on the existence and multiplicity of positive periodic solutions for first order vector differential equation abstract in this paper we consider the existence and multiplicity of positive periodic solutions for first order vector differential equation x t f t x t 0 a e t 0 under the periodic boundary value condition x 0 x here is a positive constant and f 0 r n r n is a caratheodory function some existence and multiplicity results of positive periodic solutions are derived by using a fixed point theorem in cones

remarks on first and second order periodic boundary value problems on etudie les problemes aux valeurs limites periodiques d ordre 1 et 2 suivants u f t u u 0 u 2 et u f t u u 0 u 2 u 0 u 2 on obtient l existence de solutions extremales comme limites d iterees monotones

fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm the analysis of transient wave scattering from rigid bodies using integral equation based techniques is computationally intensive if carried out using classical schemes the evaluation of the velocity potential on the surface of a three dimensional scatterer represented in terms of ns spatial basis functions for nt time steps requires o ntns2 operations the recently developed plane wave time domain pwtd algorithm permits the rapid evaluation of transient fields that are generated by bandlimited source distributions it has been shown that incorporation of the pwtd algorithm into integral equation based solvers in a two level setting reduces the computational complexity of a transient analysis to o ntns1 5 logns in this paper it is shown that casting the pwtd scheme into a multilevel framework permits the analysis of transient acoustic surface scattering phenomena in o ntnslog2ns operations using o ntns memory numerical examples that demonstrate the efficacy of the multilevel implementation are also presented

the method of lower and upper solutions for systems of boundary value problems the method of lower and upper solutions for second order differential system x f t x with dirichlet boundary condition x 0 x 1 0 is used to give sufficient conditions for the existence of at least one solution

improved generalized quasilinearization method and rapid convergence for reaction diffusion equations abstract in the method of quasilinearization or the method of generalized quasilinearization we assume that k f t x u u k exists where f t x u is the forcing function and obtain kth order of convergence in this paper we assume a weaker condition namely k 1 f t x u u k 1 exists and lipschitzian in u and develop generalized quasilinearization method to reaction diffusion equations the iterates will be different depending on k 1 f t x u u k 1 is nondecreasing or nonincreasing in u and k being even or odd finally we prove that the sequences generated by the generalized quasilinearization method converge to the unique solution of the nonlinear reaction diffusion equation and the convergence is of order k

a multilevel cartesian non uniform grid time domain algorithm a multilevel cartesian non uniform grid time domain algorithm cngtda is introduced to rapidly compute transient wave fields radiated by time dependent three dimensional source constellations cngtda leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay and amplitude compensated field samples this property is used in conjunction with a multilevel scheme in which the computational domain is hierarchically decomposed into subdomains with sparse non uniform grids used to obtain the fields for both surface and volumetric source distributions the computational cost of cngtda to compute the transient field at n s observation locations from n s collocated sources for n t discrete time instances scales as o n tn slogn s and o n tn slog 2n s in the low and high frequency regimes respectively coupled with marching on in time mot time domain integral equations cngtda can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems

a generalized upper and lower solutions method and multiplicity results for nonlinear first order ordinary differential equations abstract we introduce a generalized upper and lower solutions method for the solvability of first order ordinary differential equations u t t u t u 0 u 1 in order to cover the case when the function satisfies caratheodory conditions this method is then applied to get multiplicity results when the nonlinearity interacts with the real eigenvalue of the linearized problem our proofs are based on differential inequalities and classical leray schauder degree

nonlinear second order periodic boundary value problems abstract in this paper we study a periodic boundary value problem pbvp for brevity of second order it is well known that if and are upper and lower solutions respectively with then there exists a solution u such that u when nothing was known the main purpose of this paper is to consider this last case also we study the structure of the set of solutions of the pbvp in the sector when and we apply the results to the case

the monotone method for first order problems with linear and nonlinear boundary conditions in this paper we develop the monotone method for the first order problem u t f t u t for a e t a b when f is a caratheodory function and u w 1 1 a b we consider the nonlinear boundary conditions l u a u b 0 with l c r 2 r nondecreasing in x or nonincreasing in y and the linear boundary conditions a 0u 0 b 0u t l 0 with a 0 b 0 and l 0 r we prove the existence of solutions and the validity of the monotone method if there exists a lower solution a and an upper solution b with either a b for the linear conditions we obtain eight new concepts of lower and upper solutions which generalize previous known cases

a fast and stable solver for acoustic scattering problems based on the nonuniform grid approach a fast and stable boundary element method bem algorithm for solving external problems of acoustic scattering by impenetrable bodies is developed the method employs the burton miller integral equation which provides stable convergence of iterative solvers and a generalized multilevel nonuniform grid mlng algorithm for fast evaluation of field integrals the mlng approach is used here for the removal of computational bottlenecks involved with repeated matrix vector multiplications as well as for the low order basis function regularization of the hyper singular integral kernel the method is used for calculating the fields scattered by large acoustic scatterers including nonconvex bodies with piece wise smooth surfaces as a result the algorithm is capable of accurately incorporating high frequency effects such as creeping waves and multiple edges diffractions in all cases stable convergence of the method is observed high accuracy of the method is demonstrated by comparison with the traditional b

existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti periodic boundary conditions this paper describes the method of quasilinearization for first order nonlinear impulsive functional differential equations with anti periodic boundary conditions a monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand 2007 elsevier ltd all rights reserved

nonuniform grid time domain ngtd algorithm for fast evaluation of transient wave fields a novel algorithm to efficiently compute transient wave fields produced by known three dimensional source constellations is proposed the algorithm uses domain decomposition concepts and comprises two steps to be repeated for each subdomain considered in the first step delay and amplitude compensated fields produced by sources residing inside each subdomain are computed at a sparse set of points surrounding the observation domain in the second step total fields in the observer domain are evaluated by interpolation delay and amplitude restoration and aggregation of subdomain fields the proposed scheme is well suited to accelerate the solution of time domain integral equations by marching on in time to carry out time domain physical optics calculations and to realize near to far field transformations of transients moreover the scheme automatically adapts to and takes advantage of special geometrical features of the source observer constellation studied a key benefit when analyzing quasi planar configurations in addition it realizes a seamless transition from the dynamic to the quasi static regime thus facilitating a unified treatment of electrically large and small problems last but not least the scheme is remarkably simple to implement

boundary critical behaviour at m axial lifshitz points the special transition for the case of a surface plane parallel to the modulation axes the critical behaviour of d dimensional semi infinite systems with n component order parameter is studied at an m axial bulk lifshitz point whose wave vector instability is isotropic in an m dimensional subspace of r d field theoretic renormalization group methods are utilized to examine the special surface transition in the case where the m potential modulation axes with 0 m d 1 are parallel to the surface the resulting scaling laws for the surface critical indices are given the surface critical exponent sp t he

a monotone method for the equation uxyz f comparison theorems for the nonlinear boundary value problem u x y z f x y z u u x u y u z u x y u y z u z x with the boundary conditions u o y z a y z u x 0 z b z x u x y 0 c x y a y 0 c 0 y a 0 z b z 0 b 0 x c x 0 are established under certain conditions then it is shown that there exist sequences of lower and upper solutions which converge uniformly and monotonically to minimal and maximal solutions respectively

periodic solutions of nonlinear boundary value problems one of the well known techniques in the theory of nonlinear boundary value problems bvp is the method of differential inequalities or the method of upper and lower solutions the method of alternative problems a global variant of the lyapunov schmidt method has been used in the study of problems at resonance the investigation of periodic bvp s forms an important subclass of problems at resonance our aim is to combine the two approaches to discuss nonlinear problems at resonance we restrict ourselves in this paper to the discussion of periodic boundary value problems in section 1 we shall indicate the method of upper and lower solutions the results for systems are given in a general way so as to include known results and also offer new directions section 2 deals with the abstract existence results at resonance in the desired framework in section 3 we consider the scalar periodic bvp s by combining the two techniques namely alternative methods and the method of differential inequalities

the liouville arnold nekhoroshev theorem for non compact invariant manifolds under certain conditions generalized action angle coordinates can be introduced near non compact invariant manifolds of completely and partially integrable hamiltonian systems

existence of periodic solutions for fully nonlinear first order differential equations in this paper we establish some existence results for periodic solutions of fully nonlinear first order scalar differential equation f t x x 0 the approach here uses the viscosity solutions method developed in recent decades and the classical upper lower solutions method

approximation of solutions for nonlinear periodic boundary value problems with discontinuous upper and lower solutions we prove that it is possible to approximate the solutions of a nonlinear periodic boundary value problem via monotone sequences starting at piecewise continuous upper and lower solutions in fact we present here two different iterative methods explicit expression of each iteration is obtained by solving some linear initial value problems

rapid convergence of the iterative technique for first order initial value problems in this paper we study the convergence of the approximate solutions of the first order problem u t f t w t u o u o we prove that if there exists kf u k k 1 and it is a continuous function then it is possible to construct two sequences of approximate solutions converging to a solution with rate of convergence of order k

critical phenomena at perfect and non perfect surfaces the effect of imperfections on surface critical properties is studied for ising models with nearest neighbour ferromagnetic couplings on simple cubic lattices in particular results of monte carlo simulations for flat perfect surfaces are compared to those for flat surfaces with random weak or strong interactions between neighbouring spins in the surface layer and for surfaces with steps of monoatomic height surface critical exponents at the ordinary transition in particular are found to be robust against these perturbations

boundary critical behaviour at m axial lifshitz points of semi infinite systems with a surface plane perpendicular to a modulation axis semi infinite d dimensional systems with an m axial bulk lifshitz point are considered whose d 1 dimensional surface hyper plane is oriented perpendicular to one of the m modulation axes an n component 4 field theory describing the bulk and boundary critical behaviour when a the hamiltonian can be taken to have o n symmetry and b spatial anisotropies breaking its euclidean symmetry in the m dimensional coordinate subspace of potential modulation directions may be ignored is investigated the long distance behaviour at the ordinary surface transition is mapped onto a field theory with the boundary conditions that both the order parameter and its normal derivative n vanish at the surface plane the boundary operator expansion is utilized to study the short distance behaviour of near the surface its leading contribution is found to be controlled by the boundary operator 2 n the field theory is renormalized for dimensions d below the upper critical dimension d m 4 m 2 with a corresponding surface source term 2 n added the anomalous dimension of this boundary operator is computed to first order in d d the result is used in conjunction with scaling laws to estimate the value of the single independent surface critical exponent ord l1 for d 3 our estimate for the case m n 1 of a uniaxial lifshitz point in ising systems is in reasonable agreement with the published monte carlo results

on a way to save memory when solving time domain boundary integral equations for acoustic and vibroacoustic applications abstract solving acoustic equations in the time domain possibly coupled with the description of flexible structure dynamics remains attractive as compared to solving the same in the frequency domain this allows for better consideration of local non linearities acoustics structure and the boundary integral formulation also known as bem offers an exact description of the infinite acoustic field based on a simple surface mesh no need for 3d volume discretization some issues remain however the required memory space and computation time continue to grow rapidly when the number of elements of the surface mesh increases in the case of a structure with a regular non slender shape the computational cost measured in terms of required memory space varies by helmholtz number to the power of 4 this paper illustrates how the accelerating method called ngtd helps overcome this difficulty this paper shows the applicability of 2 level ngtd to acoustic and vibroacoustic problems described solely by the hypersingular formulation for surfaces it goes into more detail on some important aspects of the interpolation process and on the memory saving obtained implementation within the mot march on time astryd code shows the benefits of this method the memory requirement shows an estimated trend lower than power 1 35 of the number of surface elements