monotone iterative technique for partial differential equations of first order in view of the fact that first order partial differential equations arise naturally in modelling growth population of cells which constanctly change their properties a study of stable and chaotic solutions of such equations was initiated in 3 in this paper we develop monotone iterative technique for first order partial differential equations and for this purpose we need to discuss existence uniqueness and comparison results we also indicate how the monotone sequences obtained may be employed as candidates for lyapunov functions in stability theory

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

on initial boundary value problems in bounded and unbounded domains for a class of nonlinear hyperbolic equations of the third order abstract for the nonlinear hyperbolic equation u 2 1 f x t u u 1 0 u 2 0 u 0 1 u 1 1 problems on bounded solutions in a half strip and in a strip are studied unimprovable conditions of local and global solvability and unique solvability of these problems are established

monotone methods for higher order partial difference equations abstract a nonlinear difference equation of the order n m in two independent variables nx myu x y u together with appropriate initial and periodic boundary conditions is considered several comparison results for these problems are established these results are then used to provide sufficient conditions for the convergence of monotone iterative methods numerical illustrations dwelling upon the importance of our results are also included

the method of fundamental solutions for the numerical solution of the biharmonic equation abstract the method of fundamental solutions mfs is a relatively new technique for the numerical solution of certain elliptic boundary value problems it falls in the class of methods generally called boundary methods and like the well known boundary integral equation method is applicable when a fundamental solution of the differential equation is known in the mfs the approximate solution is a linear combination of fundamental solutions with singularities placed outside the domain of the problem the locations of the singularities are either preassigned or determined along with the coefficients of the fundamental solutions so that the approximate solution satisfies the boundary conditions as well as possible in many applications these quantities are determined by a least squares fit of the boundary conditions a nonlinear problem which is solved using standard software in this paper the mfs is formulated for biharmonic problems and is applied to a variety of standard test problems as well as to problems arising in elasticity and fluid flow

the method of upper lower solutions and hyperbolic partial differential equations on presente l etude de la methode des solutions superieures et inferieures pour des equations differentielles hyperboliques on considere la theorie des inegalites differentielles hyperboliques d une facon generale et on demontre un resultat d existence

existence theorems for a class of functional differential systems in recent papers 2 6 the authors have established existence and comparison theorems for the well known cauchy problem for ordinary diferential equations without using the monotone property on the given system these results are obtained under the conditions of the type which have been considered in the classical paper of miiller 8 1 the interesting feature of the results established in 2 6 is the fact that the solutions of the cauchy problem remain in the given sector in this paper we shall first establish existence and comparison theorems for a class of more general functional differential systems without using monotone property further we develop a monotone iterative technique to establish the existence of minimal and maximal solutions

the noor integral and strongly starlike functions abstract let a denote the class of analytic functions f z defined in the unit disc satisfying the condition f 0 f 0 1 0 we introduce some new subclasses of strongly starlike functions defined by the noor integral and study their properties

boundary integration and interpolation procedures for plate bending in the direct boundary element method dbem for thin plate bending analysis the integration of the kernel shape function products can lead to complications due to a combination of factors the first is the existence of a singularity at the source point leading to the singular kernel which increases in strength as the integral equation is differentiated once for rotation again for moment and yet again for shear the second factor arises from the use of piecewise interpolation polynomials in the first part of the dbem analysis where the unspecified boundary values are computed the numerical procedures are fairly straightforward it is found in this paper that special care must be taken in calculating internal actions at domain points the problems which can be encountered are demonstrated and a modified boundary interpolation procedure is described examples are given which show the superiority of the recommended approach

annihilation of boundary singularities via suitable green s functions abstract a numerical integral equation method is presented for the accurate solution of viscous flow problems in which there are inherent boundary singularities where applicable this method has the advantage over existing singularity subtraction and singularity incorporation methods since natural boundary conditions can be employed without any special form of pre or post processing results are presented for the benchmark problem of stokes flow in a lid driven cavity

some properties of certain classes of meromorphically p valent functions involving extended multiplier transformations in this paper the authors investigate interesting properties of certain subclasses of meromorphically multivalent functions which are defined here by means of extended multiplier transformations

a boundary element method for plate bending problems abstract an indirect boundary element formulation is constructed by using a fundamental solution of the biharmonic operator it is shown that the fundamental solution and its derivatives can be represented by four functions with two integers the new representation is not only a simpler representation but also reveals a structure that is exploited in the development of an algorithm based on the analytical integration of line and area integrals the analytical integral values are used to establish continuity requirements on the unknown fictitious densities numerical examples consider the consequences of satisfying and violating the continuity requirements by the unknown fictitious densities it is also shown that if the fictitious density distributions do not satisfy certain conditions then he solution can be affected by the choice of the non dimensionalizing variables numerical examples with a variety of boundary conditions demonstrate the effectiveness and limitations of the proposed algorithm

on solvability of boundary value problems for higher order nonlinear hyperbolic equations abstract in the rectangle 0 a 0 b for the nonlinear hyperbolic equation u m n i 0 m 1 h 1 i x u i n k 0 n 1 h 2 k y u m k f x y u u m 1 n 1 the boundary value problems of the type l 1 i u y 0 i 1 m l 2 k u x 0 k 1 n are considered where l 1 i c m 1 0 a r i 1 m and l 2 k c n 1 0 b r k 1 n are linear bounded functionals sufficient conditions of solvability and unique solvability of the general problem and its particular cases nicoletti type dirichlet lidstone and periodic problems are established

on a periodic problem for higher order differential equations with a deviating argument for higher order nonautonomous linear and nonlinear differential equations with deviating arguments new sufficient conditions of existence and uniqueness of a periodic solution are found

some inclusion properties of a certain family of integral operators abstract the authors introduce several new subclasses of analytic functions which are defined by means of a general integral operator i and investigate various inclusion properties of these subclasses many interesting applications involving these and other families of integral operators are also considered

the treatment of singularities in the calculation of stress intensity factors using the boundary integral equation method abstract a version of the boundary integral equation method applicable to elliptic boundary value problems for domains with curved boundaries and mixed boundary conditions dirichlet neumann and third type is described some problems arising when the region includes a slit crack are discussed and a number of novel ways for dealing with the resulting singularity are presented methods for computing the stress intensity factor sif are described and their numerical performance is assessed in three of these methods the sif appears directly as one of the unknowns in the computation or a simple linear combination of these unknowns which is a most welcome feature since it avoids the uncertainties associated with the commonly employed graphical and extrapolation techniques

some inclusion relationships and integral preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators the object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions by making use of these novel integral operators we introduce and investigate several new subclasses of starlike convex close to convex and quasi convex meromorphic functions in particular we establish some inclusion relationships associated with the aforementioned integral operators several interesting integral preserving properties are also considered

a linear operator and associated families of meromorphically multivalent functions making use of a linear operator which is defined here by means of the hadamard product or convolution the authors introduce and investigate the various properties and characteristics of two novel families of meromorphically multivalent functions they also extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions

mass and momentum conserving spectral methods for stokes flow the governing equations for stokes flow are formulated in terms of a stream function and airy stress function this formulation ensures that mass and momentum are conserved identically in terms of these new variables the equations of motion are written as a second order elliptic system these equations are embedded in biharmonic equations and the boundary conditions appropriate for this higher order system are determined using a least squares process this technique is applied to the planar stick slip problem a numerical solution to the problem is obtained using a spectral domain decomposition method an algebraic mapping is used to treat the flow domain without truncation the coefficients in a singular expansion of the stream function about the stick slip singularity are computed using a post processing technique

some properties of certain subclasses of meromorphically multivalent functions in this paper the author investigates interesting properties of certain subclasses of meromorphically multivalent functions which are defined here by means of certain linear operator

monotone method for second order periodic boundary value problems in recent years there has been an extensive study of the existence of periodic solutions l s 11 14 151 in 8 111 the existence of solutions of first and second order pbvp period boundary value problems has been obtained by a novel approach of combining the classical method of lower and upper solutions and the method of alternative problems lyapunovschmidt method which provide conditions that are easily verifiable and which covers previous known results of other authors as a constructive method for obtaining extremal solutions of initial and boundary value problems the monotone iterative procedure has been employed by several researchers 5 7 11 13 151 the objective of this paper is to employ this useful technique for second order pbvp to obtain the minimal and maximal solutions as limits of monotone iterates our method can be used to study semilinear parabolic initial boundary value problems and other problems at resonance

differential subordination and superordination results for cho kwon srivastava operator making use of the concepts of differential subordination and superordination many subordination and superordination results are obtained for analytic functions in the open unit disk using the cho kwon srivastava operator by investigating appropriate classes of admissible functions sandwich type results are also obtained

analytical treatment of boundary integrals in direct boundary element analysis of plate bending problems a direct type boundary element method bem for the analysis of simply supported and built in plates is employed the integral equations due to a combined biharmonic and harmonic governing equations are first established the boundary integrals developed are then evaluated analytically the domain integrals due to external body forces are also transformed over the boundary and subsequently evaluated analytically thus it needs only the boundary to be discretized without loss of generality the exact expression for the integrals would enhance the solution accuracy of the bem this is due to the fact that at locations where the fundamental solutions approach their singular points the value determined by numerical quadrature may be inconsistent and inaccurate also another major advantage of the exact expressions for integrations is the insensitivity to the geometrical location of the source point on the boundary the distribution of boundary quantities is approximated either over linear or quadratic boundary elements general type of plate bending problems with plates of different geometrical shapes supported simply or fixed can be handled loading may be applied point concentrated uniformly distributed within the domain or over the boundary also hydrostatic pressure can be applied the results obtained by bem in comparison with those obtained by analytical or other approximate solutions are found to be very accurate and the solution method is efficient

subclasses of meromorphic functions associated with the cho kwon srivastava operator abstract we consider a multiplier transformation and some subclasses of the class of meromorphic functions which was defined by means of the hadamard product by n e cho o s kwon and h m srivastava in n e cho o s kwon h m srivastava inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations j math anal appl 300 2004 505 520

a new boundary integral formulation for stream function and vorticity in axisymmetric stokes flow a boundary integral equation approach is presented to solve the flow stream function and vorticity in the axisymmetric stokes problem without swirl the governing equations expressed in these variables require that the fundamental solutions of the involved differential operators be found the fundamental solutions in a closed form suitable for numerical treatment of integral equations are obtained and their equivalent forms in infinite integral are derived by using fourier and hankel transforms a coupled system of boundary integral equations for the stream function and the vorticity is formulated by employing new fundamental solutions solution of these equations is realized by the collocation method numerical results are included for several bounded and unbounded domain problems to validate and demonstrate the effectiveness of the proposed approach

derivation and analytical investigation of three direct boundary integral equations for the fundamental biharmonic problem we derive and investigate three families of direct boundary integral equations for the solution of the plane fundamental biharmonic boundary value problem these three families are fairly general so that they as special cases encompass various known and applied equations as demonstrated by giving many references to the literature we investigate the families by analytical means for a circular boundary curve where the radius is a parameter we find for all three combinations of equations i that the solution of the equations is non unique for one or more critical radius radii and ii that this lack of uniqueness can always be removed by combining the integral equations with a suitable combination of one or more supplementary condition s we conjecture how the results obtained can or cannot be generalized to other boundary curves through the concept logarithmic capacity a few published general results about uniqueness are compared with our findings

biharmonic analysis of rectilinear plates by the boundary element method an improved boundary element formulation bem for two dimensional non homogeneous biharmonic analysis of rectilinear plates is presented a boundary element formulation is developed from a coupled set of poisson type boundary integral equations derived from the governing non homogeneous biharmonic equation emphasis is given to the development of exact expressions for the piecewise rectilinear boundary integration of the fundamental solution and its derivatives over several types of isoparametric elements incorporation of the explicit form of the integrations into the boundary element formulation improves the computational accuracy of the solution by substantially eliminating the error introduced by numerical quadrature particularly those errors encountered near singularities in addition the single iterative nature of the exact calculations reduces the time necessary to compile the boundary system matrices and also provides a more rapid evaluation of internal point values than do formulations using regular numerical quadrature techniques the evaluation of the domain integrations associated with biharmonic forms of the non homogeneous terms of the governing equation are transformed to an equivalent set of boundary integrals transformations of this type are introduced to avoid the difficulties of domain integration the resulting set of boundary integrals describing the domain contribution is generally evaluated numerically however some exact expressions for several commonly encountered non homogeneous terms are used several numerical solutions of the deflection of rectilinear plates using the boundary element method bem are presented and compared to existing numerical or exact solutions

well posedness of nonlocal boundary value problems with integral condition for the system of hyperbolic equations abstract a nonlocal boundary value problem with integral condition for a system of hyperbolic equations is considered relationship with the family of boundary value problems for ordinary differential equations is established sufficient and necessary conditions of well posedness of nonlocal boundary value problems with integral condition for a system of hyperbolic equations are obtained

generalized hypergeometric functions associated with k uniformly convex functions abstract for a certain linear operator which is defined by means of the hadamard product or convolution with a generalized hypergeometric function the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as for example k uniformly convex functions and k starlike functions relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out

evaluation of boundary integrals for plate bending the alternative to quadrature as a procedure for dealing with the integrations required in the direct boundary element method dbem is to carry out the integration analytically and code the results directly the potential benefits are efficient computer programs the avoidance of numerical instability and generally better accuracy the technique is developed in this paper serious problems arise when gauss quadrature is employed for the integration of functions which contain or are close to singularities a numerical integration approach may fail at the first stage of the analysis that is during the assembly of the discrete equations or it may fail at the subsequent stage of computing domain points near the boundary the severity of the problem is dependent both on the strength of the singularity and on geometry these points are illustrated with examples

bounded and periodic in a strip solutions of nonlinear hyperbolic systems with two independent variables in the strip d b x 0 b the nonlinear hyperbolic system 2u x y f x y u u x u y with the continuous right hand side f d b x 3 n n is considered sharp sufficient conditions of existence and uniqueness of bounded and periodic with respect to the first argument classical solutions are established

inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations making use of a multiplier transformation which is defined here by means of the hadamard product or convolution the authors introduce some new subclasses of meromorphic functions and investigate their inclusion relationships and argument properties some integral preserving properties in a given sector are also considered

a boundary integral equation method for plate flexure with conditions inside the domain a method for solving boundary value problems for thin plate flexure as described by kirchhoff s theory is proposed an integral formulation leads to a system of boundary integral equations involving values of deflection slope bending moment and transverse shear force along the edge a discretization leading to a matrix formulation is proposed to solve problems with inner conditions in the plate domain an elimination of boundary unknowns proves successful the degenerate case where the boundary is free which leads to a non invertible matrix is investigated three examples illustrate the efficiency of the method

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

periodic solutions of coupled semilinear parabolic boundary value problems the study of periodic solutions to parabolic differential systems goes back to j fourier who investigated the linear heat equation for the determination of temperature oscillation on earth cf 141 in recent years attention has been given to nonlinear parabolic boundary value problems cf l 2 4 6 7 15 16 however most of the discussions in the literature are concerned with a single parabolic equation under dirichlet type boundary condition due to the recent development in the biochemical and biological fields there arise various types of reactiondiffusion systems e g see lo 121 an interesting problem in some of these systems such as the belousov zhabotinskii reaction model is an understanding of the oscillating nature of the solution in this paper we investigate periodic solutions for a coupled system of parabolic boundary value problems in a one dimensional domain under various boundary conditions specifically the equations under consideration are given by

the numerical solution of plane potential problems by improved boundary integral equation methods abstract a modified boundary integral bie method which facilitates accurate solution of laplacian boundary value problems is presented this method is designed specifically for treatment of problems in which singularities occur on the interface between two regions with different physical properties and is illustrated by application to two physical problems analytic expressions for the integrals arising in the piecew se linear and piecewise quadratic bie approximations are also presented these analytical expressions afford an appreciable reduction in computational time when compared with previously employed quadrature formulae

certain subclasses of meromorphically multivalent functions associated with generalized hypergeometric function in this paper we introduce and study two subclasses s p q s a 1 a b l and s p q s a 1 a b l of meromorphic p valent functions of order l email protected email protected

certain classes of meromorphic multivalent functions in this paper we introduce and investigate two new classes of meromorphic multivalent functions such results as subordination properties coefficient inequalities convolution properties and integral representations are proved several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived

singular lidstone boundary value problem with given maximal values for solutions abstract the singular problem 1 nx 2n f t x x 2n 2 x 2j 0 x 2j t 0 0 j n 1 max x t 0 t t a depending on the parameter is considered here the positive caratheodory function f may be singular at the zero value of all its phase variables the paper presents conditions which guarantee that for any a 0 there exists a 0 such that the above problem with a has a solution x ac2n 1 0 t which is positive on 0 t the proofs are based on the regularization and sequential techniques and use the leray schauder degree and vitali s convergence theorem

direct evaluation of singular boundary integrals in two dimensional biharmonic analysis development of techniques to provide rapid and accurate evaluation of the integrations required in boundary element method bem formulations are receiving more attention in the literature in this work a series of direct expressions for surface integrals required for a boundary element solution of the non homogeneous biharmonic over a general two dimensional curvilinear surface are presented the concept of an isoparametric representation usually applied to the variation of the field variables and the geometry is extended to the parametric mapping of the curvilinear geometry the result renders the typically complicated jacobian function into a series of polynomial expressions based on the shape function set and several discrete jacobian values an application of the isoparametric approximation of the jacobian for a quadratic element representation is developed implementation of this approximation significantly improves the accuracy of the boundary integral solution by eliminating error associated with numerical quadrature overall computational efficiency is improved by reducing the time necessary to calculate individual surface integrals and evaluate field variables at internal points a numerical solution of the boundary integral equations of phenomena governed by the biharmonic equation is presented and compared with an exact analysis

the integral operator method for finding almost periodic solutions of nonlinear wave equations on considere une equation d onde autonome semilineaire de la forme u tt u x x a u x b u t c u f u x t r 2 ou a b c sont des constantes et f u est une fonction continue dans r on cherche une solution non constante satisfaisant la condition presque periodique par rapport a x t

hermitian cubic boundary elements for two dimensional potential problems a hermite interpolation based formulation is presented for the boundary element analysis of two dimensional potential problems two three noded hermitian cubic elements hce are introduced for the modelling of corners or points with non unique tangents on the boundary these elements along with the usual two noded hce are used in numerical examples the results obtained show that faster convergence can be achieved using hce compared with using lagrange interpolation type quadratic elements qe for about the same amount of computing resources

monotone iterative technique for delay differential equations in abstract cones a monotone iterative technique is developed for delay differential equations in a banach space by utilizing the method of upper and lower solutions

on integral operators abstract let fn z z 1 z n 1 n no and f 1 n be defined such that f n f 1 n z 1 z where denotes convolution hadamard product let f be analytic in the unit disc e we define a new operator inf f 1 n f which is analogous to one defined by ruscheweyh using this operator the classes m n are defined a function f analytic in e is in m n if and only if inf is close to convex the properties of f m n are discussed in some detail it is shown that m n m n 1 for n no and for n 0 1 m n consists entirely of univalent functions closure properties of some integral operators defined on m n are also given

an integral equation method for the solution of singular slow flow problems a biharmonic boundary integral equation bbie method is used to solve a two dimensional contained viscous flow problem in order to achieve a greater accuracy than is usually possible in this type of method analytic expressions are used for the piecewise integration of all the kernel functions rather than the more time consuming method of gaussian quadrature

existence and uniqueness of periodic solutions for higher order hyperbolic partial differential equations abstract assuming the smoothness and a generalized lipschitz condition we establish the existence and uniqueness of the periodic solutions of higher order nonlinear hyperbolic partial differential equations

on nonlinear integro differential equations of hyperbolic type abstract this paper considers unified initial boundary value problems for integro differential equations of hyperbolic type for such problems where the forcing functions satisfy certain monotonicity conditions monotone sequences converging to coupled minimal maximal solutions may be constructed from a single pair of coupled lower upper solutions the coupled minimal maximal solutions coincide in a unique solution provided the problem satisfies certain one sided lipschitz conditions

classes of analytic functions associated with the generalized hypergeometric function using the generalized hypergeometric function we introduce and study a class of analytic functions with negative coefficients coefficients estimates distortion theorems extreme points and the radii of convexity and starlikeness for this class are given relevant connections of these results with those in several earlier investigations are indicated

well posedness of nonlocal boundary value problem for a system of loaded hyperbolic equations and an algorithm for finding its solution abstract the article introduces a new general solution to a family of loaded ordinary differential equations and discusses its properties it provides necessary and sufficient conditions for the well posedness of a linear nonlocal boundary value problem for a system of loaded hyperbolic equations with mixed derivatives algorithms for solving the boundary value problems for loaded differential equations are proposed

some subclasses of meromorphically multivalent functions associated with the generalized hypergeometric function in the present paper we introduce and investigate each of the following new subclasses f p k q s a a 1 f g p q s a a 1 f andh p q s a a 1 f as well as f p k q s a a 1 f g p q s a a 1 f andh p q s a a 1 f of meromorphically p valent functions which is defined by means of a certain meromorphically p modified version of the familiar dziok srivastava linear operator involving the generalized hypergeometric function such results as inclusion relationships integral representations and convolution properties for these function classes are proved the results presented here provide extensions of those given in some earlier works several other new results are also obtained

periodic solutions of hyperbolic partial differential equations abstract constructive methods by obtaining multiple solutions of first and second order nonlinear hyperbolic periodic boundary value problems are given appropriate partial differential inequalities are developed and are then employed to derive the iterative schemes which yield the desired solutions the advantage of these methods is that the solutions of the given nonlinear problems are constructed as uniform limits of monotone iterates these iterates being solutions of linear problems are explicitly computable

an extension of the biharmonic boundary integral method to free surface flow in channels abstract the biharmonic boundary integral solution of two dimensional creeping flow of an incompressible newtonian fluid is extended to problems with free surfaces iterative construction of the free surface with the normal stress condition is achieved with a shooting method that is most appropriate for thin films and menisci of widely varying curvature a continuation scheme is also introduced to systematically construct the solution as a function of a given parameter these new techniques combined with the known storage and computational advantages of the biharmonic boundary integral method allow construction of difficult free surfaces we demonstrate this by solving the bretherton problem of a two dimensional air bubble traveling in a channel agreement with asymptotic theory and the finite difference method is shown other problems on formation and transport of bubbles in channels are also tackled

boundary element discretization of plane elasticity and plate bending problems particular attention is paid to the efficiency of the interpolation used in approximating the boundary quantities and to the precision and computational convenience in evaluating the boundary integrals the proposed discretization model is based on the use of a quadratic b spline approximation to represent the boundary variables and on the results from the analytical integration to compute the boundary coefficients

the vallee poussin problem for higher order nonlinear hyperbolic equations for higher order nonlinear hyperbolic equations nonclassical boundary value problems of vallee poussin type are studied and unimprovable in a sense sufficient conditions of solvability unique solvability and well posedness are established