an orlicz space approach to superlinear elliptic systems in this paper we study superlinear elliptic systems in hamiltonian form using an orlicz space setting we extend the notion of critical growth to superlinear nonlinearities which do not have a polynomial growth existence of nontrivial solutions is proved for superlinear nonlinearities which are subcritical in this generalized sense

a general procedure for the adaptation of multistep algorithms to the integration of oscillatory problems this paper introduces a general technique for the construction of multistep methods capable of integrating without local truncation error homogeneous linear odes with constant coefficients including those in particular that result in oscillatory solutions moreover these methods can be further adapted through coefficient modification for the exact integration of forced oscillations in one or more frequencies even confluent ones that occur from nonhomogeneous terms in the differential equation our procedure allows the derivation of many of the existing codes with similar properties as well as the improvement of others that in their original design were only able to integrate oscillations in a single frequency the properties of the methods are studied within a general framework and numerical examples are presented these demonstrate the way in which the new algorithms perform distinctly better than the general purpose codes particularly when integrating the class of equations with perturbed oscillatory solutions the methods developed are mainly applicable to the accurate and efficient integration of problems for which the oscillation frequencies are known as occurs in satellite orbit propagation the underlying ideas have already been applied to the improvement of some chebyshev methods that are not multistep

a superquadratic indefinite elliptic system and its morse conley floer homology we study critical points of the indefinite functional f h u v int nabla u cdot nabla v h x u v mathrm d x by applying floer s homology construction to the ordinary gradient flow of the functional f on a suitable sobolev space one of our main observations is that even though this flow is well posed in both time directions and lacks any kind of smoothing property one can still obtain compactness of connecting orbit spaces and thus define the floer homology for f h

infinitely many solutions for symmetric and non symmetric elliptic systems we study an elliptic system equivalent to a fourth order elliptic equation by using variational and perturbative methods we prove the existence of infinitely many solutions both in the symmetric and in the non symmetric case

multiple solutions for asymptotically linear elliptic systems in this article we consider cooperative and noncooperative elliptic systems that are asymptotically linear at infinity we obtain infinitely many solutions with small energy if the potential is even if the noncooperative system is resonant both at zero and at infinity then the number of nontrivial solutions depends on the dimension of the eigenspaces between resonant values

variational identities and applications to differential systems j serrin 1 introduction in the work of ponos p and in recent work of pucci serrin ps variational identities are discussed which are useful for solving various ques tions about elliptic differential equations and particular elliptic systems here we obtain a number of further applications of these identities to systems it was noted in ps that these identities are closely related to noether s theorem for variational problems by working out the divergence term arising in noether s theorem and making some simplifications one obtains a general identity for variational problems if a variational integral has a symmetry group g with the following infinitesimal generator

a two step explicit p stable method of high phase lag order for linear periodic ivps in this paper we present a nonlinear two step explicit p stable method of fourth algebraic order and 12th phase lag order for solving one dimensional second order linear periodic initial value problems ivps of ordinary differential equations based on a special vector arithmetic with respect to an analytic function the method can be extended to be vector applicable for multi dimensional problems directly some numerical results are reported to illustrate the efficiency of the method

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

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 note on superlinear hamiltonian elliptic systems this paper is concerned with the superlinear periodic elliptic systems of hamiltonian type in the whole space the existence of a ground state solution as well as an infinite number of geometrically distinct solutions is obtained

infinitely many solutions for diffusion equations without symmetry abstract we consider the following diffusion system t u x u b t x x u v x u h v t x u v t v x v b t x x v v x v h u t x u v t x r r n which is an unbounded hamiltonian system in l 2 r r n r 2 m z u v r r n r m r m b c r r n r n v c r n r and h c 1 r r n r 2 m r suppose that h b and v depend periodically on t and x and that h t x z is superquadratic in z as z without a symmetry assumption on h we establish the existence of infinitely many geometrically distinct solutions via a variational approach

a two step explicit p stable method of high phase lag order for second order ivps this paper presents a two step explicit p stable method of high phase lag order for solving second order ordinary differential equations basing on a special vector operation with respect to a smooth function the method can be extended to be vector applicable in multi dimensional space

on the existence of positive solutions of a perturbed hamiltonian system in rn using the legendre fenchel transformation and the mountain pass theorem due to ambrosetti and rabinowitz we establish an existence result for perturbations of periodic and asymptotically periodic semilinear hamiltonian systems of the type pw u u w2 x v p 1vinrn v v w1 x u q 1uinrn u x v x 0as x u 0 v 0inrn n 2 here the numbers p q 1 are below the critical hyperbola if n 3 that is they satisfy 1 p 1 1 q 1 n 2 n while no additional restrictions on p and q are required if n 2 the functions wi i 1 2 are bounded positive continuous functions

the nehari manifold for systems of nonlinear elliptic equations abstract this paper deals with the existence and multiplicity results of nonlocal positive solutions to the following system p u u p 1 2 u 1 u u 1 v 1 q v v q 2 v 1 u 1 v 1 v together with dirichlet or mixed boundary conditions under some hypotheses on the parameters p p 1 and q more precisely the system considered corresponds to a perturbed eigenvalue equation combined with a second equation having concave and convex nonlinearities the study is based on the extraction of palais smale sequences in the nehari manifold the behaviour of the energy corresponding to these positive solutions with respect to the real parameters and is established

multiple positive solutions of strongly indefinite systems with critical sobolev exponents and data that change sign abstract in this paper we study the existence of multiple positive solutions to some hamiltonian elliptic systems v u u p 1 u ef x u v v q 1 v eg x in u 0 v 0 in u v 0 on where is a smooth bounded domain in r n n 3 f g c 1 p q 1 r for the subcritical and critical cases we prove that problem has at least two positive solutions for any e 0 e and has no positive solutions for any e e e in the supercritical case we find that the existence of solutions of problem for 0 is closely related to the existence of nonnegative solutions of some linear elliptic system

approximation algorithms for the assembly line crew scheduling problem given an m n nonnegative matrix we study the problem of independently permuting the elements in each column so as to minimize the maximum row sum this problem is np hard even when we restrict it to the m 3 case a special case of our problem is the multiprocessor scheduling problem without precedence constraints in this paper we give a 2 1 m algorithm for the general m n case we also design a 3 2 algorithm for the m 3 case which applies a restricted longest processing time first heuristic finally using an edge matching algorithm we produce a more elaborate algorithm that guarantees a bound of 4 3 for the m 3 case

a family of numerov type exponentially fitted predictor corrector methods for the numerical integration of the radial schro dinger equation a family of predictor corrector exponential numerov type methods is developed for the numerical integration of the one dimensional schrodinger equation the formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions the new methods are very simple and integrate more exponential functions than both the well known fourth order numerov type exponentially fitted methods and the sixth algebraic order runge kutta type methods numerical results also indicate that the new methods are much more accurate than the other exponentially fitted methods mentioned above

nonnegative solutions for nonlinear elliptic systems abstract in this paper we show that the semilinear elliptic systems of the form 0 1 u v g v v u f u x u v 0 x possess at least one nonnegative nontrivial solution pair u v h 0 1 h 0 1 where is a smooth bounded domain in r n

the nehari manifold for a semilinear elliptic system involving sign changing weight functions abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e with sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

new finite difference formulas for numerical differentiation conventional numerical differentiation formulas based on interpolating polynomials operators and lozenge diagrams can be simplified to one of the finite difference approximations based on taylor series and closed form expressions of these finite difference formulas have already been presented in this paper we present new finite difference formulas which are more accurate than the available ones especially for the oscillating functions having frequency components near the nyquist frequency closed form expressions of the new formulas are given for arbitrary order a comparison of the previously available three types of approximations is given with the presented formulas a computer program written in mathematica based on new formulas is given in the appendix for numerical differentiation of a function at a specified mesh point

permuting elements within columns of a matrix in order to minimize maximum row sum we study the problem of permuting the elements within columns of a given m n matrix a so as to minimize its maximum row sum sum of the elements in a row we introduce and analyze an approximation algorithm of greedy type for this np complete problem we prove that our algorithm produces matrices with maximum row sums no more than 3 2 1 2m times greater than those found by an optimization rule moreover examples are presented which achieve this relative performance thus our algorithm represents a substantial improvement in that all earlier algorithms have a worst case performance that is asymptotically twice that of an optimization rule we verify that our algorithm requires at most o m2n time which is a modest increase over the earlier algorithms requiring mn log n time in the worst case

an extended numerov type method for the numerical solution of the schrodinger equation abstract a new method which is based on the new property of phase lag for computing eigenvalues of schrodinger equations with potentials is developed in this paper we investigate two cases 1 i the specific case in which the potential v x is an even function with respect to x it is assumed also that the wavefunctions tend to zero for x 2 ii the general case for positive and negative eigenvalues and for the well known cases of the morse potential and of the woods saxon or optical potential numerical and theoretical results show that this new method is more efficient compared with previously derived methods

multiple solutions for elliptic systems with nonlinearities of arbitrary growth abstract we prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of arbitrary growth moreover if the symmetry of the problem is broken by a small enough perturbation term we find at least three solutions the proofs utilise a variational setting given by de figueiredo and ruf in order to prove an existence s result and the algebraic approach based on the pohozaev s fibering method

four step methods for y f x y abstract a systematic investigation is undertaken here on the possible practical consequences of the fact that the linear four step methods for y f x y form a family with a certain structure the mentioned property is found to be surprisingly rich in consequences and three of them are of particular importance i drastic reduction in the number of iterations at each step ii increased flexibility with respect to the start of integration and to the modification of the step size during the integration process iii possibility of direct and simple appraisal of the local truncation error

workforce planning in mixed model assembly systems serial assembly systems are formed by arranging several production cells or stations in series we study a popular class of serial assembly lines where all stations have the same production cycle we address a workforce planning problem for such lines which finds applications in labor intensive operations in automobile fire engine aircraft and pc board assembly the problem presented can be applied to lines that produce several variations of a basic stable design i e mixed model transfer lines given a set of n jobs we want to find a sequence that minimizes the maximum workforce requirements over all production cycles an optimal polynomial algorithm for the two station line is presented and the three station case is proved to be strongly x1d4a9 x1d4ab complete several heuristic algorithms that produce upper and lower bounds are developed for the general problem worst case behavior of the upper bounds as well as average performance of lower and upper bounds are reported computational results show that s

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

a family of trigonometrically fitted partitioned runge kutta symplectic methods abstract we are presenting a family of trigonometrically fitted partitioned runge kutta symplectic methods of fourth order with six stages the solution of the one dimensional time independent schrodinger equation is considered by trigonometrically fitted symplectic integrators the schrodinger equation is first transformed into a hamiltonian canonical equation numerical results are obtained for the one dimensional harmonic oscillator and the exponential potential

a p stable exponentially fitted method for the numerical integration of the schrodinger equation a p stable exponentially fitted method is developed in this paper for the numerical integration of the schrodinger equation an application to the resonance problem of the radial schrodinger equation indicates that the new method is generally more efficient than the previously developed exponentially fitted methods of the same kind

a generator of high order embedded p stable methods for the numerical solution of the schro dinger equation a generator of new embedded p stable methods of order 2n 2 where n is the number of layers used by the embedded methods for the approximate numerical integration of the one dimensional schrodinger equation is developed in this paper these new methods are called embedded methods because of a simple natural error control mechanism numerical results obtained for one dimensional differential equations of the schrodinger type show the validity of the developed theory

explicit exponentially fitted methods for the numerical solution of the schrodinger equation we present here some accurate explicit methods for the numerical integration of the radial schrodinger equation the formulae considered contain free parameters which are defined in order to integrate exponential functions numerical results also indicate that the new methods are much more accurate than other explicit numerov type wellknown methods

a family of four step exponential fitted methods for the numerical integration of the radial schrodinger equation abstract a family of exponential four step methods is developed for the numerical integration of the one dimensional schrodinger equation the formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions the new methods integrate more exponential functions and are very simple compared with the well known sixth algebraic order runge kutta type methods numerical results indicate that the new methods are much more accurate than other exponentially fitted methods

p stable exponentially fitted methods for the numerical integration of the schrodinger equation a p stable exponentially fitted method is developed in this paper for the numerical integration of the schrodinger equation an application to the bound states problem we solve the radial schrodinger equation in order to find eigenvalues for which the wavefunction and its derivative are continuous and the boundary conditions are satisfied and the resonance problem the point of a resonance is that phase changes rapidly through of the radial schrodinger equation indicates that the new method is generally more efficient than the previously developed exponentially fitted methods of the same kind the method can be applied to any problem of physics and chemistry which can be expressed as system of coupled second order differential equations which have oscillatory or periodic solutions this is because it has the property of the p stability i e the interval of periodic stability of the proposed method is equal to 0 which allow is to integrate successful problems with high oscillatory or periodic solution

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 two step explicit p stable method for solving second order initial value problems the conceptions of periodicity interval and p stability were introduced by lambert and watson j inst math appl 18 1976 189 in connection with multistep methods for second order initial value problems this paper presents a new two step explicit p stable method of order two for solving initial value problems of second order ordinary differential equations based on a special vector operation the method can be extended to be vector applicable

ground state solutions for a diffusion system in this paper we study the following diffusion system t u x u v x u g t x v t v x v v x v f t x u where z u v r r n r 2 v x c r n r is a general periodic function under weaker conditions on nonlinearity we establish the existence of ground state solutions via variational methods

a variational approach to subquadratic perturbations of elliptic systems abstract we consider subquadratic perturbations of semilinear elliptic systems which are in variational form a unified approach to both the cooperative and noncooperative problems is presented and a condition of nonquadraticity at infinity is introduced to treat the resonant cases through minimax techniques

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

a finite difference method for the numerical solution of the schro dinger equation a new approach which is based on a new property of phase lag for computing eigenvalues of schrodinger equations with potentials is developed in this paper we investigate two cases i the specific case in which the potential v x is an even function with respect to x it is assumed also that the wave functions tend to zero for x ii the general case of the morse potential and of the woods saxon or optical potential numerical and theoretical results show that this new approach is more efficient compared to previously derived methods

the strong coupling expansion for anharmonic oscillators we accurately calculate the strong coupling expansion for anharmonic oscillators by means of a robust and stable numerical algorithm the method applies to any state and to any anharmonicity degree by means of the perturbation coefficients we estimate the location of the branch points that determine the convergence radius of the strong coupling expansion

minmax earliness tardiness costs with unit processing time jobs the problem addressed in this paper is defined by m parallel identical machines n jobs with identical unit processing time job dependent weights and a common due date for all jobs the objective is of a minmax type i e we are interested in minimizing the cost of the worst scheduled job in the case of a non restrictive i e sufficiently large common due date the problem is shown to have a solution that is polynomial in the number of jobs the solution in the case of a restrictive due date remains polynomial in the number of jobs but is exponential in the number of machines we introduce a lower bound on the optimal cost and an efficient heuristic we show that the worst case relative error of the heuristic is bounded by 2 and that this bound is tight we also prove that the heuristic is asymptotically optimal under very general assumptions finally we provide an extensive numerical study demonstrating that in most cases the heuristic performs extremely well

solutions of a class of hamiltonian elliptic systems in rn we study the existence of ground state solutions for the following elliptic systems in rn u b xu u hv x u v v b xv v hu x u v where b b1 bn is a constant vector and h c1 rn r2 r is nonperiodic in variables x and super quadratic as z by a recent critical point theorem for strongly indefinite problem we obtain the existence of at least one ground state solution

strongly indefinite systems with critical sobolev exponents we consider an elliptic system of hamiltonian type on a bounded domain in the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms our proof is based on an adaptation of the dual variational method as applied before to the scalar case introduction existence and non existence of solutions of semilinear elliptic srstems has been a subject of active research recently see for example ff l3 ps such systems are called variational if solutions can be viewed as critical points of an associated functional defined on a suitable function space restricting our attention to systems with two unknowns we distinguish two classes of variational elliptic systems a potential systems b hamiltonian systems potential systems are of the form a llu u v ztl2v u v where l1 and l2 are second order selfadjoint elliptic operators formally these are the euler lagrange equations of the functional f u v l1u u i l2v v th u v here is the l2 inner product for functions defined on the underlying domain and tt u v s h u x v x dx the functional f is often called the lagrangian its critical points correspond to weak soltbtions of a the appropr ate choice of the function spaces for u and v follows by requiring that the quadratic part of f be well defined this naturally leads to sobolev spaces with square irltegrable first derivatives since also a must be well defined by virtue of the embedding theorems some growth restrictions on this latter function are required an extra difficulty appears if we consider system a with a plus sign in the second equation for then the corresponding functiorl f has a strongly indefinite quadratic part for systems of superlinear type and with sllbcritical growth the mountain pass theorem ar or in the strongly indefinite case the benci rabinowitz theorem received by the editors june 5 1996 1991 mathematics subject classification primary 35j50 35j55 35j65

embedded methods for the numerical solution of the schrodinger equation abstract new methods for the approximate numerical integration of the one dimensional schrodinger equation are developed in this paper complete phase lag analysis of the new methods is included these new methods are called embedded methods because of a simple natural error control mechanism numerical results obtained for a one dimensional schrodinger equation show the validity of the developed theory

critical growth fractional elliptic systems with exponential nonlinearity abstract we study the existence of positive solutions for the system of fractional elliptic equations of the type 1 2 u p p q f x u p 2 u v q h 1 u v e u 2 v 2 in 1 1 1 2 v q p q f x u p v q 2 v h 2 u v e u 2 v 2 in 1 1 u v 0 in 1 1 u v 0 in r 1 1 where 1 p q 2 h 1 u v 2 u 2 u 2 u v h 2 u v 2 v 2 u v 2 v and 2 here 1 2 is the fractional laplacian operator we show the existence of multiple solutions for suitable range of by analyzing the fibering maps and the corresponding nehari manifold we also study the existence of positive solutions for a superlinear system with critical growth exponential nonlinearity

existence and non existence of radial solutions for elliptic equations with critical exponent in ℝ2 where 2 2 n n 2 is the critical sobolev exponent for the embedding h 52 c l2 0 criticality and subcriticality play important rbles concerning the solvability of equation 1 1 using by now classical variational methods one sees that equation 1 1 is solvable i f f has subcritical growth and satisfies some additional hypotheses while for f u iuip u the well known pohoiaev identity shows that the solvability of equation 1 1 is lost if p reaches 2 and r is starshaped in their important paper 6 brezis nirenberg showed that for n e 4 solvability is regained if one adds a lower order linear term to the critical term more precisely they showed that for f r ar lr12 2r one has a denotes the 1st eigenvalue of a on ha r

ground state solutions of hamiltonian elliptic systems in dimension two the aim of this paper is to study hamiltonian elliptic system of the form 0 1 where 2 is a bounded domain in the second place we present existence results for the following stationary schrodinger systems defined in the whole plane 0 2 we assume that the nonlinearities f g have critical growth in the sense of trudinger moser by using a suitable variational framework based on the generalized nehari manifold method we obtain the existence of ground state solutions of both systems 0 1 and 0 2

the existence of solutions for superquadratic hamiltonian elliptic systems on rn abstract this paper is concerned with the following hamiltonian elliptic system u v x u h u x u v in r n v v x v h v x u v in r n u x 0 and v x 0 as x where v x c r n r and h x z is superquadratic in z as z with z u v by applying a critical point theorem for strongly indefinite functionals we obtain infinitely many solutions for the above system

an exponentially fitted eighth order method for the numerical solution of the schrodinger equation an eighth algebraic order exponentially fitted method is developed for the numerical integration of the schrodinger equation the formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions an comparative error analysis is also given numerical and theoretical results indicate that the new method is much more efficient than other classical and exponentially fitted methods

existence of solutions for a class of noncooperative elliptic systems we establish the existence of a nontrivial solution for a class of noncooperative elliptic systems with nonlinearities of superlinear growth moreover if there is resonance we also find at least a solution all results are obtained by the minimax methods in critical point theory

a class of two step explicit methods for periodic ivps in this paper we present a class of non linear explicit second order methods for solving one dimensional periodic initial value problems ivps which are p stable in the sense of lambert and watson and of high order phase lag error for multi dimensional problems we introduce a special vector operation such that our methods can be extended to be vector applicable directly however it is not sufficient to investigate the stability behavior of the vector form of the methods based on the scalar test equation y l 2y after introducing a new test system and extending the definitions of the interval of periodicity and the phase lag order we discuss the stability property and the phase lag of the vector applicable methods the methods are p stable and of high phase lag for one frequency problems for multi frequency problems methods are of only second phase lag order and may have not a primary interval of periodicity some numerical results illustrate the conclusions

multiplicity for strongly indefinite semilinear elliptic system abstract in this paper we study a multiplicity result for a strongly indefinite semilinear elliptic system 2 u u g x v q 1 v in r n 2 v v f x u p 1 u in r n our interest is the relation between the number of solutions and the topology of the global minima set of a suitable ground energy function

existence of solutions for nonperiodic superquadratic hamiltonian elliptic systems abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u r v x u v in r n v v x v r u x u v in r n u x 0 and v x 0 as x where r x z is superquadratic in z as z with z u v by applying a critical point theorem for strongly indefinite functionals we prove the existence of solution for the above system

multiple positive solutions of nonhomogeneous elliptic systems with strongly indefinite structure and critical sobolev exponents abstract in this paper we study the existence of multiple positive solutions to some hamiltonian elliptic systems v u u p ef x u v v q g x in u v 0 in u v 0 on where is a bounded domain in r n n 3 0 f g l 1 p 1 1 q 1 n 2 n p q 1 0 using sub and supersolution method and based on an adaptation of the dual variational approach we prove the existence of at least two nontrivial positive solutions for all 0 1 and e 0 0 where 1 is the first eigenvalue of the laplace operator with zero dirichlet boundary conditions and 0 is a positive number

on strongly indefinite systems involving the fractional laplacian abstract this paper is devoted to study strongly indefinite systems involving the fractional laplacian on bounded domains explicitly we obtain existence and non existence results a p r i o r i estimates of gidas spruck type and a symmetry result in addition we give a different proof for the a p r i o r i estimate for nonlinear elliptic problems with the fractional laplacian obtained in cabre and tan 2010 and tan 2013

existence and multiplicity of semiclassical solutions for asymptotically hamiltonian elliptic systems abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system e 2 u v x u h u x u v in r n e 2 v v x v h v x u v in r n u x 0 and v x 0 as x where e 0 is a small parameter and the potential v is bounded below and h is asymptotically linear in z as z with z u v by applying a generalized linking theorem of strongly indefinite functionals we obtain the existence of multiple semiclassical solutions for the above system

a four step method for the numerical solution of the schro dinger equation abstract a new four step exponentially fitted method is developed in this paper the expressions for the coefficients of the method are found such as to ensure the optimal approximation to the eigenvalue schrodinger equation i e equivalent to positive energy

on a new class of elliptic systems with nonlinearities of arbitrary growth abstract we guarantee the existence of infinitely many different pairs of solutions to the system u v p in v f u in u v 0 on where 0 p 2 n 2 is a bounded domain in r n and the continuous nonlinear term f has an unusual oscillatory behavior the sequence of solutions tends to zero resp infinity with respect to certain norms and the nonlinear term f may enjoy an arbitrary growth at infinity resp at zero whenever f oscillates near zero resp at infinity our results provide the first applications of ricceri s variational principle in the theory of coupled elliptic systems

a family of four step exponentially fitted predictor corrector methods for the numerical integration of the schro dinger equation a family of predictor corrector exponential four step methods is developed for the numerical integration of the one dimensional schrodinger equation the formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions the new methods integrate more exponential functions and are very simple compared with the well known sixth algebraic order runge kutta type methods numerical results indicate that the new method is much more accurate than other exponentially fitted methods

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates

multiple solutions of an even order nonlinear problem with convex concave nonlinearity abstract we study multiple solutions of an even order nonlinear partial differential equation with a dirichlet boundary condition a related class of nonlinear systems is investigated

asymptotically linear elliptic systems in rn abstract in this paper we show that semilinear elliptic systems of the form u u v v g v v v u u f u x r n possess at least one nontrivial solution pair u v h 1 r n h 1 r n where and are positive numbers f t and g t are continuous functions on r and asymptotically linear as t