems abstract a cohomological conley index is defined for flows on infinite dimensional real hilbert spaces generated by vector fields of the form f h h f x lx k x where l h h is a bounded linear operator satisfying certain technical assumptions and k is a completely continuous perturbation generalized morse inequalities for morse decompositions of isolated invariant sets are proved simple examples are presented to show how the theory can be applied to strongly indefinite problems

multiple solutions for an asymptotically linear problem in rn abstract we consider a semilinear problem of the type lu f b u in l 2 r n where f b u bu as u 0 and f b u b u as u b b we assume that the essential spectrum of l is bounded below by a number greater than b and that there exist a finite number of eigenvalues between b and b we prove existence and multiplicity results for nontrivial solutions under suitable assumptions on g we give an application to the schrodinger equation

existence of solutions for an asymptotically linear dirichlet problem via lazer solimini results abstract in this paper we prove that an asymptotically linear dirichlet problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first k eigenvalues of minus laplacian without any restriction about nondegeneracy of solutions a pair is of one sign positive and negative respectively we construct a third solution using arguments of the type lazer solimini see a c lazer s solimini nontrivial solutions of operator equations and morse indices of critical points of min max type nonlinear anal 12 8 1988 761 775 this gives a partial answer to a conjecture stated in j cossio s herron nontrivial solutions for a semilinear dirichlet problem with nonlinearity crossing multiple eigenvalues j dyn differential equations 16 3 2004 795 803 moreover in the particular case of nondegenerate critical points we prove that there are at least four nontrivial solutions the one sign solutions are of morse index equal to 1 the third solution has morse index k and there is a fourth solution for this case we use the leray schauder degree and lazer solimini results

periodic solutions of some resonant hamiltonian systems abstract based on the galerkin approximation and the morse inequality an existence theorem of periodic solutions of the hamiltonian system j z h t z is given where h t z is asymptotically linear and resonant at infinity existence of periodic solutions of the resonant asymmetric p laplacian equation is also discussed

modelling accelerated failure time with a dirichlet process the relationship between survival times and covariates is modelled via the accelerated failure time model with a dirichlet process prior assumed for the underlying baseline survival fucntion emphasis is placed on estimating the survival distribution for future individuals with given covariates a method of estimating regression coefficients which uses the marginal distribution for observed censored data is given

computations of critical groups and applications to some differential equations at resonance abstract in this paper we first consider the computations of the critical groups of a functional with generalized ahmad lazer paul type conditions both at zero and infinity then the abstract results are applied to investigate some new cases of the existence of nontrivial solutions of the second order hamiltonian systems and elliptic boundary value problems which may be resonant both at zero and infinity

implicit high order method for calculating rarefied gas flow in a planar microchannel an efficient numerical algorithm for calculating rarefied gas flows in planar microchannels on the basis of the boltzmann kinetic equation with the linearized s model collision integral is presented the algorithm consists of a high order spatial discretisation on unstructured meshes conservative procedure to calculate macroscopic quantities and efficient one step implicit time evolution method it therefore works across all flow regimes from the free molecular to nearly continuum ones and provides rapid convergence to steady state solutions the parallel implementation is provided via mpi programming paradigm the performance of the method is illustrated by computing the flow for length to the width ratios for up to 10 3 in the wide range of knudsen numbers numerical estimates of efficiency of implicit time marching and parallel performance as well as convergence studies in both physical and velocity spaces are provided the end effects and other essentially two dimensional features of the flow are analysed and a detailed comparison with the case of an infinitely long channel is carried out the presented numerical data can be used as reference for future studies of nonlinear flows as well as for comparison with other numerical approaches and flow models

short note complement to the kolgan project these notes amplify the paper by bram v leer on vladimir kolgan and his work they give some additional information and share the vision of kolgan by the people coming from the same country

remarks on multiple nontrivial solutions for quasi linear resonant problems in this paper morse theory and local linking are used to study the existence of multiple nontrivial solutions for a class of dirichlet boundary value problems with double resonance at infinity and at 0

existence and multiplicity results for classes of elliptic resonant problems in this paper we prove some new existence results of nontrivial solutions for classes of elliptic resonant problems we also establish several multiplicity results the methods used here are based on combining the minimax methods and the morse theory especially some new observations on the critical groups of a local linking type degenerate critical point

morse type index theory for flows and periodic solutions for hamiltonian equations an index theory for flows is presented which extends the classical morse theory for gradient flows on compact manifolds the theory is used to prove a morse type existence statement for periodic solutions of a time dependent periodic in time and asymptotically linear hamiltonian equation

nontrivial solutions for some fourth order boundary value problems with parameters abstract in this paper we prove some new existence results concerning nontrivial solutions to some fourth order boundary value problems u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f c 1 0 1 r r r are parameters satisfying 4 2 1 the methods used here are based on combining the minimax methods and the morse theory

a historical oversight vladimir p kolgan and his high resolution scheme the russian landmark paper application of the principle of minimizing the derivative to the construction of finite difference schemes for computing discontinuous solutions of gas dynamics by vladimir p kolgan is discussed in a historical technical perspective the 1972 paper already featured a godunov type scheme for the euler equations with second order spatial accuracy and a limiter to make it monotonicity preserving the work remained little known within and completely unknown outside the ussr largely because of kolgan s untimely death in 1978 to honor kolgan s contribution to cfd an english translation of his paper is included in this issue of the journal of computational physics facts about kolgan s life are presented here and an appraisal is given of the originality of his ideas

global bifurcations of critical orbits of g invariant strongly indefinite functionals abstract let h be a separable hilbert space which is an orthogonal representation of a compact lie group g and let h r be a g invariant strongly indefinite functional of the class c 1 to study critical orbits of we have defined the degree for g invariant strongly indefinite functionals which is an element of the euler ring u g using this degree we have formulated the rabinowitz alternative for g invariant strongly indefinite functionals the abstract results are applied to the study of global bifurcations of weak solutions of non cooperative systems of elliptic differential equations

nontrivial periodic solutions for asymptotically linear hamiltonian systems with resonance abstract in this paper we establish some existence results of nontrivial 1 periodic solutions to the first order asymptotically linear hamiltonian systems under the assumptions that the linear operators have different maslove indices at the origin and at infinity the results obtained in this paper are also valued for the case that both of the asymptotic matrices may be degenerate resonant type and time dependent

bayesian nonparametric inference for random distributions and related functions in recent years bayesian nonparametric inference both theoretical and computational has witnessed considerable advances however these advances have not received a full critical and comparative analysis of their scope impact and limitations in statistical modelling many aspects of the theory and methods remain a mystery to practitioners and many open guestions remain in this paper we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the bayesian nonparametric and or semiparametric framework

multiple periodic orbits of asymptotically linear autonomous convex hamiltonian systems we investigate multiple periodic solutions of convex asymptotically linear autonomous hamiltonian systems our theorem generalizes a result by mawhin and willem

remarks on the resonant elliptic problem we consider the semilinear elliptic equation u f x u with the dirichlet boundary value for resonant nonlinearity at infinity using the morse theory and perturbation method some existence results of solution and multiple solutions are proved

periodic solutions of asymptotically linear autonomous hamiltonian systems abstract in this paper we study the existence and the continuation of periodic solutions of autonomous hamiltonian systems we apply the degree for g invariant strongly indefinite functionals defined in gol biewska and rybicki 2011 2 we consider resonant as well as nonresonant case at stationary solutions

nontrivial critical points for asymptotically quadratic function abstract in this paper we study the existence of nontrivial critical points as applications we study the existence of nontrivial solutions of the dirichelet problem for nonlinear elliptic pde and periodic boundary value problem for nonlinear ope

bayesian semiparametric estimation of proportional hazards models abstract this paper proposes a semiparametric analysis of proportional hazards models this approach consists in specifying the relation between a duration and explanatory variables without specifying the data distribution the parameters involved in this relation are then considered as parameters of interest and the data distribution is treated as a nuisance parameter we propose a bayesian estimation method the principle of which is to specify a prior distribution on the nuisance parameter we then obtain semiparametric estimators for the parameters of interest by computing their posterior distribution conditional on the data and integrated with respect to the nuisance parameter

multiplicity of periodic solutions for second order systems with a small forcing term some multiplicity results are obtained for periodic solutions of second order systems with a small forcing term by using the implicit function theorem and the morse theory

a twist condition and periodic solutions of hamiltonian systems abstract in this paper we investigate existence of nontrivial periodic solutions to the hamiltonian system hs j z h t z z r 2 n under a general twist condition for the hamiltonian function in terms of the difference of the conley zehnder index at the origin and at infinity we establish existence of nontrivial periodic solutions compared with the existing work in the literature our results do not require the hamiltonian function to have linearization at infinity our results allow interactions at infinity between the hamiltonian and the linear spectra the general twist condition raised here seems to resemble more the spirit of poincare s last geometric theorem

existence of solutions for quasilinear elliptic equations abstract using variational methods we study the existence and multiplicity of solutions of the dirichlet problem for the equation div a u p u p 2 u f x u

multiplicity results for problems involving the hardy sobolev operator via morse theory we establish some multiplicity results for a class of boundary value problems involving the hardy sobolev operator using morse theory c 2009 elsevier ltd all rights reserved

multiple solutions of some nonlinear fourth order beam equations abstract several new existence theorems on three solutions and infinitely many solutions for the following fourth order beam equation are obtained u 4 f t u t t 0 1 u 0 u 1 u 0 u 1 0 where f c 1 0 1 r 1 r 1 the morse theory is employed to discuss this problem

critical point theorem for asymptotically quadratic functional without compactness in this paper we build an abstract critical point theorem for the asymptotically quadratic functional without compactness application is devoted to the existence of nontrivial periodic solution of second order hamiltonian systems

existence and multiplicity results for a semilinear elliptic problem abstract in this paper we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues we make extensive use of variational methods and characterizations of the local degree of critical points furthermore uniqueness and qualitative properties of the solutions are investigated

existence of nontrivial periodic solutions for a class of resonance hamiltonian systems abstract in this paper we study the asymptotically linear hamiltonian systems jz h t z with resonance at infinity via the morse theory and the galerkin methods and obtain some new existence results about the nontrivial periodic solutions of this system

nontrivial solutions of operator equations and morse indices of critical points of min max type on montre que si les hypotheses du theoreme de point selle sont satisfaites si dim y 2 et si f 1 c contient seulement des points critiques non degeneres alors f 1 c contient au moins un point critique u 0 tel que 2 indice de morse u 0 dim y

spectral flow and bifurcation of critical points of strongly indefinite functionals part i general theory abstract spectral flow is a well known homotopy invariant of paths of selfadjoint fredholm operators we describe here a new construction of this invariant and prove the following theorem let i u rbe ac2function on the product of a real intervali a b with a neighborhood u of the origin of a real separable hilbert space h and such that for each in i 0is a critical point of the functional assume that the hessian l of at0is fredholm and moreover that laand lbare nonsingular if the spectral flow of the path l idoes not vanish then the interval i contains at least one bifurcation point from the trivial branch for solutions of the equation x x 0 equivalently every neighborhood of i 0 contains points of the form x wherex 0 is a critical point of

multiple solutions for nonlinear dirichlet problems via bifurcation and additional results abstract in this paper we study the existence of multiple solutions for semilinear elliptic boundary value problems first when the nonlinearity is asymptotically linear and then when it has an arbitrary behavior for large values of the argument our proofs use extensively the global bifurcation theorem and bifurcation from infinity additionally when we can apply the lyapunov schmidt reduction method we show the existence of multiple solutions we give an exact number of solutions and we provide qualitative properties of these solutions

on resonance hamiltonian systems without the palais smale condition abstract in this paper we study periodic solutions of resonance hamiltonian systems by combining conley index theory and galerkin approximation method we prove the existence of periodic solutions of hamiltonain systems where both the palais smale condition and the strong resonance method fail

multiple solutions of a class of neumann problem for semilinear elliptic equations abstract the multiplicity results are obtained for solutions of the neumann problem for nonlinear elliptic equations with unbounded nonlinearity by the implicit function theorem and the morse theory

nonlinear elliptic equations with an asymptotically linear reaction term abstract we examine nonlinear elliptic problems driven by the p laplacian and with a reaction term which asymptotically at exhibits a p 1 linear growth 1 p using tools from critical point theory and from morse theory we prove existence theorems and we provide information about the sign of the solutions