a monotone iterative technique for solving the bending elastic beam equations abstract this paper discusses the solvability of the fourth order boundary value problem u 4 f t u u 0 t 1 u 0 u 1 u 0 u 1 0 which models a statically bending elastic beam whose two ends are simply supported where f 0 1 r 2 r is continuous we build a maximum principle for the corresponding linear equation using this maximum principle we develop a monotone iterative technique in the presence of lower and upper solutions to solve the nonlinear equation and obtain some existence and uniqueness results

positive unbounded and monotone solutions of the singular second painleve equation on the half line abstract in this paper we study singular boundary value problems on the half line and we prove the existence of a global monotone positive and unbounded solution the latter satisfies a neumann condition at the origin and has prescribed asymptotic behavior at infinity our approach is based on a generalization of the kneser s property continuum of the cross sections of the solutions funnel i e on the properties of the so called consequent mapping and on properties of the associated vector field on the face space two applications one on the well known second painleve type equation which is related to superconductivity theory and a second in the theory of colloids clarify our results

multiple positive solutions for first order nonlinear integro differential equations in banach spaces by using the fixed point index theory the author obtains the existence of two positive solutions for a boundary value problem of first order nonlinear integro differential equations on an infinite interval in a real banach space

the method of lower and upper solutions for fourth order two point boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u iv f x u x u x u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

nonlinear second order equations with functional implicit impulses and nonlinear functional boundary conditions abstract in this paper we present existence results for solutions of nonlinear second order boundary value problems with impulses our impulses are applied at p points in the interval and given implicitly by nonlinear functions of the solution moreover we allow functional dependence on the solution our existence results follow from the existence of a pair of well ordered lower and upper solutions we generalize earlier results of cabada and tomec ek allowing more general compatible boundary conditions impulses and laplacian equations

upper and lower solution methods for fully nonlinear boundary value problems abstract sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions the conditions assume the existence of a strong upper solution lower solution pair a concept that is defined in the paper the differential equation has nonlinear dependence on all lower order derivatives of the unknown in particular appropriate nagumo conditions are obtained and employed

existence of solution for m point boundary value problems of second order differential systems with impulses with the help of the coincidence degree continuation theorem we get a general theorem concerning the existence of solution of the m point boundary value problems for second order differential systems with impulses we also give a definition of autonomous curvature bound set relative to this m point boundary value problems and by using this definition and the above existence theorem we obtain some simple existence conditions of solution for these boundary value problems in particular when the impulses are absent our results can be applied to study the usual m point boundary value problems at resonance

interior curvature estimates and the asymptotic plateau problem in hyperbolic space we show that for a very general class of curvature functions defined in the positive cone the problem of finding a complete strictly locally convex hypersurface in h satisfying f 0 1 with a prescribed asymptotic boundary at infinity has at least one smooth solution with uniformly bounded hyperbolic principal curvatures moreover if is euclidean starshaped the solution is unique and also euclidean starshaped while if is mean convex the solution is unique we also show via a strong duality theorem that analogous results hold in de sitter space a novel feature of our approach is a global interior curvature estimate

a hopf differential for constant mean curvature surfaces in s2 r and h2 r a basic tool in the theory of constant mean curvature cmc surfaces in space forms is the holomorphic quadratic differential discovered by h hopf in this paper we generalize this differential to immersed cmc surfaces in the product spaces s r and h r and prove a corresponding result about the geometry of immersed cmc spheres s in these target spaces

solutions of 2nth lidstone boundary value problems and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem 1 n u 2n x f x u x u x u 2 n 1 x 0 u 2i 0 u 2i 1 0 0 i n 1 some monotone conditions are imposed on f which enable us to apply a new maximum principle to deduce the existence of solution the emphasis here is that f depends on higher order derivatives two examples are also included to dwell upon the importance of the results obtained

transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations abstract using a new method for dealing with the impulse term of second impulsive differential equations we are concerned with determining values of for which there exist positive solutions of the following boundary value problems in the form of x t f t x t 0 t j t t k x t k x t k c k x t k k 1 2 n a x 0 b x 0 a x 1 b x 1 0 1 h s x t d t where 0 is a positive parameter c k is a real sequence with c k 1 k 1 2 n the dependence of positive solution x t on the parameter is also studied i e lim x or lim x 0 the proof of our main result is based upon transformation techniques and fixed point theories this is probably the first time the existence of positive solutions of second order impulsive differential equations has been studied by applying this technique

notes on submanifolds in warped products in this paper we study submanifolds in the warped product m fr where m is a riemannian manifold f is the warping function we investigate the graphs with positive gaussian curvature in m2 r the minimal graphs in m fr and the totally geodesic submanifolds in m fr

positive solutions for higher order lidstone boundary value problems a new approach via sperner s lemma abstract consider the higher order nonlinear scalar differential equation where associated to the lidstone boundary conditions existence of a solution of boundary value problems bvp 1 2 such that are given under superlinear or sublinear growth in f similarly existence for the bvp 1 3 under the same assumptions is proved such that we further prove analogous results for the case when i e derivatives of the obtaining solution satisfy inverse inequalities the approach is based on an analysis of the corresponding vector field on the face plane and the well known from combinatorial analysis knaster kuratowski mazurkiewicz s principle or as it is known sperner s lemma

upper and lower solution method for fourth order four point boundary value problems this paper is concerned with the fourth order ordinary differential equation u 4 t f t u t u t 0 0 some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique

singular perturbations in option pricing after the celebrated black scholes formula for pricing call options under constant volatility the need for more general nonconstant volatility models in financial mathematics motivated numerous works during the 1980s and 1990s in particular a lot of attention has been paid to stochastic volatility models in which the volatility is randomly fluctuating driven by an additional brownian motion we have shown in derivatives in financial markets with stochastic volatility cambridge university press cambridge uk 2000 internat j theoret appl finance 13 2000 pp 101 142 that in the presence of a separation of time scales between the main observed process and the volatility driving process asymptotic methods are very efficient in capturing the effects of random volatility in simple robust corrections to constant volatility formulas from the point of view of pdes this method corresponds to a singular perturbation analysis the aim of this paper is to deal with the nonsmoothness of the payoff

extremal solutions for nonlinear functional ϕ laplacian impulsive equations abstract in this paper we deal with some nonlinear laplacian second order boundary value problems with impulses subject to a general type of boundary value conditions which cover dirichlet and periodic boundary data as particular cases our approach is that of upper and lower solutions together with growth restrictions of nagumo s type the impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear in both cases functional dependence on the solution is allowed

nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature abstract let m g be a complete simply connected riemannian manifold with nonpositive curvature k its scalar curvature and k a smooth function on m we obtain a nonexistence result of complete metrics on m conformal to g and with k as their scalar curvature

stochastic volatility asymptotics of stock loans valuation and optimal stopping abstract a stock loan or equity security lending service is a loan which uses stocks as collateral the borrower has the right to repay the principal with interest and regain the stock or make no repayment and surrender the stock therefore the valuation of stock loan is an optimal stopping problem related to a perpetual american option with a negative effective interest rate the negative effective interest rate makes standard techniques for perpetual american option pricing failure using a fast mean reverting stochastic volatility model we applied a perturbation technique to the free boundary value problem for the stock loan price an analytical pricing formula and optimal exercise boundary are derived by means of asymptotic expansion

periodic solutions of some lienard and duffing equations on etudie certains aspects du probleme periodique u f u u g t u 0 u 0 u 2 u 0 u 2 ou f est une fonction continue sur r et g t u est une fonction de caratheodory soumise a certaines restrictions de croissances on donne deux resultats d existence

existence of solutions of boundary value problems with integral boundary conditions for second order impulsive integro differential equations in banach spaces this paper investigates the existence of solutions for a class of second order boundary value problems with integral boundary conditions of nonlinear impulsive integro differential equations in banach spaces the arguments are based upon the fixed point theorem of strict set contraction operators meanwhile an example is worked out to demonstrate the main results

complete spacelike hypersurfaces with constant mean curvature in r h n abstract in this paper by applying the omori yau generalized maximum principle for complete riemannian manifolds we obtain bernstein type results concerning complete spacelike hypersurfaces with constant mean curvature immersed in the lorentzian product space r h n

a class of three point boundary value problems for second order impulsive integro differential equations in banach spaces abstract in this paper we consider the following boundary value problems for second order three point nonlinear impulsive integro differential equation of mixed type in a real banach space e x t f t x t x t a x t b x t t j t t k x t t k i k x t k x t t k i k x t k x t k k 1 2 m x 0 x 1 x where is the zero element of e a x t 0 t g t s x s d s b x t 0 1 h t s x s d s g c d r d t s j j t s h c j j r and x t t k denotes the jump of x t at t t k x t t k denotes the jump of x t at t t k some new results are obtained for the existence and multiplicity of positive solutions of the above problems by using the fixed point index theory and fixed point theorem in the cone of strict set contraction operators meanwhile an example is worked out to demonstrate the main results

nonlinear second order equations with functional implicit impulses and nonlinear functional boundary conditions in this paper we deal with nonlinear second order boundary value problems with impulses the impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear in both cases functional dependence on the solution is allowed the existence results follow from the existence of a pair of well ordered lower and upper solutions

fourth order two point boundary value problems estimates by two sided bounds on presente une methode simple pour transformer des problemes aux deux points limites d ordre 4 en problemes d ordre 2

hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity in this paper we study the problem of finding smooth complete hypersurfaces of constant mean curvature in hyperbolic space with a prescribed asymptotic boundary at infinity our main results are proved by deriving a priori global gradient estimates based on the classical maximum principle for elliptic equations

on the dirichlet problem for minimal graphs in hyperbolic space soit r n n 2 un domaine borne on etudie le probleme de dirichlet suivant f f i f j f ij 1 df 2 n f 0 dans f 0 dans f 0 sur on considere le comportement a la frontiere de la solution

solvability of an m point boundary value problem for second order ordinary differential equations let 0 1 r2 r be a function satisfying caratheodory s conditions and e t l1 0 1 let i 0 1 ai r all of the ai s having the same sign i 1 2 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a solution for the m point boundary value problem x t t x t x t e t t 0 1 e formula conditions for the existence of a solution for the above boundary value problem are given using the leray schauder continuation theorem

a remark on the mean curvature of a graph like hypersurface in hyperbolic space in this paper we investigate the mean curvature h of a radial graph in hyperbolic space hn 1 we obtain an integral inequality for h and find that the lower limit of h at infinity is less than or equal to 1 and the upper limit of h at infinity is more than or equal to 1 as a byproduct we get a relation between the n dimensional volume of a bounded domain in an n dimensional hyperbolic space and the n 1 dimensional volume of its boundary we also sharpen the main result of a paper by p a nitsche dealing with the existence and uniqueness of graph like prescribed mean curvature hypersurfaces in hyperbolic space

entire radially symmetric graphs with prescribed mean curvature in warped product spaces abstract this study investigates entire radially symmetric graphs in the warped product m f r where m is a riemannian manifold with a pole and f m r is the warping function the main results demonstrate the existence and uniqueness of entire radially symmetric graphs with prescribed mean curvature

singular perturbations for boundary value problems arising from exotic options we study the pricing of three exotic derivative securities barrier lookback and passport options which can be characterized by boundary value pde problems in the context of popular markovian sv models of stock prices by extending the fast mean reverting asymptotic analysis in j p fouque g papanicolaou and k r sircar derivatives in financial markets with stochastic volatility cambridge university press london 2000 the usual greek correction to the black scholes prices of these contracts is further corrected by a boundary integral term that is rapidly computed numerically in the case of the passport option the asymptotic method is effective in accounting for sv effects in a simple and robust fashion even in the presence of a highly nonlinear embedded stochastic control problem

upper and lower solutions for periodic problems upper and lower solutions method topological degree and miranda fixed point theorem are applied to obtain the existence of at least one periodic solution for second order and first order nonlinear differential systems

a unique solution of initial value problems for first order impulsive integro differential equations of mixed type in banach spaces in this paper we investigate initial value problem for first order impulsive integro differential equation of mixed type in a banach space without any compactness type assumption we obtain a unique solution of the equation an explicit iterative approximation of the solution and an error estimate of the approximation sequence our result improves and extends many recent results

alternative models for stock price dynamics abstract this paper evaluates the role of various volatility specifications such as multiple stochastic volatility sv factors and jump components in appropriate modeling of equity return distributions we use estimation technology that facilitates nonnested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns we consider two broad families of models 1 the multifactor loglinear family and 2 the affine jump family both classes of models have attracted much attention in the derivatives and econometrics literatures there are various tradeoffs in considering such diverse specifications if pure diffusion sv models are chosen over jump diffusions it has important implications for hedging strategies if logarithmic models are chosen over affine ones it may seriously complicate option pricing comparing many different specifications of pure diffusion multifactor models and jump diffusion models we find that 1 log linear models have to be extended to two factors with feedback in the mean reverting factor 2 affine models have to have a jump in returns stochastic volatility or probably both models 1 and 2 are observationally equivalent on the data set in hand in either 1 or 2 the key is that the volatility can move violently as we obtain models with comparable empirical fit one must make a choice based on arguments other than statistical goodness of fit criteria the considerations include facility to price options to hedge and parsimony the affine specification with jumps in volatility might therefore be preferred because of the closed form derivatives prices

solutions of two point bvps at resonance for higher order impulsive differential equations in this paper the resonance two point boundary value problems for impulsive 2n order differential equation x 2n t f t x t x t x 2n 1 t 0 t 1 x i sk ii k x sk x 2n 1 sk i 1 2n 1 k 1 p with following two point boundary value conditions x 2i 1 0 x 2i 1 1 i 0 n 1 and for n order differential equation x n t f t x t x t x n 1 t 0 t 1 x i sk ii k x sk x 2n 1 sk i 1 n 1 k 1 p with following periodic boundary value conditions x i 0 x i 1 0 i 0 n 1 are considered sufficient conditions which guarantee the existence of at least one solution for these problems are established the interest is that we allow the degree of variables of f to be greater than 1 the methods used and results obtained are new and they shows us that the solvability of these two problems are very much alike

warping functions of some warped products abstract in this paper we study the warping functions of some warped products let h n be the n dimensional hyperbolic space with sectional curvature 1 we prove that if the warping function f of the warped product h n f r has a critical point then h n f r h n 1 if and only if f x k cosh r x where k is a positive constant r x denotes the hyperbolic distance from x to a fixed point we also prove that if the sectional curvature of the warped product m f r is nonnegative then f is constant providing that the riemannian manifold m is complete and connected

pricing of options in the singular perturbed stochastic volatility model the pricing of options in the fast mean reverting stochastic volatility model using the singular perturbation method has received a considerable amount of attention in the last two decades however it is not to easy to estimate the accuracy of the approximation if the payoff function is not smooth or bounded as is the case for european call options in this article we introduce a new novel approach for pricing options in the fast mean reverting stochastic volatility model combinations of fourier analysis and singular perturbation methods enable us to estimate the accuracy easily we also show that this method allows us to derive the price of european and bermudan options in the fast mean reverting stochastic volatility environment with jumps

existence and uniqueness results for the bending of an elastic beam equation at resonance etude d un probleme non lineaire aux valeurs limites pour la flexion d une poutre elastique en appui simple aux deux extremites dans le cas de resonance theoremes d existence et d unicite

solutions of lidstone bvps for higher order impulsive differential equations abstract in this paper the lidstone boundary value problems for 2 n order impulsive differential equation x 2 n t f t x t x t x 2 n 1 t 0 t 1 x i s k i i k x s k x 2 n 1 s k i 1 2 n 1 k 1 p with one of following boundary conditions x 2 i 0 x 2 i 1 0 i 0 n 1 and x 2 i 1 0 x 2 i 1 0 i 0 n 1 are considered sufficient conditions which guarantee the existence of at least one solution for these problems are established the results are new examples illustrate our main results

regularity at infinity for area minimizing hypersurfaces in hyperbolic space equipped with the hyperbolic metric y z dxz dy2 a standard compactification of ih involves adding the boundary r 0 w so that i i is simply the one point compactification of the euclidean closed half space r 0 suppose 0 7 any interior singularities of m must remain in a bounded region of hyperbolic space near points of f in the euclidean topology m w f may thus be described as the graph of a function this function is the solution of an interesting partial differential equation that becomes degenerate along the part of the boundary corresponding to f the second author has recently established l a boundary higher regularity result for this equation which implies in particular that m w f is r if f is cgk for k 2 3 finally in case f bounds a star

eigenvalue of fourth order m point boundary value problem with derivatives this paper deals with the existence of positive solutions for the fourth order nonlinear ordinary differential equation x t lg t f t x t x t 0 0 are constants such that r a d a c b d 0 and x i 0 1 h i 0 i 1 2 m 2 by means of a fixed point theorem due to krasnaselskii some new existence results of positive solutions for the above multi point boundary value problem are obtained which improve the main results of graef et al j r graef c qian b yang a three point boundary value problem for nonlinear fourth order differential equations j math anal appl 287 2003 217 233 an example is given to demonstrate the main results of this paper

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when

complete minimal varieties in hyperbolic space it is a basic problem in the subject of minimal varieties to determine the class of complete minimal and area minimizing varieties m k in a given riemannian manifold n besides being of their own intrinsic interest the cases r of euclidean space and mn sn of the sphere are fundamental in understanding the local structure of minimal varieties due to the existence of tangent cones to general minimal varieties there has been much study of the complete areaminimizing varieties in these cases in particular relating to the bernstein conjecture and minimizing cones e g l2 f1 nevertheless many deep problems remain unsolved this paper is centered around the question of existence of complete areaminimizing varieties in hyperbolic space h here by way of contrast to the situation in ir n or s we find a comparatively complete solution to the problem of existence in fact the main result of this paper exhibits a wealth of complete area minimizing varieties in h in all dimensions and codimensions more precisely we have