hopf bifurcation in a delayed reaction diffusion advection population model abstract in this paper we investigate a reaction diffusion advection model with time delay effect the stability instability of the spatially nonhomogeneous positive steady state and the associated hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction diffusion advection model and the model can exhibit oscillatory pattern through hopf bifurcation the effect of advection on hopf bifurcation values is also considered and our results suggest that hopf bifurcation is more likely to occur when the advection rate increases

hopf bifurcation in a diffusive lotka volterra type system with nonlocal delay effect abstract the dynamics of a diffusive lotka volterra type model for two species with nonlocal delay effect and dirichlet boundary conditions is investigated in this paper the existence and multiplicity of spatially nonhomogeneous steady state solutions are obtained by means of lyapunov schmidt reduction the stability of spatially nonhomogeneous steady state solutions and the existence of hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system by the normal form theory and the center manifold reduction the stability and bifurcation direction of hopf bifurcating periodic orbits are derived finally our theoretical results are illustrated by a model with homogeneous kernels and one dimensional spatial domain

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

blow up of solutions of semilinear euler poisson darboux equations with nonlocal boundary conditions this article studies the hyperbolic initial nonlocal boundary value problem u t t k t u t u x x u 0 0 u x 0 u 0 x u t x 0 0 0 0 u a t 0 an y u y t q dy t 0 where k is a real number p and q are nonnegative constants and u 0 m and n are given functions criteria for u to blow up in finite time are given

spatially nonhomogeneous equilibrium in a reaction diffusion system with distributed delay we consider a reaction diffusion system with general time delayed growth rate and kernel functions the existence and stability of the positive spatially nonhomogeneous steady state solution are obtained moreover taking minimal time delay as the bifurcation parameter hopf bifurcation near the steady state solution is proved to occur at a critical value 0 especially the hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold the general results are applied to competitive and cooperative systems with weak or strong kernel function respectively

boundary value problems for second order nonlinear differential equations on infinite intervals in this paper we consider boundary value problems for nonlinear differential equations on the semi axis 0 and also on the whole axis under the assumption that the left hand side being a second order linear differential expression belongs to the weyl limit circle case the boundary value problems are considered in the hilbert spaces l2 0 and l2 and include boundary conditions at infinity the existence and uniqueness results for solutions of the considered boundary value problems are established

multiple solutions of singular three point boundary value problems on 0 abstract in this paper we study the existence of single and multiple solutions of three point boundary value problems for the following nonlinear singular second order differential equations x t p x t q x t h t f t x t 0 t 0 a x 0 b x 0 k x c 0 lim t x t e r t d 0 where p b 0 a k 0 q 0 0 r 0 p p 2 4 q 2 h 0 0 is continuous and may be singular at t 0 f 0 0 is continuous and may take a negative value by applying the technique of lower and upper solutions and the theory of topological degree we obtain the conditions for the existence of at least one solution and at least three solutions respectively

unbounded solutions for three point boundary value problems with nonlinear boundary conditions on 0 abstract the existence and multiplicity of unbounded solutions is investigated for second order three point differential equations with nonlinear boundary conditions on 0 where the growth of the nonlinear term with respect to the third variable is allowed to be quadratic by applying the techniques of unbounded upper and lower solutions and the topological degree theory the existence of at least one solution and three solutions respectively is shown for the above problem one example is worked out to indicate the applications of our main results

bivariate splines on hexagonal lattice for digital image processing in this paper the applications of multi variable spline functions in the digital signal processing was investigated further several two dimensional spline functions were constructed for hexagonal lattice they are actually variation of bivariate cardinal splines on regular triangular partition that were constructed earlier those bivariate cardinal splines have a number of desirable features which make it applicable for image processing and other areas one feature lies in the fact that the coefficients of the interpolation representations with bivariate cardinal splines are basically the sample data at the interpolation points the interpolations converge uniformly to the function being interpolated as the sampling increment approaches zero compare to the popular tensor product with the same degree of smoothness our bivariate cardinal splines has the same degree of accuracy with smaller local support lower degree of the polynomials therefore it should lead to the reduction of computation time and storage space

existence of at least three solutions of a second order three point boundary value problem abstract we study existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type x f t x x t i 0 1 x 0 0 x 1 x 0 1 0 1 the growth of f with respect to x is allowed to be quadratic we use some degree theory arguments to get the multiplicity result

singular boundary value problems on a half line singular boundary value problems of nonlinear second order differential equations on a half line are considered the main methods used are modified upper and lower solution techniques necessary and sufficient conditions for the existence of solutions to a class of sublinear singular boundary value problems are obtained

singular boundary value problems for superlinear second order ordinary and delay differential equations abstract existence criteria are established for singular boundary value problems for nonlinear second order ordinary and delay differential equations the theorems obtained are very general and complement previous known results

existence theory for nonlinear fredholm and volterra integral equations on half open intervals in this chapter we present existence theory for the nonlinear fredholm integral equation y t h t smallint 0 t k t s g s y s ds 4 1 1 and the nonlinear volterra integral equation y t h t smallint 0 t k t s g s y s ds 4 1 2 when both are defined on the compact interval 0 t naturally we first concern ourselves with existence principles for both 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

two dimensional spline interpolation for image reconstruction a scheme of two dimensional 2 d spline interpolation for image reconstruction is presented it is aimed to be applied in image data compression an impulse response derived from 2 d quadratic spline functions is theoretically analysed then it is approximated to be a finite duration one fir for practical implementation with this scheme compression rate of greater than 12 is achieved for x ray left ventricular cineangiogram image data compression

monotone iterative method for the second order three point boundary value problem with upper and lower solutions in the reversed order abstract this article introduces a new concept of upper and lower solutions and studies the existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order the sufficient conditions for the existence and uniqueness of solutions are obtained by using the monotone iterative method meantime the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution are given some results of previous literature are extended and improved a numerical example is also included to illustrate the effectiveness of the proposed results

positive solution of singular dirichlet boundary value problems for second order differential equation system this paper investigates the existence of positive solutions of singular dirichlet boundary value problems for second order differential system a necessary and sufficient condition for the existence of c 0 1 c 0 1 positive solutions as well as c1 0 1 c1 0 1 positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems our nonlinearity fi t x1 x2 may be singular at x1 0 x2 0 t 0 and or t 1 i 1 2

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

twin solutions to singular dirichlet problems the existence of two nonnegative solutions to dirichlet second order boundary value problems is established in this paper our nonlinearity may be singular at y 0 t 0 and or t 1

multiple positive solutions of the singular boundary value problems for second order differential equations on the half line abstract in this paper the existence of multiple positive solutions for singular sturm liouville boundary value problems on the half line is investigated by applying the fixed point index theorem of cone map some existence and multiplicity results of positive solutions are derived our results improve and generalize many well known results two examples are presented to demonstrate the application of our main results

solutions in weighted spaces of singular boundary value problems on the half line in this paper we establish the existence of an unbounded solution to a second order boundary value problem on the half line also the existence of multiple unbounded positive solutions is discussed using the theory of fixed point index

input output properties of the page hinkley detector we consider the stochastic input output properties of a simple non linear dynamical system the so called page hinkley detector playing a key role in change detection and also in queuing theory we show that for l mixing inputs with negative expectation the output process of this system is l mixing the result is applied to get an upper bound for the false alarm rate the proof is then adapted to get a similar result for the case of random i i d inputs possible extensions and open problems are given in the discussion

existence of positive solutions for a semipositone boundary value problem on the half line in this paper we consider the boundary value problem on the half line x t k 2 t x t lm t f t x t 0 t 0 x 0 0 limt x t 0 where k 0 0 and f 0 x 0 r are continuous we show the existence of positive solutions by using a fixed point theorem in cones

hopf bifurcation in a reaction diffusion equation with distributed delay and dirichlet boundary condition abstract the stability and hopf bifurcation of the positive steady state to a general scalar reaction diffusion equation with distributed delay and dirichlet boundary condition are investigated in this paper the time delay follows a gamma distribution function through analyzing the corresponding eigenvalue problems we rigorously show that hopf bifurcations will occur when the shape parameter n 1 and the steady state is always stable when n 0 by computing normal form on the center manifold the direction of hopf bifurcation and the stability of the periodic orbits can also be determined under a general setting our results show that the number of critical values of delay for hopf bifurcation is finite and increasing in n which is significantly different from the discrete delay case and the first hopf bifurcation value is decreasing in n examples from population biology and numerical simulations are used to illustrate the theoretical results

existence of positive solutions for second order semipositone differential equations on the half line in this paper by means of constructing a special cone we obtain a sufficient condition for the existence of positive solution for semipositone singular sturm liouville boundary value problem on the half line the results obtained generalize and improve the corresponding results of zhang and liu in papers x g zhang l s liu positive solutions of superlinear semipositone singular dirichlet boundary value problems j math anal appl 316 2006 525 537 y s liu existence and unboundedness of positive solutions for singular boundary value problems on half line appl math comput 144 2003 543 556

stability and bifurcation analysis of a reaction diffusion equation with spatio temporal delay abstract the spatio temporal patterns of a general reaction diffusion equation with non local delay are considered by analyzing the characteristic equations and applying the complex plane theory the stability of the constant steady state and the possible hopf bifurcations are obtained with the mean delay as a bifurcation parameter the absolute stable conditional stable and unstable region can be explicitly divided by the coefficients of the term without delay and the term with non local delay by investigating the effect of any weight function on the dynamics of the system we establish the existence of spatially homogeneous and inhomogeneous bifurcating periodic solutions and the algorithm for determining the direction and stability of hopf bifurcation is derived by computing the normal form on the center manifold the result shows that for the case of strong kernel the average delay may induce the stability switches finally the theoretical results are applied to a diffusive food limited population model numerical simulations show the existence of the orbit connecting the unstable spatially inhomogeneous periodic solutions to stable spatially homogeneous periodic solutions

order continuous of monotone set function and convergence of measurable functions sequence in this paper we introduce the concept of strongly order continuity of a set function and use it to investigate the convergence of measurable functions sequence and of integral sequence on fuzzy measure space several equivalent conditions of strongly order continuity are presented it is shown that a necessary and sufficient condition that lebesgue s theorem remains valid for a monotone set function is that the set function possesses strongly order continuity

calculus of variations for a boundary value problem of differential system on the half line boundary value problem of second order differential equations on the half line is investigated in this paper the method mainly depends on the calculus of variations to the classical functionals sufficient conditions are obtained for the existence of the solutions

simple algorithms and architectures for b spline interpolation it is proved that the toeplitz binary value matrix inversion associated with mth order b spline interpolation can be implemented using only 2 m 1 additions pipelined architectures are developed for real time b spline interpolation based on simple running average filters it is shown that an ideal interpolating function which is approximated by a truncated sinc function with m half cycles can be implemented using b splines with m 2 multiplies with insignificant loss of performance the coefficients at the knots of the truncated sinc function can be approximated using coefficients which are powers of two the resulting implementation requires only m 4m 6 additions it is believed that the truncated sinc function approximated by zero order b spline functions actually achieves the best visual performance

change detection in teletraffic models we propose a likelihood based ratio test to detect distributional changes in common teletraffic models these include traditional models like the markov modulated poisson process and processes exhibiting long range dependency in particular gaussian fractional arima processes a practical approach is also developed for the case where the parameter after the change is unknown it is noticed that the algorithm is robust enough to detect slight perturbations of the parameter value after the change a comprehensive set of numerical results including results for the mean detection delay is provided

multivariate spline spaces in principle all of the properties and applications of multivariate spline functions can be derived from the basic theories in chapter 1 the expressions of the multivariate spline functions in 2 of chapter 1 are inconvenient to be applied directly because the expressions also rely on the solutions of the global conformality conditions so as to determine all the smooth cofactors

approximation by smooth multivariate splines abstract one of the important properties of univariate splines is that in most senses smooth splines approximate just as well as do piecewise polynomials on the same mesh this report shows this to be untrue in the multivariate setting in particular it details the cost in approximating power one may have to pay for the luxury of a smooth piecewise polynomial approximant in an extreme case piecewise polynomials of total degree r on a rectangular grid with all derivatives of order or rho continuous will fail to approximate certain smooth functions at all as the grid goes to zero unless rho is kept below r 3 2 during the analysis of approximation on a certain regular triangular grid a novel kind of bivariate b spline is introduced this b spline in contrast to the established multivariate b spline derived from a simplex can be made to have all its breaklines in a given regular grid this makes it a prime candidate for use in the construction of smooth multivariate piecewise polynomial approximation and its properties will be explored further

multiple change point analysis fast implementation and strong consistency one of the main challenges in identifying structural changes in stochastic processes is to carry out analysis for time series with dependency structure in a computationally tractable way another challenge is that the number of true change points is usually unknown requiring a suitable model selection criterion to arrive at informative conclusions to address the first challenge we model the data generating process as a segment wise autoregression which is composed of several segments time epochs each of which modeled by an autoregressive model we propose a multiwindow method that is both effective and efficient for discovering the structural changes the proposed approach was motivated by transforming a segment wise autoregression into a multivariate time series that is asymptotically segment wise independent and identically distributed to address the second challenge we derive theoretical guarantees for almost surely selecting the true number of change points of segment wise independent multivariate time series specifically under mild assumptions we show that a bayesian information criterion like criterion gives a strongly consistent selection of the optimal number of change points while an akaike information criterion like criterion cannot finally we demonstrate the theory and strength of the proposed algorithms by experiments on both synthetic and real world data including the eastern u s temperature data and the el nino data the experiment leads to some interesting discoveries about temporal variability of the summer time temperature over the eastern u s and about the most dominant factor of ocean influence on climate which were also discovered by environmental scientists

persistence and extinction in two species reaction diffusion systems with delays abstract both uniform persistence and global extinction are established for two species predator prey and competition reaction diffusion systems with delays in terms of the principal eigenvalues of the scalar elliptic eigenvalue problems by appealing to the theories of abstract persistence asymptotically autonomous semiflows and monotone dynamical systems

eigenvalues of a general class of boundary value problem with derivative dependent nonlinearity we consider a general class of boundary value problem bvp comprising the differential equation y m t f t y t y t y t y q t t 0 1 where 1 q m 1 and 0 together with multi point boundary conditions y 0 y 0 y 0 y q 1 0 0 a i y q t j y q 1 t j y m 1 t j 0 j r 0 1 i m q where 0 t 0 t 1 t r 1 particular cases of this general bvp include the well known abel gontscharoff focal m p sturm liouville and complementary lidstone bvps it is noted that bvps with derivative dependent nonlinear terms are less investigated in the literature due to technical difficulty in this paper a new technique is developed to characterize the eigenvalues so that the bvp has a positive solution explicit eigenvalue intervals are also established we include several well known examples in the literature to illustrate the results obtained

solvability of some nonlinear boundary value problems on etablit l existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme y f t y y o o t 1

structure of a class of singular boundary value problem with superlinear effect abstract this paper investigates the structure of solutions of singular boundary value problem with superlinear effect it is proved that the closure of positive solution set possesses a maximal subcontinuum c i e a maximal closed connected subset of solutions which comes from 0 and tends to 0 finally as a corollary the existence of multiple positive solutions and the behavior of solutions according to parameter are obtained

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

existence and uniqueness for an m point boundary value problem at resonance on infinite intervals this paper investigates an m point boundary value problem with nonlinear boundary conditions at resonance on infinite intervals by establishing a general continuation theorem the existence and uniqueness of unbounded solutions is obtained on the basis of a suitable homotopy leray schauder degree properties and a priori estimate this paper provides a new method to solve boundary value problems with nonlinear boundary conditions at resonance on infinite intervals

boundary value problems for impulsive integro differential equations on unbounded domains in a banach space in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of two point boundary value problems bvps for second order non linear impulsive integro differential equations on infinite intervals in a banach space

unbounded solutions for singular boundary value problems on the semi infinite interval upper and lower solutions and multiplicity this paper presents a lower and upper solution technique for singular second order boundary value problems on the half line and discusses sufficient and necessary conditions for the existence of positive solutions also multiplicity is discussed using the fixed point index

unbounded upper and lower solutions method for sturm liouville boundary value problem on infinite intervals abstract unbounded upper and lower solutions theories are established for the sturm liouville boundary value problem of a second order ordinary differential equation on infinite intervals by using such techniques and the schauder fixed point theorem the existence of solutions as well as the positive ones is obtained nagumo conditions play an important role in the nonlinear term involved in the first order derivatives

unbounded solutions of the singular boundary value problems for second order differential equations on the half line this paper presents some results on the existence of multiple unbounded solutions for the boundary value problems for second order differential equations on half line and on the uniqueness of unbounded solution

dynamics of the diffusive nicholson s blowflies equation with distributed delay in this paper we study the diffusive nicholson s blowflies equation generalizing previous works we model the generation delay by using an integral convolution over all past times and results are obtained for general delay kernels as far as possible the linearized stability of the non zero uniform steady state is studied in detail mainly by using the principle of the argument global stability both of this state and of the zero state are studied by using energy methods and by employing a comparison principle for delay equations finally we consider what bifurcations are possible from the non zero uniform state in the case when it is unstable

stability and bifurcation in a reaction diffusion model with nonlocal delay effect in this paper the existence stability and multiplicity of spatially nonhomogeneous steady state solution and periodic solutions for a reaction diffusion model with nonlocal delay effect and dirichlet boundary condition are investigated by using lyapunov schmidt reduction moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

hopf bifurcation for a delayed predator prey diffusion system with dirichlet boundary condition a delayed predator prey diffusion system with beddington deangelis functional response under dirichlet boundary condition is investigated the existence and stability of the positive spatially nonhomogeneous steady state solution are obtained via the implicit function theorem moreover taking feedback time delay as the bifurcation parameter hopf bifurcation near the positive steady state solution is proved to occur at a sequence of critical values we can show that feedback time delay can induce nonhomogeneous periodic oscillatory patterns the direction of hopf bifurcation is forward when parameter m in model 1 2 is sufficiently large numerical simulations and numerical solutions are presented to illustrate our theoretical results

polynomial spline signal approximations filter design and asymptotic equivalence with shannon s sampling theorem the least squares polynomial spline approximation of a signal g t in l sub 2 r is obtained by projecting g t on s sup n r the space of polynomial splines of order n it is shown that this process can be linked to the classical problem of cardinal spline interpolation by first convolving g t with a b spline of order n more specifically the coefficients of the b spline interpolation of order 2n 1 of the sampled filtered sequence are identical to the coefficients of the least squares approximation of g t of order n it is shown that this approximation can be obtained from a succession of three basic operations prefiltering sampling and postfiltering which confirms the parallel with the classical sampling reconstruction procedure for bandlimited signals the frequency responses of these filters are determined for three equivalent spline representations using alternative sets of shift invariant basis functions of s sup n r the standard expansion in terms of b spline coefficients a representation in terms of sampled signal values and a representation using orthogonal basis functions

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

solutions of impulsive boundary value problems on the half line abstract this paper presents some existence results for a class of impulsive boundary value problems with nonhomogeneous boundary data on the half line by applying fixed point theorems on cones we obtain the existence of positive bounded and unbounded solutions our methods are integral equations approximate solutions a priori bounds and modified arzela techniques

a necessary and sufficient condition for existence of positive solutions of nonlinear boundary value problems abstract we study the nonlinear boundary value problem u f t u u u t 0 1 u 2 i 0 u 2 i 1 0 i 0 1 and obtain a necessary and sufficient condition for the existence of symmetric positive solutions we also discuss the application of our result to the special case where f is a power function of u and its derivatives moreover similar conclusions for a more general higher order boundary value problem are established our analysis mainly relies on the lower and upper solution method

normal forms and hopf bifurcation for partial differential equations with delays the paper addresses the computation of normal forms for some partial functional differential equations pfdes near equilibria the analysis is based on the theory previously developed for autonomous retarded functional differential equations and on the existence of center or other invariant manifolds as an illustration of this procedure two examples of pfdes where a hopf singularity occurs on the center manifold are considered

stability and bifurcations in a nonlocal delayed reaction diffusion population model abstract a nonlocal delayed reaction diffusion equation with dirichlet boundary condition is considered in this paper it is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium the stability instability of the bifurcated positive equilibrium and associated hopf bifurcation are investigated providing us with a complete picture of the dynamics

existence and unboundedness of positive solutions for singular boundary value problems on half line by constructing a special cone and using cone compression and expansion fixed point theorem this paper presents some existence results of positive solutions of singular boundary value problem bvp for short on half line for a class of second order differential equations at the same time the boundedness and unboundedness of positive solutions for bvp are considered also

stability analysis of a stage structure model with spatiotemporal delay effect this paper is concerned with a stage structure model with spatiotemporal delay and homogeneous dirichlet boundary condition the existence of steady state solution bifurcating from the trivial equilibrium is obtained by using lyapunovschmidt reduction the stability analysis of the positive spatially nonhomogeneous steady state solution is investigated by a detailed analysis of the characteristic equation using the properties of the omega limit set we obtain the global convergence of the solution with finite delay

boundary value problems on the half line with impulses and infinite delay this paper presents some results on the existence and uniqueness of solutions for the boundary value problems on the half line with impulses and infinite delay moreover an existence theorem of multiple solutions is obtained also the problems may be singular at the boundary

boundary value problems on half line for functional differential equations with infinite delay in a banach space in this paper the monch fixed point theorem is used to investigate the existence of unbounded solutions of boundary value problem for functional differential equations with infinite delay in a banach space moreover an uniqueness theorem is obtained also

necessary and sufficient conditions for the existence of symmetric positive solutions of multi point boundary value problems abstract we study the nonlinear boundary value problem with multi point boundary condition u p 1 u f t u u u t 0 1 u 2 i 0 u 2 i 1 j 1 m a i j u 2 i t j i 0 1 necessary and sufficient conditions are obtained for the existence of symmetric positive solutions of this problem using fixed point theorems on cones applications of our results to the special case where f is a power function of u and its derivatives are also discussed moreover similar conclusions for a more general higher order boundary value problem are established our results extend some recent work in the literature on boundary value problems for ordinary differential equations

global structure of solutions for a class of two point boundary value problems involving singular and convex or concave nonlinearities abstract this paper investigates the following two point singular boundary value problems bvp x t x q x p t 0 1 x t 0 t 0 1 x 0 x 1 0 where q 0 and p 0 are fixed given numbers r 0 is a parameter the results obtained are the global structure of solutions and exact number of solutions when p 1 or p 1 and q is sufficiently small

positive solutions for singular semipositone boundary value problems on infinite intervals by using the fixed point theory on a cone with a special norm and space we discuss the existence of positive solutions for a class of semipositone boundary value problems on infinite intervals the work improves many known results including singular and non singular cases

bivariate box splines and smooth pp functions on a three direction mesh abstract let s denote the space of bivariate piecewise polynomial functions of degree k and smoothness on the regular mesh generated by the three directions 1 0 0 1 1 1 we construct a basis for s in terms of box splines and truncated powers this allows us to determine the polynomials which are locally contained in s and to give upper and lower bounds for the degree of approximation for 2k 2 3 k 2 3 the case of minimal degree k for given smoothness we identify the elements of minimal support in s and give a basis for s loc f s supp f with a convex subset of r 2