a semi linear elliptic equation in a strip arising in a two dimensional flame propagation model on montre l existence d une solution stationnaire pour un probleme a 2 dimensions pour l equation elliptique semilineaire de la forme u v y u x g u dans la bande s x y r 2 x r 0 0

some theorems on reverse inequalities application de la theorie de la programmation dynamique pour formuler des theoremes sur les inegalites inverses

model flames in the boussinesq limit the effects of feedback we have studied the fully nonlinear behavior of premixed flames in a gravitationally stratified medium subject to the boussinesq approximation the key results include the establishment of criteria for when such flames propagate as simple planar flames elucidation of scaling laws for the effective flame speed and a study of the stability properties of these flames the simplicity of some of our scaling results suggests that analytical work may further advance our understandings of buoyant flames

propagation in a fisher kpp equation with non local advection abstract we investigate the influence of a general non local advection term of the form k u to propagation in the one dimensional fisher kpp equation this model is a generalization of the keller segel fisher system when k l 1 r we obtain explicit upper and lower bounds on the propagation speed which are asymptotically sharp and more precise than previous works when k l p r with p 1 and is non increasing in 0 and in 0 we show that the position of the front is of order o t p if p and o e t for some 0 if p and k 0 we use a wide range of techniques in our proofs

existence of traveling waves in the stokes boussinesq system for reactive flows abstract we consider the stokes boussinesq equations in a slanted that is not aligned with gravity s direction cylinder of any dimension and with an arbitrary rayleigh number we prove the existence of a non planar traveling wave solution propagating at a constant speed and satisfying the dirichlet boundary condition in the velocity and the neumann condition in the temperature

oscillation for nonlinear second order dynamic equations on a time scale abstract we obtain some oscillation criteria for solutions to the nonlinear dynamic equation x q t x p t f x 0 on time scales in particular no explicit sign assumptions are made with respect to the coefficients p t q t we illustrate the results by several examples including a superlinear emden fowler dynamic equation

dynamic programming and inequalities one applies the theory of inequalities to solve mathematical programming problems in association with the method of lagrange parameters and the dynamic programming approach one calls it an integrated method in contrast to the traditional calculus method this is the motivation of this paper

oscillation of certain second order nonlinear difference equations abstract in this paper we consider the second order nonlinear difference equation formula where y n y n 1 y n is the forward difference operator f c r r f is nondecreasing and uf u 0 as u 0 q n is a real sequence some new sufficient conditions for the oscillation of all solutions of 1 are obtained

coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming abstract in this paper the existence and iterative approximation of coupled fixed points for mixed monotone condensing set valued operators are discussed the results presented here extend and improve the corresponding results of d guo and v lakshmikantham coupled fixed points of nonlinear operators 1 2 as an application we utilize the results obtained in section 2 to study the existence problem of solutions for a class of functional equations arising in dynamic programming

oscillation of second order damped dynamic equations on time scales abstract the study of dynamic equations on time scales has been created in order to unify the study of differential and difference equations the general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so called time scale which may be an arbitrary closed subset of the reals this way results not only related to the set of real numbers or set of integers but those pertaining to more general time scales are obtained in this paper by employing the riccati transformation technique we will establish some oscillation criteria for second order linear and nonlinear dynamic equations with damping terms on a time scale t our results in the special case when t r and t n extend and improve some well known oscillation results for second order linear and nonlinear differential and difference equations and are essentially new on the time scales t h n h 0 t q n for q 1 t n 2 etc some examples are considered to illustrate our main results

oscillation criteria for second order nonlinear neutral delay dynamic equations in this paper we will establish some oscillation criteria for the second order nonlinear neutral delay dynamic equation r t y t p t y t f t y t 0 on a time scale t here 0 is a quotient of odd positive integers with r t and p t real valued positive functions defined on t to the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales so this paper initiates the study

the principle and models of dynamic programming v in this article we introduce two new concepts namely dynamic geometry and dynamic pattern the former can be further developed in conjunction with computer graphics while the latter can be further developed in conjunction with the concept of dp in the sense of zelkowitz et al

asymptotic behavior of solutions of a third order nonlinear dynamic equation on time scales in this paper we will establish some sufficient conditions which guarantee that every solution of the third order nonlinear dynamic equation c t a t x t q t f x t 0 t t0 oscillates or converges to zero

oscillation criteria for second order matrix dynamic equations on a time scale we obtain oscillation criteria for a second order self adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function we illustrate our results with some nontrivial examples

continuous dynamic programming approach to inequalities ii where p and q represent the state and decision vectors respectively t represents the transformation of the process and f p represents the optimal return function with initial state p here opt denotes max or min basically using suitable functional equations of the form l lwamoto 9 io established a class of classical discrete inequalities by he dp approach while wang 16 181 established them by the functional equation approach e g see related references in 133 for a more detailed account very recently lwamoto and wang 133 established the holder

oscillatory behavior of second order half linear damped dynamic equations by refining the generalized riccati transformation technique we obtain new oscillation criteria for a class of second order half linear delay dynamic equations with damping on a time scale assumptions in our theorems are less restrictive these results complement and improve related contributions to the subject in particular the results obtained amend related results reported in the literature

oscillation theorems for general quasilinear second order difference equations the authors consider difference equations of the form where an 0 qn 0 f and are continuous real valued functions and uf u 0 for u 0 they give oscillation results for equation e examples are included to illustrate the results

oscillation criteria of second order half linear dynamic equations on time scales in this paper by using the riccati transformation technique chain rule and inequalitya l lab l 1 l 1 b l 0 l 1 where a and b are positive constants we will establish some oscillation criteria for the second order half linear dynamic equation p t x d t c d q t x c t 0 t a b on time scales where c 1 is an odd positive integer our results not only unify the oscillation of half linear differential and half linear difference equations but can be applied on different types of time scales and improve some well known results in the difference equation case some examples are considered here to illustrate our main results

oscillatory and nonoscillatory behavior of second order functional difference equations abstract the asymptotic and oscillatory behavior of solutions of second order difference equations with deviating argument of the form a n y n p n y n q n f y n 1 0 n 0 1 is studied examples are inserted to illustrate the results

beckenbach inequality and its variants on montre que deux theoremes sur l inegalite de beckenbach peuvent s obtenir de facon unifiee par une utilisation directe de l inegalite de holder usuelle

oscillation of nonlinear dynamic equations on time scales by means of riccati transformation techniques we establish some new oscillation criteria for the second order nonlinear dynamic equation p t x d t d q t f x s t 0 email protected a b on time scales in terms of the coefficients and the graininess function we illustrate our results with a nontrivial example

on the existence of traveling waves in the 3d boussinesq system we extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium subject to the boussinesq approximation for three dimensional channels not aligned with the gravity direction and under the dirichlet boundary conditions in the fluid velocity it is shown that a non planar traveling wave corresponding to a non zero reaction exists under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the prandtl and rayleigh numbers or when the advection term in the flow equations is neglected

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

a necessary and sufficient condition for oscillation of the sturm liouville dynamic equation on time scales in this paper we investigate oscillatory properties of the second order sturm liouville dynamic equation on a time scale r t x c t x 0 using the so called trigonometric transformation we establish a necessary and sufficient condition for oscillation of this condition is then used to derive an explicit oscillation criterion for this equation

on a disconjugacy criterion for second order dynamic equations on time scales in this paper a sufficient condition for disconjugacy of second order differential equations on time scales is given for this purpose a mean value result on time scales is employed

characteristics of nonlinear positive functionals and their applications in 1966 1967 beckenbach 3 4 extended among other things the holder and minkowski inequalities by a method of the differentiability of multivariable real functions in 1979 wang 21 established the a g arithmetic geometric holder minkowski and beckenbach inequalities by means of the convexity of multivariable real functions however their results dealt with only the discrete case of the inequalities in the development of the theory of inequalities the discrete and continuous cases of the inequalities have always been examined hand in hand see beckenbach and bellman s hardy littlewood and polya 111 iwamoto and wang 131 and mitrinovic 16 this examination has concerned not only the forms of the inequalities but also the methods used to establish them e g see iwamoto and wang 131 for this reason we investigate here the continuous counterparts of the works of beckenbach and wang mentioned above indeed the set of classical inequalities for integrals has been established by various other methods e g see s 11 13 161 as well it is evident that the forms of inequalities for integrals can be regarded as nonlinear functionals see 7 14 191 on the other hand in the study of nonlinear operators and or functionals the differentiability of operators has been intensively and successfuly used to provide approximate solutions for nonlinear functional equations e g see 7 14 19 while their convexity has been used in a somewhat restricted manner see collatz 7 334 341 i although the differentiability and convexity of nonlinear functionals have attracted considerable attention of many investigators see 7 9 14 15 17 19 it seems to have escaped notice that they can be employed to establish the

an application of discrete inequality to second order nonlinear oscillation abstract by using some simple discrete inequalities oscillation criteria are provided for the second order difference equations 2 y n a n 1 y n 1 0 n n where the operator is defined by yn yn 1 yn an is a real sequence the function is such that u u 0 for u 0 and u v g u v u v for u v 0 for some nonnegative function g

lo keng hua inequality and dynamic programming 2 where k cx n lx h n a 3 inequality 1 is a very interesting and useful as indicated in hua s inequality it appears that this inequality has not been cited as a problem or example elsewhere in an english text however ozeki and aoyagi cited it as an example on page 157 of their inequalities 9 in japanese with a proof indeed there are at least four proofs availabe for inequality 1 moreover inequality 1 can be naturally generalized and its continuous counterpart can also be given this is a major purpose of this paper we now summarize our findings in two theorems as follows

oscillation criteria for second order nonlinear delay dynamic equations abstract in this paper we consider the second order nonlinear delay dynamic equation r t x t p t f x t 0 on a time scale t by employing the generalized riccati technique we will establish some new sufficient conditions which ensure that every solution oscillates or converges to zero the obtained results improve the well known oscillation results for dynamic equations and include as special cases the oscillation results for differential equations some applications and examples are considered to illustrate the main results

a generalization of the holder inequality through dynamic programming approach on etablit une generalisation de l inegalite de holder basee sur la programmation dynamique on etablit les equations de recurrence associees

fronts in reactive convection bounds stability and instability this paper examines a simplified active combustion model in which the reaction influences the flow we consider front propagation in a reactive boussinesq system in an infinite vertical strip nonlinear stability of planar fronts is established for narrow domains when the rayleigh number is not too large planar fronts are shown to be linearly unstable with respect to long wavelength perturbations if the rayleigh number is sufficiently large we also prove uniform bounds on the bulk burning rate and the nusselt number in the kpp reaction case 2003 wiley periodicals inc