existence of solutions for impulsive neutral functional differential equations with nonlocal conditions abstract the existence uniqueness and continuous dependence of a mild solution of an impulsive neutral functional differential evolution nonlocal cauchy problem in general banach spaces are studied by using the fixed point technique and semigroup of operators

bifurcation properties for a sequence of approximation of delay equations where 1 0 and b ay f x y oforx o see 4 lo or theevenmore restricted equation dx dt a x t 1 the outstanding fact established for the first time by wright lo is the existence of a class of slowly oscillating solutions for 1 in which the trivial solution x 0 appears as an equilibrium whose stability changes with 2 this class determines a convex cone of initial data invariant under the equation and the change of equilibrium the bifurcation to new equilibria can be expressed through a family of poincare operators on the cone in contrast little has been done regarding equations of the type

regular problem for solutions of a retarded semilinear differential nonlocal equation abstract this paper deals with the regularity and existence of solutions of a retarded semilinear differential equation with nonlocal condition by using the fundamental solution in the case where the principal operators are unbounded operators

existence of solutions for semilinear neutral stochastic functional differential equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii fixed point theorem the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions is studied the results are a generalization and continuation of the recent results on this issue an example is provided to illustrate the theory

existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α norm abstract this paper is concerned with the existence of mild and strong solutions for some neutral partial differential equations with nonlocal conditions in the norm the linear part of the equations is assumed to generate a compact analytic semigroup of uniformly bounded linear operators and the nonlinear part satisfies some lipschitz conditions with respect to the norm by using a fixed point theorem of sadovskii we establish some existence results which generalize the recent conclusions on this issue in the end the obtained results will be applied to a class of partial differential equations with nonlocal conditions

integral comparison theorems and extremal points for linear differential equations abstract comparison theorems of integral type are developed for linear differential equations of the form 1 l n y p t y 0 and 2 l n y q t y 0 under the assumption that 2 has no nontrivial solution satisfying given homogeneous two point boundary conditions it follows that the same is true for 1 provided certain sign and integral conditions hold the criteria may be thought of as rather general extensions of the hille wintner type and also include and extend recent results of elias

the existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1 α 2 this paper is mainly concerned with the existence of mild solutions for fractional differential equations with nonlocal conditions of order 1 a 2 the results are obtained by the fixed point theorem combined with solutions operator theorems

existence for neutral impulsive differential inclusions with nonlocal conditions abstract in this paper by using a fixed point theorem for condensing multi valued maps we have investigated the existence of mild solutions for a class of semilinear impulsive neutral functional differential inclusions with nonlocal conditions as an application an example has been presented to illustrate the results obtained

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

on a nonlocal problem for semilinear differential equations with upper semicontinuous nonlinearities in general banach spaces abstract sufficient conditions on the existence of mild solutions for the following semilinear nonlocal evolution inclusion with upper semicontinuous nonlinearity u t a t u t f t u t 0 t d u 0 g u are given when g is completely continuous and lipschitz continuous in general banach spaces respectively an example concerning the partial differential equation is also presented

nonlinear differential equations with nonlocal conditions in banach spaces abstract in this paper we study the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions in banach spaces we derive conditions under which the integral solutions exist

extremal solutions for nth order linear difference equations abstract after the fashion of uri elias we analyze the characteristics of extremal solutions for linear difference equations of the form ly t p t y t 0 where l is an n th order disconjugate linear difference operator given its polya hartman factorization and where p t is nonzero and of constant sign on the interval i a a a 1 this work is based on and extends the work concerning the classification of solutions done by allan peterson and darrel hankerson

existence of nondensely defined evolution equations with nonlocal conditions abstract this paper is concerned with the existence for nondensely defined evolution equations with nonlocal conditions using the techniques of fixed point theory and approximate solutions existence results are obtained for integral solutions when the nonlocal item is lipschitz continuous or continuous respectively examples are also given to illustrate our results

on a new class of abstract integral equations and applications abstract in this paper we introduce a new class of abstract integral equations which enables us to study in a unified manner several different types of differential equations

existence of solutions for nonlocal impulsive partial functional integrodifferential equations via fractional operators in this paper by using the leray schauder alternative we have investigated the existence of mild solutions to first order impulsive partial functional integrodifferential equations with nonlocal conditions in an a norm we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a lipschitz continuous function with respect to the fractional power norm of the linear part an example is also given to illustrate our main results

transform trellis coding of images at low bit rates a transform trellis coding scheme is used to encode images at rates below 1 b pel resulting in high snr values and very good subjective performance a discrete cosine transform dct is used to decorrelate the data samples and a trellis encoder is used to encode the transformed coefficients to overcome image nonstationarity a clustering algorithm is used to segment the transformed image into distinct regions and a separate trellis diagram is then constructed for each cluster to further improve the image quality particularly to reduce the blocking effect a scalar quantizer is used to quantize large magnitude coefficients of the error image in the transform domain the performance of the proposed scheme is found to be better than that of other recently reported schemes

on solutions of neutral nonlocal evolution equations with nondense domain in this paper with sadovskii s and banach s fixed point theorems applied we establish some results on the existence of integral solutions strong solutions and strict solutions for a class of nondensely defined neutral evolution equations with nonlocal conditions also an example is given in the end to show the applications of the obtained results

nonlocal cauchy problems close to an asymptotically stable equilibrium point abstract in this work we investigate the existence of solutions for semilinear cauchy problems with nonlocal initial conditions in the neighborhood of an asymptotically stable equilibrium point of the evolution equation using granas continuation principle for contractive maps and the qualitative theory of differential equations in banach spaces under mild assumptions we prove the existence of a unique solution we also show that the main abstract result can be applied to nonlocal initial boundary value problems for reaction diffusion equations with non convex nonlinearities

on the factorizations of ordinary linear differential operators etude des modes de factorisation de certains operateurs differentiels lineaires d ordre n a l aide des wronskiens

discrete polynomial interpolation green s functions maximum principles error bounds and boundary value problems abstract we construct discrete interpolating polynomials provide explicit representations of discrete green s functions give several identities and inequalities for these green s functions use the explicit forms of the interpolating polynomials and that of green s functions to establish several maximum principles further we obtain error bounds in discrete polynomial interpolation and use them to study existence and uniqueness of the discrete boundary value problems these bounds are also used to provide sufficient conditions for the convergence of the picard s method the approximate picard s method quasilinearization and the approximate quasilinearization the monotone convergence of the picard s iterative method is also analysed

a classification of the solutions of a differential equation according to their behaviour at infinity ii the solutions of the differential equation l n y p y 0 where l n is a disconjugate operator are classified according to their behaviour as the solution space is decomposed into disjoint sets we study the dominance properties of the solutions which belong to different sets

existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators abstract this paper is mainly concerned with existence of mild solutions for a first order impulsive neutral integrodifferential inclusions with nonlocal initial conditions in norm we assume that the linear part generates an analytic semigroup and transform it into an integral inclusion by using a fixed point theorem for multi valued maps due to dhage a main existence theorem is established finally we present an example to illustrate this main theorem

nonlocal nonlinear differential equations with a measure of noncompactness in banach spaces abstract in this paper we give the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions under the assumptions of the hausdorff measure of noncompactness in separable and uniformly smooth banach spaces

the method of lines applied to nonlinear nonlocal functional differential equations this paper discusses nonlinear functional differential equation in a real reflexive banach space with nonlocal history condition by using the method of lines the existence and uniqueness of a strong solution are established finally some applications of the abstract results are presented

semilinear integrodifferential equations with nonlocal initial conditions abstract of concern is the cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions under general and natural hypotheses we establish some new theorems about the existence and uniqueness of solutions for the cauchy problem as a consequence we unify and extend the corresponding theorems given previously for the cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions moreover we present two examples one of which comes from heat conduction in materials with memory to show that the existing results are not applicable to them in contrast with ours

controllability of impulsive differential systems with nonlocal conditions abstract the paper is concerned with the controllability of impulsive functional differential equations with nonlocal conditions using the measure of noncompactness and monch fixed point theorem we establish some sufficient conditions for controllability firstly we require the equicontinuity of evolution system and next we only suppose that the evolution system is strongly continuous since we do not assume that the evolution system generates a compact semigroup our theorems extend some analogous results of impulsive control systems

a classification of the solutions of a difference equation according to their behavior at infinity on considere l equation aux differences lineaires d ordre n ly t p t y t 0 ou p t est de signe defini sur a a a 1 a est un entier

growth properties of solutions to a linear differential equation on compare les proprietes de dominance des solutions de lny p x y 0 ou ln est un operateur non conjugue aux proprietes de dominance des solutions de son adjointe

focal boundary value problems for nonlinear difference equations ii on considere l unicite des solutions impliquant l existence des solutions de problemes aux valeurs limites de type focal pour l equation aux differences non lineaire d ordre n u t n f t u t u t n 1 ou f a r n r est continue et l equation u n 1 f t u 1 u n peut etre resolue pour u 1 comme fonction continue des variables t u 2 u u 1

existence results of semilinear differential equations with nonlocal initial conditions in banach spaces abstract in this paper we establish the existence results for semilinear differential systems with nonlocal initial conditions in banach spaces the approaches used are fixed point theorems combined with convex power condensing operators the first result obtained will be applied to a class of semilinear parabolic equations

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

existence of solutions for neutral functional differential evolution equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii s fixed point theorem we study the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions the results we obtained are a generalization and continuation of the recent results on this issue in the end an example is given to show the application of our results

existence of solutions for a class of abstract differential equations with nonlocal conditions abstract we discuss the existence of mild classical and strict solutions for a class of abstract differential equations with nonlocal conditions our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution some concrete applications to partial differential equations are considered

existence uniqueness and regularity of solutions to semilinear nonlocal functional differential problems abstract in this paper we consider a semilinear nonlocal functional differential problem in a banach space we first establish the existence uniqueness and continuation of a mild solution we then prove some regularity results for this mild solution under different conditions finally we consider some applications of the abstract results

existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions abstract in this work we establish several results about the existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions we assume that the linear part generates a strongly continuous semigroup on a general banach space

a trellis code construction and coding theorem for stationary gaussian sources corresp for stationary discrete time gaussian sources and the squared error distortion measure a trellis source code is constructed the encoder consists of a karhunen loeve transform on the source output followed by a search on a trellis structured code where the decoder is a time variant nonlinear filter the corresponding code theorem is proved using the random coding argument the proof technique follows that of viterbi and omura who proved the trellis coding theorem for memoryless sources the resultant coding scheme is implementable and applicable at any nonzero rate to a stationary gaussian source with a bounded and continuous power spectrum therefore for stationary sources it is more general than berger s tree coding scheme which is restricted to autoregressive gaussian sources in a region of high rate low distortion

existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions abstract this paper deals with a nonlocal problem governed by the nonlinear differential inclusions with multivalued perturbations in banach spaces first using the approach of geometry of banach space hausdorff metric the measure of noncompactness and fixed point existence results are obtained we have removed from previous papers the crucial restriction on the semigroup then we establish the asymptotic properties of integral solutions when t finally for illustration a partial differential equation is worked out

approximations of solutions to neutral functional differential equations with nonlocal history conditions abstract this work is concerned with a class of neutral functional differential equations with nonlocal history conditions in a hilbert space the approximation of solution to a class of such problems is studied moreover the convergence of faedo galerkin approximation of solution is shown for illustration an example is worked out