nonlocal differential equations with multivalued perturbations in banach spaces abstract we discuss the existence of mild solutions for nonlocal differential inclusions with multivalued perturbations in banach spaces and establish new existence theorems for related cauchy problems which extend some existing results in this area using the established results we investigate a special nonlocal problem finally we also consider a partial functional differential equation

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

new symplectic 4 manifolds with b 1 in 1995 dusa mcduff and dietmar salamon conjectured the existence of symplectic 4 manifolds x which satisfy b 1 k2 0 k 0 and which fail to be of lefschetz type this is equivalent to finding a symplectic homology t2 s2 manifold with nontorsion canonical class and a cohomology ring which is not isomorphic to the cohomology ring of t2 s2 they needed such examples to complete a list of possible symplectic 4 manifolds with b 1 in that same year tian jun li and ai ko liu working from a different point of view questioned whether there existed symplectic 4 manifolds with b 1 with seiberg witten invariants that did not depend on the chamber structure of the moduli space the purpose of this paper is to construct an infinite number of examples which satisfy both requirements

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

a class of nonlinear evolution equations subjected to nonlocal initial conditions abstract we prove the existence of c 0 solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions of the form u t a u t f t f t f t u t u 0 g u where a d a x x is an m accretive operator acting on the infinite dimensional banach space x f 0 2 d a x is an almost strongly weakly u s c multi function which satisfies an appropriate sign condition while g c 0 2 d a d a is a continuous function

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

exotic smooth structures on small 4 manifolds with odd signatures let m be 2n 1 mathbb cp 2 2n overline mathbb cp 2 for any integer n 1 we construct an irreducible symplectic 4 manifold homeomorphic to m and also an infinite family of pairwise non diffeomorphic irreducible non symplectic 4 manifolds homeomorphic to m we also construct such exotic smooth structures when m is mathbb cp 2 4 overline mathbb cp 2 or 3 mathbb cp 2 k overline mathbb cp 2 for k 6 8 10

knots links and 4 manifolds in this paper we investigate the relationship between isotopy classes of knots and links in s and the di eomorphism types of homeomorphic smooth 4 manifolds as a corollary of this initial investigation we begin to uncover the surprisingly rich structure of di eomorphism types of manifolds homeomorphic to the k3 surface in order to state our theorems we need to view the seiberg witten invariant of a smooth 4 manifold as a multivariable laurent polynomial to do this recall that the seiberg witten invariant of a smooth closed oriented 4 manifold x with b2 x 1 is an integer valued function which is de ned on the set of spinc structures over x cf w km ko1 t1 in case h1 x z has no 2 torsion which will be the situation in this paper there is a natural identi cation of the spinc structures of x with the characteristic elements of h2 x z in this case we view the seiberg witten invariant as

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

mild solutions of semilinear evolution equation on an unbounded interval and their applications the aim of this paper is to give an existence theorem for a semilinear equation of evolution on an unbounded interval in the case when the generator of a semigroup depends on time parameter the considerations of this paper are based on the concept of a measure of noncompactness in frechet space and the classical tichonov fixed point principle moreover an application of the main theorem to the second order parabolic pde is given

necessary and sufficient conditions for delay moments in fifo multiserver queues with an application comparing s slow servers with one fast one in this paper we establish the weakest known sufficient conditions for the existence of stationary delay moments in fifogi gi s queues fors 2 these conditions involve not only the service time distribution as in the classic kiefer and wolfowitz conditions but also the interplay of the traffic intensity and the number of servers in the queue we then prove the necessity of our conditions for a large class of service times having finite first but infinite ath moment for some finite a such service time distributions include many but not all of the class of heavy tailed distributions the pareto and cauchy are members the weibull is not our results are then applied to provide one answer to the classic question when ares slow servers operating at rate 1 s better than one fast server operating at rate 1 we consider this question with respect to the rate of decay of the tail of stationary customer delay in a system characterized by service times that have finite mean but lack some higher moments such as are often used to model telecommunications traffic fors greater than a traffic related constant the answer isalways our results help to quantify the benefits of extra servers while also pointing the way towards the derivation of bounds and asymptotics for the stationary delay distribution of multiserver queues having these types of service times such queues are attracting a great deal of academic research motivated by their practical use modeling telecommunications systems

asymptotic properties of some non autonomous systems in banach spaces abstract let x be a reflexive banach space we introduce the notion of weakly almost nonexpansive sequences x n n 0 in x and study their asymptotic behavior by showing that the nonempty weak limit set of the sequence x n n n 1 always lies on a convex subset of a sphere centered at the origin of radius d lim n x n n subsequently we apply our results to study the asymptotic properties of unbounded trajectories for the quasi autonomous dissipative system d u d t a u f where a is an accretive possibly multivalued operator in x x and f f l p 0 x for some f x and 1 p these results extend recent results of j s jung and j s park j s jung j s park asymptotic behavior of nonexpansive sequences and mean points proc amer math soc 124 1996 475 480 and j s jung j s park and e h park j s jung j s park e h park asymptotic behaviour of generalized almost nonexpansive sequences and applications proc nonlinear funct anal 1 1996 65 79 as well as our results cited below containing previous results by several authors

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

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

nonlocal cauchy problems for neutral functional differential and integrodifferential inclusions in banach spaces in this paper we investigate the existence of mild solutions on a compact interval to initial value problems for neutral functional differential and integrodifferential inclusions in banach spaces with nonlocal conditions the results are obtained by using a fixed point theorem for condensing maps due to martelli