periodic impact behavior of a class of hamiltonian oscillators with obstacles abstract in this paper we study the existence of harmonic and subharmonic solutions of a class of non smooth hamiltonian systems then apply its results to the vibration problems x q x x 2 g t x f t x t 0 x t 0 x t 0 if x t 0 0 infinitely many harmonic and subharmonic bouncing solutions are always obtained if q x satisfies some coercive conditions

periodic solutions of the lienard equation with one sided growth restrictions in this article we are concerned with the problem of the existence of periodic solutions to the periodically forced scalar lienard equation x f x x g x e t d dt 1 where f g e r r are continuous functions and e is periodic we are looking for solutions of 1 having the same period of the forcing term e throughout the paper we assume without loss of generality see e g 22 36 p 693 that

variationally consistent modeling of finite strain plasticity theory with non linear kinematic hardening abstract variational constitutive updates provide a physically and mathematically sound framework for the numerical implementation of material models in contrast to conventional schemes such as the return mapping algorithm they are directly and naturally based on the underlying variational principle hence the resulting numerical scheme inherits all properties of that principle in the present paper focus is on a certain class of those variational methods which relies on energy minimization consequently the algorithmic formulation is governed by energy minimization as well accordingly standard optimization algorithms can be applied to solve the numerical problem a further advantage compared to conventional approaches is the existence of a natural distance semi metric induced by the minimization principle such a distance is the foundation for error estimation and as a result for adaptive finite elements methods though variational constitutive updates are relatively well developed for so called standard dissipative solids i e solids characterized by the normality rule the more general case i e generalized standard materials is far from being understood more precisely int j sol struct 2009 46 1676 1684 represents the first step towards this goal in the present paper a variational constitutive update suitable for a class of nonlinear kinematic hardening models at finite strains is presented two different prototypes of armstrong frederick type are re formulated into the aforementioned variationally consistent framework numerical tests demonstrate the consistency of the resulting implementation

deterministic near optimal controls part ii dynamic programming and viscosity solution approach near optimization is as sensible and important as optimization for both theory and applications this paper concerns dynamic near optimization or near optimal controls for systems governed by deterministic ordinary differential equations and uses dynamic programming to study the near optimality since nonsmoothness is inherent in this subject the viscosity solution approach is employed to investigate the problem the dynamic programming equation is derived in terms of e superdifferential subdifferential the relationships among the adjoint functions the value functions and the hamiltonian along near optimal trajectories are revealed verification theorems with which near optimal feedback controls can be constructed are obtained

periodic solutions of a second order ordinary differential equation a necessary and sufficient condition for nonresonance the nonlinearity g in 1 1 is a continuous function from r to r and the forcing term h is taken in l o 27r nonresonance means that 1 1 admits at least one solution x for any given h integrating eq 1 1 over a period one immediately sees that a necessary condition for nonresonance is that the function g be unbounded from above and from below on r it will appear later cf 1 6 that this unboundedness can be looked at as a condition relating the behaviour at infinity of the nonlinearity g with respect to the first eigenvalue 1 0 of the associated linear problem xf ax in 0 27r x 0 x 27r x 0 x1 271 1 2

nonresonance conditions for asymptotically positively homogeneous differential systems the fucik spectrum and its generalization in this article we propose how to define the fucik spectra for differential systems in rnwith jumping nonlinearities the propertyp a generalization of the non fucik spectra to positively homogeneous nonautonomous differential systems is also defined in the most general setting a quantitative estimate result concerning the parameterized completely continuous positively homogeneous perturbations of the identity in banach spaces is given in this article such a result is a generalization of one property in the spectrum theory for completely continuous linear operators using this estimate result we will give some significantly improved nonresonance results from the fucik spectra and propertypfor asymptotically positively homogeneous differential systems

linear quadratic control of backward stochastic differential equations this paper is concerned with optimal control of linear backward stochastic differential equations bsdes with a quadratic cost criteria or backward linear quadratic blq control the solution of this problem is obtained completely and explicitly by using an approach which is based primarily on the completion of squares technique two alternative though equivalent expressions for the optimal control are obtained the first of these involves a pair of riccati type equations an uncontrolled bsde and an uncontrolled forward stochastic differential equation sde while the second is in terms of a hamiltonian system contrary to the deterministic or stochastic forward case the optimal control is no longer a feedback of the current state rather it is a feedback of the entire history of the state a key step in our derivation is a proof of global solvability of the aforementioned riccati equations although of independent interest this issue has particular relevance to the blq problem since these riccati equations play a central role in our solution last but not least it is demonstrated that the optimal control obtained coincides with the solution of a certain forward linear quadratic lq problem this in turn reveals the origin of the riccati equations introduced

near optimal control for stochastic recursive problems it is well documented e g zhou 1998 8 that the near optimal controls as the alternative to the exact optimal controls are of great importance for both the theoretical analysis and practical application purposes due to its nice structure and broad range availability feasibility as well as flexibility however the study of near optimality on the stochastic recursive problems to the best of our knowledge is a totally unexplored area thus we aim to fill this gap in this paper as the theoretical result a necessary condition as well as a sufficient condition of near optimality for stochastic recursive problems is derived by using ekeland s principle moreover we work out an e optimal control example to shed light on the application of the theoretical result our work develops that of 8 but in a rather different backward stochastic differential equation bsde context

finite strain viscoplasticity with nonlinear kinematic hardening phenomenological modeling and time integration abstract this article deals with a viscoplastic material model of overstress type the model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part an additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of armstrong frederick type two implicit time stepping methods are adopted for numerical integration of evolution equations such that the plastic incompressibility constraint is exactly satisfied the first method is based on the tensor exponential the second method is a modified euler backward method special numerical tests show that both approaches yield similar results even for finite inelastic increments the basic features of the material response predicted by the material model are illustrated with a series of numerical simulations

efficient iteration schemes for anisotropic hyperelasto plasticity numerical issues arising when integrating hyperelasto plastic constitutive equations with elastic anisotropy stemming from anisotropic damage and plastic anisotropy as represented by kinematic hardening are discussed in particular solution algorithms for the corresponding non linear system of equations due to implicit integration algorithms are addressed it is shown that algorithms like staggered iteration and quasi newton techniques are superior to a pure newton technique when the cpu time is compared however the drawback of the staggered and the quasi newton technique is that rather small time steps must be taken to ensure convergence which can be of importance when applying complex constitutive models in a finite element programme copyright 2005 john wiley sons ltd

exact expansions of arbitrary tensor functions f a and their derivatives a general method is presented for determining the exact expansions of a tensor function f a where a is a second order tensor in n dimensional euclidean space and f a is defined by the power series it is shown that f a can be obtained by differentiating a scalar function of the eigenvalues of a using this method closed form singularity free expressions of arbitrary tensor functions and their first derivatives are deduced in two and three dimensional cases

semilinear duffing equations crossing resonance points abstract in this paper using a generalized form of the poincare birkhoff theorem and a fixed point theorem we prove under weaker conditions two theorems for the equation x g x p t p t p t 2 of which one shows the existence of a harmonic solution the other that the equation may have an infinite number of harmonic solutions in the resonance case this is an enhancement of the results already obtained

dynamic programming principle for one kind of stochastic recursive optimal control problem and hamilton jacobi bellman equation in this paper we study one kind of stochastic recursive optimal control problem with the obstacle constraint for the cost functional described by the solution of a reflected backward stochastic differential equation we give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding hamilton jacobi bellman equation

nonresonance to the right of the first eigenvalue for the one dimensional p laplacian a quasilinear two point boundary value problem was considered this problem is given by the equation

periodic solutions of rayleigh equations via time maps abstract in this paper we study the existence of periodic solutions of rayleigh equations x f t x g x e t where f r 2 r is continuous and t periodic with respect to the first variable g e r r are continuous and e is t periodic we prove that the given equation possesses at least one t periodic solution provided that either lim sup c c lim inf c c t or lim inf c c lim sup c c t is satisfied where is the time map defined in section 1

multiplicity of periodic solutions of semilinear duffing s equation at resonance in this paper we prove an infinity of periodic solutions to the periodically forced nonlinear duffing equation under new conditions

application of the dunford taylor integral to isotropic tensor functions and their derivatives in this paper we obtain closedform representations for isotropic tensor functions and their derivative using the dunfordtaylor integral these representations are given in terms of eigenvalues of t

a continuation lemma and its applications to periodic solutions of rayleigh differential equations with subquadratic potential conditions in this paper we study the existence of periodic solutions of rayleigh equations x f t x g x e t where f g e are continuous functions and f is t periodic with the first variable e is t periodic by developing a continuation lemma for rayleigh equations we prove that the given equation has at least one t periodic solution provided that f t y is sublinear with respect to the variable y and g x 0xg u du satisfies some subquadratic conditions

necessary and sufficient conditions for near optimality in stochastic control of fbsdes abstract we consider control problems for systems governed by a nonlinear forward backward stochastic differential equation fbsde we establish necessary as well as sufficient conditions for near optimality satisfied by all near optimal controls these conditions are described by two adjoint processes corresponding to the forward and backward components and a nearly maximum condition on the hamiltonian the proof of the main result is based on ekeland s variational principle and some estimates on the state and the adjoint processes with respect to the control variable as is well known optimal controls may fail to exist even in simple cases this justifies the use of near optimal controls which exist under minimal assumptions and are sufficient in most practical cases moreover since there are many nearly optimal controls it is possible to choose suitable ones that are convenient for implementation

towards variational constitutive updates for non associative plasticity models at finite strain models based on a volumetric deviatoric split in this paper an enhanced variational constitutive update suitable for a class of non associative plasticity theories at finite strain is proposed in line with classical numerical formulations for plasticity models such as the by now established return mapping algorithm variational constitutive updates represent a numerical method for computing the unknown state variables however in contrast to conventional algorithms variational constitutive updates are fully variational i e all unknown variables follow jointly from minimizing a certain potential in addition to the physical and mathematical elegance of these variational schemes they show several practical advantages as well for instance numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem since mathematically plasticity is a non smooth problem and often it leads to highly singular systems of equations as known from single crystal plasticity a robust implementation is of utmost importance so far variational constitutive updates have been developed for different classes of standard dissipative solids i e solids characterized by associative evolution equations and flow rules in the present paper this framework is extended to a certain class of non associative plasticity models at finite strain all models falling into this class show a volumetric deviatoric split of the helmholtz energy and the yield function typical prototypes are drucker prager or mohr coulomb models playing an important role in soil mechanics the efficiency and robustness of the resulting algorithmic formulation is demonstrated by means of selected numerical examples

periodic solutions for p laplacian neutral functional differential equation with deviating arguments by using the theory of coincidence degree we study a kind of periodic solutions to p laplacian neutral functional differential equation with multiple deviating arguments a new result on the existence of periodic solutions is obtained

brief paper near optimal control problems for linear forward backward stochastic systems herein we study the near optimality of linear forward backward stochastic control systems as the theoretical results some sufficient and necessary conditions of the near optimality are established in the form of pontryagin stochastic maximum principle as an illustration and practical application one e optimal control example is figured out and solved using our theoretical results

the computation of the exponential and logarithmic mappings and their first and second linearizations we describe two simple methods for the evaluation of the exponential and logarithmic mappings and their first and second linearizations based on the taylor expansion and the spectral representation we also provide guidelines for switching between those representations on the basis of the size of the argument the first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of systems of linear ordinary differential equations this representation does not require the use of perturbation formulae for eigenvalues and eigenvectors our approach leads to workable and straightforward expressions for the first and second linearizations of the exponential and logarithmic mappings regardless of degeneracies in the spectral decomposition of the argument

closed form matrix exponential and its application in finite strain plasticity summary a new method to compute numerically efficient closed form representation of matrix exponential and its derivative is developed for 3 3 matrices with real eigenvalues the matrix exponential is obtained by automatic differentiation of an appropriate scalar generating function in a general case and highly accurate asymptotic expansions are derived for special cases in which the general formulation exhibits ill conditioning for instance for almost equal eigenvalues accuracy and numerical efficiency of the closed form matrix exponential as compared with the truncated series approximation are studied the application of the closed form matrix exponential in the finite strain elastoplasticity is also presented to this end several time discrete evolution laws employing the exponential map are discussed for j2 plasticity with isotropic hardening and nonlinear kinematic hardening of armstrong frederick type the discussion is restricted to the case of elastic isotropy and implicit time integration schemes in this part the focus is on a general automatic differentiation based formulation of finite strain plasticity models numerical efficiency of the corresponding incremental schemes is studied in the context of the fem copyright 2014 john wiley sons ltd

stochastic differential games and viscosity solutions of hamilton jacobi bellman isaacs equations in this paper we study zero sum two player stochastic differential games with the help of the theory of backward stochastic differential equations bsdes more precisely we generalize the results of the pioneering work of fleming and souganidis indiana univ math j 38 1989 pp 293 314 by considering cost functionals defined by controlled bsdes and by allowing the admissible control processes to depend on events occurring before the beginning of the game this extension of the class of admissible control processes has the consequence that the cost functionals become random variables however by making use of a girsanov transformation argument which is new in this context we prove that the upper and the lower value functions of the game remain deterministic apart from the fact that this extension of the class of admissible control processes is quite natural and reflects the behavior of the players who always use the maximum of available information its combination with bsde methods in particular that of the notion of stochastic backward semigroups introduced by peng bsde and stochastic optimizations in topics in stochastic analysis science press beijing 1997 allows us then to prove a dynamic programming principle for both the upper and the lower value functions of the game in a straightforward way the upper and the lower value functions are then shown to be the unique viscosity solutions of the upper and the lower hamilton jacobi bellman isaacs equations respectively for this peng s bsde method is extended from the framework of stochastic control theory into that of stochastic differential games

on the implementation of rate independent standard dissipative solids at finite strain variational constitutive updates this paper is concerned with an efficient variationally consistent implementation for rate independent dissipative solids at finite strain more precisely focus is on finite strain plasticity theory based on a multiplicative decomposition of the deformation gradient adopting the formalism of standard dissipative solids which allows to describe constitutive models by means of only two potentials being the helmholtz energy and the yield function or equivalently a dissipation functional finite strain plasticity is recast into an equivalent minimization problem in contrast to previous models the presented framework covers isotropic and kinematic hardening as well as isotropic and anisotropic elasticity and yield functions based on this approach a novel numerical implementation representing the main contribution of the paper is given in sharp contrast to by now classical approaches such as the return mapping algorithm and analogously to the theoretical part the numerical formulation is variationally consistent i e all unknown variables follow naturally from minimizing the energy of the considered system consequently several different numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem extending previously published works on variational constitutive updates the advocated model does not rely on any material symmetry and therefore it can be applied to a broad range of different plasticity theories as two examples an anisotropic hill type and a barlat type model are implemented numerical examples demonstrate the applicability and the performance of the proposed implementation

on the theoretical and numerical modelling of armstrong frederick kinematic hardening in the finite strain regime abstract on the theoretical level the present paper presents a detailed comparison of recent finite strain models for armstrong frederick kinematic hardening thereby two strategies are discussed 1 chaboche type concepts considering the back stress as internal variable 2 continuum mechanical extensions of the classical rheological model using only strain like internal variables it is shown in the paper that models of the second kind can be recast in the format of anisotropic inelasticity with structure tensors second the work focuses on the algorithmic treatment of the kinematic hardening concepts presented before this problem has been tackled up to now only in the context of linearized models in contrast to isotropic finite elastoplasticity the integration cannot be carried out with respect to principal axes therefore a new integration algorithm is developed which is suitable for the anisotropic case but still retains plastic incompressibility in the case of small elastic deformation the algorithm reduces to a system of only one non linear equation and twelve linear equations in general the computational effort of the new scheme does not exceed the one of the backward euler scheme which has the disadvantage that plastic incompressibility is not fulfilled automatically several numerical examples show that the representatives of both approaches 1 and 2 yield similar results if physically reasonable material parameters are chosen

periodic solutions of duffing s equations with superquadratic potential abstract this paper is devoted to the study of harmonic and subharmonic solutions for the second order scalar nonlinear duffing s equation x g x p t x x where g and p are continuous functions with p bounded and periodic in the first variable and g satisfying the assumption g x sign x as x among other results we prove the existence of infinitely many harmonic and subharmonic solutions of any order p p t and if the potential g x of g x satisfies certain conditions of superquadratic growth at the new existence results can be applied to situations in which the more classical superlinear growth condition g x x as x is not satisfied in this manner various preceding theorems are improved and sharpened see the introduction for more details proofs are based on a generalized version of the poincare birkhoff twist theorem due to w ding

periodic solutions for systems of second order differential equations abstract we consider vector differential equtions x g t x x f t x r n and show the existence of periodic solutions under conditions which show that growth conditions on g required in earlier results are not needed

on the numerical treatment and analysis of finite deformation ductile single crystal plasticity abstract this contribution is concerned with the numerical analysis and simulation of instability phenomena such as shearband localization in plastic flow processes within the framework of ductile single fcc crystal viscoplasticity to this end a family of implicit constitutive algorithms and their implementation are considered in detail issues of accuracy and conservation of plastic incompressibility are examined moreover the implementation within an overall newton raphson finite element solution strategy relies on the correct evaluation of the algorithmic tangent moduli which result from linearizing the stress update integrator likewise these algorithmic tangent moduli are employed within the numerical analysis of the spatial localization tensor examples demonstrating the performance of the proposed strategy at the local constitutive level as well as at the global structural level are given

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

periodic solutions for a kind of lienard equation with a deviating argument abstract by means of continuation theorem of coincidence degree theory we study a kind of lienard equation with a deviating argument as follows x t f x t x t g x t t x t e t some new results on the existence of periodic solutions are obtained

computation of the exponential and other isotropic tensor functions and their derivatives abstract in the present paper we focus on numerical aspects of the computation of isotropic tensor functions and their derivative in the general case of non symmetric tensor arguments only two numerical algorithms appear to be appropriate the first one represents a recurrent procedure resulting from the taylor power series expansion of an isotropic tensor function the second algorithm is based on a recently proposed closed form representation which can be obtained from the definition of an isotropic tensor function either by the tensor power series or by the dunford taylor integral to improve the accuracy in the case of nearly equal eigenvalues a series expansion of this closed formula is proposed both algorithms are finally illustrated by an example of the exponential tensor function where emphasis is placed on the precision issue

exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals this paper presents a new stress update algorithm for large strain rate independent single crystal plasticity the theoretical frame is the well established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts a distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts resulting in a very convenient representation of the schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of eulerian vectors the key contribution of this paper is an algorithmic formulation of the exponential map exp sl 3 sl 3 for updating the special linear group sl 3 of unimodular plastic deformation maps this update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration the resulting fully implicit stress update algorithm treats the possibly redundant constraints of single crystal plasticity by means of an active set search it exploits intrinsically the simple representation of the schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of eulerian vectors updates the performance of the proposed algorithm is demonstrated by means of a representative numerical example

a new fixed point theorem and periodic solutions of nonconservative weakly coupled systems abstract in this paper we prove a new fixed point theorem for the coupling of twist conditions and poincare bohl type conditions as its applications we prove the existence of periodic solutions for various nonconservative mixed type weakly coupled systems

near optimal controls of random switching lq problems with indefinite control weight costs in this paper we consider hybrid controls for a class of linear quadratic problems with white noise perturbation and markov regime switching where the regime switching is modeled by a continuous time markov chain with a large state space and the control weights are indefinite the use of large state space enables us to take various factors of uncertain environment into consideration yet it creates computational overhead and adds difficulties aiming at reduction of complexity we demonstrate how to construct near optimal controls first in the model we introduce a small parameter to highlight the contrast of the weak and strong interactions and fast and slow motions this results in a two time scale formulation in view of the recent developments on lq problems with indefinite control weights and two time scale markov chains we then establish the convergence of the system of riccati equations associated with the hybrid lq problem based on the optimal feedback control of the limit system obtained using the system of riccati equations we construct controls for the original problem and show that such controls are near optimal a numerical demonstration of a simple system is presented here

periodic solutions for a kind of second order differential equation with multiple deviating arguments by means of continuation theorem of coincidence degree theory some new results on the existence and nonexistence of periodic solutions for a kind of second order functional differential equation with multiple deviating arguments are obtained

a general framework for the numerical solution of problems in finite elasto plasticity this article discusses a general framework for the analysis of initial boundary value problems of rate independent finite elasto plasticity based on the theory of green and naghdi a constitutive model is developed within the context of the above theory employing generalized measures of lagrangian strain and work conjugate measures of stress computational implications of the proposed formulation are discussed in conjunction with an implicit time integrator for the differential algebraic equations of plastic flow representative numerical simulations demonstrate the applicability and predictive capacity of the model in the presence of large plastic deformations

maximum principles for a class of partial information risk sensitive optimal controls in this technical note we study a class of partial information risk sensitive optimal controls the main results are some necessary and sufficient conditions for these partial information control problems for illustration one example is proposed and then solved using our results

stochastic near optimal controls necessary and sufficient conditions for near optimality near optimization is as sensible and important as optimization for both theory and applications this paper concerns dynamic near optimization or near optimal controls for systems governed by the ito stochastic differential equations sdes where both the drift and diffusion terms are allowed to depend on controls and the systems are allowed to be degenerate necessary and sufficient conditions for a control to be near optimal are studied it is shown that any near optimal control nearly maximizes the hh function which is a generalization of the usual hamiltonian and is quadratic with respect to the diffusion coefficients in some integral sense and vice versa if certain additional concavity conditions are imposed error estimates for both the near optimality of the controls and the near maximum of the hh function are obtained based on some delicate estimates of the adjoint processes examples are presented to demonstrate the results

existence of periodic solutions for second order duffing equations with p laplacian like operators the existence of periodic solutions for second order duffing equations with p laplacian like operator is studied by applying a new generalization of polar coordinates

unified explicit basis free expressions for time rate and conjugate stress of an arbitrary hill s strain abstract this paper provides simple and unified explicit basis free expressions for time rate and conjugate stress of an arbitrary hill s strain for the first time which are valid for all cases of the eigenvalues of the right stretch tensors

near optimality conditions in stochastic control of jump diffusion processes abstract this paper is concerned with necessary as well as sufficient conditions for near optimality of controlled jump diffusion processes necessary conditions for a control to be near optimal are derived using ekeland s variational principle and some stability results on the state and adjoint processes with respect to the control variable in a second step we show that the necessary conditions for near optimality are in fact sufficient for near optimality provided some concavity conditions are fulfilled finally as an illustration some examples are solved explicitly

a closed form representation for the derivative of non symmetric tensor power series in the present paper a closed form representation for the derivative of non symmetric tensor power series is proposed particular attention is focused on the special case of repeated eigenvalues in this case a non symmetric tensor can possess no spectral decomposition in diagonal form such that the well known solutions in terms of eigenprojections as well as basis free representations for isotropic functions of symmetric tensor arguments cannot be used thus our representation seems to be the only possibility to calculate the derivative of non symmetric tensor power series in a closed form finally this closed formula is illustrated by an example being of special importance in large strain anisotropic elasto plasticity as such we consider the exponential function of the velocity gradient under simple shear right in this loading case the velocity gradient has a triple defective eigenvalue excluding the application of any other solutions based on the spectral decomposition

periodic solutions of lienard differential equations with subquadratic potential conditions abstract in this paper we study the second order forced lienard equation x f x x g x e t we obtain the existence of periodic solutions under some subquadratic conditions

near maximum principle for general recursive utility optimal control problem in this study we introduce a general recursive utility optimal control problem driven by a fully nonlinear stochastic differential system in order to investigate pontryagin s stochastic maximum p

existence and multiplicity results for periodic solutions of semilinear duffing equations we obtain existence an multiplicity of harmonic and subharmonic solutions to the periodically forced nonlinear duffing s equation x g x p t in the semi linear case 0 a g x x b for x large we introduce new conditions of nonresonance with respect to the spectrum of the associated linear differential operator x x and show by some nonlinear counterexamples that the results are sharp

on the derivatives of a subclass of isotropic tensor functions of a nonsymmetric tensor this paper studies a subclass of isotropic tensor valued functions of a nonsymmetric tensor which satisfy the commutative condition and their derivatives this subclass of tensor functions includes tensor power series exponential tensor function etc and is more general than those investigated before in the case of three distinct eigenvalues the derivatives of these tensor functions are constructed by solving a tensor equation which is acquired by differentiating the commutative condition by taking limits the results are extended to the cases of repeated eigenvalues