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Let (M,0T″) be a compact strongly pseudo convex CR structure with dimRM=2n-1. Then, in [Michigan Math. J. 50 (2002) 517–549], the construction of the versal family of CR structures is settled. The purpose of this paper is to introduce a canonical Kaehler metric for the parameter space of this versal family if the CR structure admits a normal vector field and a non-vanishing CR n-form with the condition H1(M,OM)=0 and where Z1 is introduced in [Compositio Math. 85 (1993) 57–85]. [Copyright &y& Elsevier]

Abstract: An n species nonautonomous competitive Lotka–Volterra system is considered in this paper. The average conditions on the coefficients are given to guarantee that all but one of the species are driven to extinction. The generalization for the result is presented, that is, for each the average conditions on the coefficients are provided to guarantee that r of the species in the system are permanent while the remaining are driven to extinction. It is shown that these average conditions are improvement of those of Ahmad and Montes de Oca [Appl. Math. Comput. 90 (1998) 155–166] and Montes de Oca and Zeeman [Proc. Amer. Math. Soc. 124 (1996) 3677–3687] and [J. Math. Anal. Appl. 192 (1995) 360–370]. [Copyright &y& Elsevier]

In this paper we generalize, under slightly more restrictive conditions on the kernel K, the classical theorem on halfspace estimates of Agmon, Douglis and Nirenberg [Comm. Pure Appl. Math. 12 (1959) 623–727] to generalized Lebesgue spaces . In particular this yields -estimates in for the Laplace equation and the Stokes system. [Copyright &y& Elsevier]

In the case of oscillatory potentials, we establish an oscillation theorem for the forced sublinear differential equation , . No restriction is imposed on the forcing term to be the nth derivative of an oscillatory function. In particular, we show that all solutions of the equation , , are oscillatory for all if . This provides an analogue of a result of Nasr [Proc. Amer. Math. Soc. 126 (1998) 123] for the forced superlinear equation and answers a question raised in an earlier paper [J.S.W. Wong, SIAM J. Math. Anal. 19 (1988) 673]. [Copyright &y& Elsevier]

The aim of this paper is to study Birkhoff integrability for multi-valued maps F :Ω→cwk(X), where (Ω,Σ,μ) is a complete finite measure space, X is a Banach space and cwk(X) is the family of all non-empty convex weakly compact subsets of X. It is shown that the Birkhoff integral of F can be computed as the limit for the Hausdorff distance in cwk(X) of a net of Riemann sums ∑nμ(An)F(tn). We link Birkhoff integrability with Debreu integrability, a notion introduced to replace sums associated to correspondences when studying certain models in Mathematical Economics. We show that each Debreu integrable multi-valued function is Birkhoff integrable and that each Birkhoff integrable multi-valued function is Pettis integrable. The three previous notions coincide for finite dimensional Banach spaces and they are different even for bounded multi-valued functions when X is infinite dimensional and X* is assumed to be separable. We show that when F takes values in the family of all non-empty convex norm compact sets of a separable Banach space X, then F is Pettis integrable if, and only if, F is Birkhoff integrable; in particular, these Pettis integrable F''s can be seen as single-valued Pettis integrable functions with values in some other adequate Banach space. Incidentally, to handle some of the constructions needed we prove that if X is an Asplund Banach space, then cwk(X) is separable for the Hausdorff distance if, and only if, X is finite dimensional. [Copyright &y& Elsevier]

In this paper, the unbounded solutions for the following nonlinear planar system: is discussed, where a±,b± are positive constants satisfying x±=max{±x,0}, y±=max{±y,0}, ω∈R+&z.drule;Q, f(t),g(t)∈L∞[0,2π] are 2π-periodic functions. [Copyright &y& Elsevier]

In this paper, we study a 2D dissipative Klein–Gordon equation with periodic boundary condition. The existence and uniqueness of a time-periodic solution is proved by the Galerkin method and Leray–Schauder fixed point theorem. [Copyright &y& Elsevier]

Let U(p,k) denote the class of functions f which are areally mean p-valent and have k maximal growth directions in Δ={z: &z.sfnc;z&z.sfnc;<1}. In this paper we give an asymptotic formula of the mean square of the logarithmic derivative f′/f for f∈U(p,k) with some restricted condition. This generalizes the corresponding result in [J. Anal. Math. 36 (1979) 36–43]. Also we construct a function f∈U(p,k) which does not satisfy this asymptotic formula. [Copyright &y& Elsevier]

In this paper, new classes of generalized (F,α,ρ,d)-type I functions are introduced for differentiable multiobjective programming. Based upon these generalized functions, first, we obtain several sufficient optimality conditions for feasible solution to be an efficient or weak efficient solution. Second, we prove weak and strong duality theorems for mixed type duality. [Copyright &y& Elsevier]

The paper presents new random fixed point results for pseudo-contractive random operators. [Copyright &y& Elsevier]

This paper is concerned with a class of quasilinear parabolic equations with singularity and arbitrary degeneracy. The existence and uniqueness of generalized solutions to a kind of boundary value problem is established. [Copyright &y& Elsevier]

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered. [Copyright &y& Elsevier]

In this paper, Schaefer''s fixed point theorem and nonlinear alternative of Leray–Schauder type are used to investigate the existence of solutions for second order boundary value problem for impulsive dynamic equations on time scales. [Copyright &y& Elsevier]

This paper investigates the existence of minimal and maximal solutions of periodic boundary value problem for first order impulsive integro-differential equations of mixed type by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique. [Copyright &y& Elsevier]

In this paper, we will study two classes of difference equations which are piecewise-linear and of similar forms. We will show that all non-trivial solutions of both equations are eventually periodic with prime period six. [Copyright &y& Elsevier]

Pantograph type equations have been studied extensively owing to the numerous applications in which these equations arise. These studies focused primarily on the case when the functional argument is linear, and the origin is either a repelling or attracting fixed point. The nonlinear case has been studied by Oberg [Trans. Amer. Math. Soc. 161 (1971) 302–327] and Marshall et al. [J. Math. Anal. Appl. 268 (2002) 157–170], but the focus again was on repelling or attracting fixed points. Oberg (op. cit.), however, did consider briefly the neutral fixed point case and found a connexion with Siegel discs. In this paper we build on Oberg''s work and study the neutral fixed point case. We show that, for nonlinear functional arguments with neutral fixed points, pantograph type equations have nonconstant holomorphic solutions only if the functional argument has a Siegel disc centered at the fixed point. We then show that the boundary of the Siegel disc forms a natural boundary for the nonconstant holomorphic solutions. [Copyright &y& Elsevier]

In this paper, we consider generalized vector pre-variational inequality problems as well as vector pre-quasivariational inequality problems in abstract space setting. We establish several existence results for these two classes of problems by employing the Ky Fan lemma and a scalarization technique, respectively. [Copyright &y& Elsevier]

In this paper the approach via time-map is used to investigate the existence of periodic solutions for second order equation with time-dependent potential. Our theorem generalized the results obtained by Ding, Habets, Omari and Zanolin which are for time-independent potential and relate the behavior of the primitive of the nonlinearity with respect to the Fučik spectrum of the periodic problem. [Copyright &y& Elsevier]

In this paper, both the local and global weighted Sobolev–Poincaré imbedding inequalities and Poincaré inequalities for the composition T∘G are established, where T is the homotopy operator and G is Green''s operator applied to A-harmonic forms on manifolds. [Copyright &y& Elsevier]

In this paper, we will investigate the generalized Hyers–Ulam–Rassias stability of an n-dimensional quadratic functional equation in Banach modules over a C*-algebra and unitary elements. [Copyright &y& Elsevier]

The object of the present paper is to investigate some properties of certain integral operator Qβα introduced and studied recently by Jung, Kim, and Srivastava [J. Math. Anal. Appl. 176 (1993) 138–147]. [Copyright &y& Elsevier]

After the analysis of the q-even translation and the q-cosine Fourier transform by A. Fitouhi and F. Bouzeffour in [q-cosine Fourier transform and q-heat equation, Ramanujan J., in press], it is natural to look for the q-analogue of some well-known classical theorems. In this paper, we purpose to give a q-version of the Paley–Wiener theorem related to this Fourier transform using standard methods of the q-calculus. [Copyright &y& Elsevier]

In the paper we shall present a survey of recent results on substochastic semigroups and provide new methods for determining their honesty. These methods are applied to the fragmentation equation with mass loss, yielding sufficient conditions for the existence of conservative and shattering solutions. Our results provide a mathematical framework that clarifies the discussion of [Phys. Rev. A 43 (1991) 656, Phys. Rev. A 41 (1990) 5755, J. Phys. A 24 (1991) 3967] on shattering fragmentation in such models showing, among others, that there occurs an unexpected mass loss associated with shattering which is not accounted for by the discrete and continuous mass loss, contrary to the conjecture of [Phys. Rev. A 43 (1991) 656, Phys. Rev A 41 (1990) 5755]. [Copyright &y& Elsevier]

The idea of almost convergence was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283–294] and they also characterized the four dimensional strong regular matrices. In this paper we define the M-core for double sequences and determine those four dimensional matrices which transform every bounded double sequence x=[xjk] into one whose core is a subset of the M-core of x. [Copyright &y& Elsevier]

In this paper, we consider a kind of neutral functional differential equation as follows: x(t)−cx(t−τ)′=gt,xt−μ(t)+e(t) in the critical case &z.sfnc;c&z.sfnc;=1. By employing the topological degree theory and some analysis techniques, we obtain some new results on the existence of periodic solutions. [Copyright &y& Elsevier]

The idea of almost convergence for double sequences was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283–294] and they also characterized the four dimensional strong regular matrices. In this paper we define and characterize the almost strongly regular matrices for double sequences and apply these matrices to establish a core theorem. [Copyright &y& Elsevier]

Consider the persistence and the global asymptotic stability of the following discrete model of pure-delay nonautonomous Lotka–Volterra type: Ni(p+1)=Ni(p)expci(p)−∑lower limit j=1, upper limit n ∑lower limit l=0, upper limit m aijl(p)Nj(p−kl),p=0,1,2,…, 1&les;i&les;n,Ni(p)=Ni,p&ges;0, p&les;0, and Ni,0>0, 1&les;i&les;n, where each ci(p) and aijl(p) are bounded for p&ges;0 and inflower limit p&ges;0 ∑lower limit l=0, upper limit m aiil(p)>0, aijl(p)&ges;0, i&les;j&les;n, 1&les;i&les;n, and kl&ges;0, 1&les;l&les;m. In this paper, for the above discrete system of pure-delay type, by improving the former work [J. Math. Anal. Appl. 273 (2002) 492–511] which extended the averaged condition offered by S. Ahmad and A.C. Lazer [Nonlinear Anal. 40 (2000) 37–49], we offer conditions of persistence, and considering a Lyapunov-like discrete function to the above discrete system, we establish sufficient conditions of global asymptotic stability. [Copyright &y& Elsevier]

In this paper we study the behavior of general integral operators on weighted Lp spaces. Particular cases include the main index transforms and the operators with complex Gaussian kernels. We also extend some previous results established in [E.R. Negrin, Proc. Amer. Math. Soc. 123 (1995) 1185–1190]. [Copyright &y& Elsevier]

The definition of the pα-, pβ- and pγ-duals of a sequence space was defined by Et [Internat. J. Math. Math. Sci. 24 (2000) 785–791]. In this paper we compute pα- and N-duals of the sequence spaces Δmv(X) for X=ℓ∞, c and c0, and compute β- and γ-duals of the sequence spaces Δmv(X) for X=ℓ∞, c and c0. [Copyright &y& Elsevier]

In this paper, we study existence of solutions of first order dynamic inclusions on time scales with general boundary conditions. Both the ∇-derivative and Δ-derivative cases are considered. Examples are presented to illustrate that the Δ-derivative case needs more restrictive assumptions. [Copyright &y& Elsevier]

The purpose of this paper is to investigate when a weight ϕ on a partial O&ast;-algebra M is a trace weighted by a positive self-adjoint operator Ω, that is, ϕ(X†□X)=tr(X†&ast;Ω)&ast;(X†&ast;Ω) whenever X∈M s.t. X†∈L(X) and ϕ(X†□X)<∞. It is shown that if M contains the inverse N of a positive compact operator such that the weak multiplication N□N is defined, then every weight ϕ on M+ satisfying ϕ(N□N)<∞ is a trace weighted by some positive trace operator. [Copyright &y& Elsevier]

In this paper, we give the exact upper densities of Hausdorff measures of a class of symmetric perfect sets. [Copyright &y& Elsevier]

In this paper we consider a competitor–competitor–mutualist model with cross-diffusion. We prove some existence and non-existence results concerning non-constant positive steady-states (patterns). In particular, we demonstrate that the cross-diffusion can create patterns when the corresponding model without cross-diffusion fails. [Copyright &y& Elsevier]

In this paper, we deal with a class of pseudoparabolic problems with integral boundary conditions. We will first establish an a priori estimate. Then, we prove the existence, uniqueness and continuous dependence of the solution upon the data. Finally, some extensions of the problem are given. [Copyright &y& Elsevier]

In this paper, we show that if L is a completely distributive commutative subspace lattice or a J-subspace lattice, then the space of all bounded derivations of algL is reflexive. We also study when local automorphisms on some algebras are automorphisms. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

This paper is concerned with the nonoscillatory problems of odd-dimensional systems of linear retarded functional differential equations. Based upon the corresponding characteristic equations, we get some criteria for nonoscillations by utilizing the matrix measures. [Copyright &y& Elsevier]

In this paper, a pair of nondifferentiable multiobjective programming problems is first formulated, where each of the objective functions contains a support function of a compact convex set in Rn. For a differentiable function h :Rn×Rn→R, we introduce the definitions of the higher-order F-convexity (F-pseudo-convexity, F-quasi-convexity) of function f :Rn→R with respect to h. When F and h are taken certain appropriate transformations, all known other generalized invexity, such as η-invexity, type I invexity and higher-order type I invexity, can be put into the category of the higher-order F-invex functions. Under these the higher-order F-convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems related to a properly efficient solution. [Copyright &y& Elsevier]

In this paper, we consider positive solutions of the logistic type p-Laplacian equation −Δpu=a(x)&z.sfnc;u&z.sfnc;p−2u−b(x)&z.sfnc;u&z.sfnc;q−1u, x∈RN (N&ges;2). We show that under rather general conditions on a(x) and b(x) for large &z.sfnc;x&z.sfnc;, the behavior of the positive solutions for large &z.sfnc;x&z.sfnc; can be determined. This is then used to show that there is a unique positive solution. Our results improve the corresponding ones in J. London Math. Soc. (2) 64 (2001) 107–124 and J. Anal. Math., in press. [Copyright &y& Elsevier]

In this paper we characterize matrices that map every bounded sequence into one whose σ-core is a subset of the I-core of the original sequence. [Copyright &y& Elsevier]

This paper is concerned with the nonoscillation of first order delay differential equations of the form x′(t)+p(t)xτ(t)=0, t&ges;t0, where p,τ∈C([t0,∞),R+), R+=[0,∞), τ(t) is nondecreasing, τ(t) for t&ges;t0 and limt→∞τ(t)=∞. New nonoscillation conditions are obtained. These conditions concern the case when the well-known nonoscillation condition ∫τ(t)tp(s) ds&les;1/e is not satisfied. [Copyright &y& Elsevier]

Let f be a nonconstant entire function, and let k (&ges;2) be an integer. We denote by Ef(z)={z∈C: f(z)=z, counting multiplicities} the set consisting of all the fixed points of f. This paper proves that if f and f′ have the same fixed points, namely, Ef(z)=Ef′(z), and if f(k)(z)=z whenever f(z)=z, then f≡f′. [Copyright &y& Elsevier]

We consider the nth order nonlinear neutral differential equation of the form x(t)+∫lower limit a, upper limit b p(t,μ)xτ(t,μ) dμ(n)+λ∫lower limit c, upper limit d q(t,ξ)fxσ(t,ξ) dξ=h(t). In this paper, we obtain sufficient conditions which ensure that all solutions are either oscillatory or limt→∞&z.sfnc;x(t)&z.sfnc;=∞ or else liminft→∞&z.sfnc;x(t)&z.sfnc;=0. [Copyright &y& Elsevier]

In this paper we develop the monotone method in the presence of lower and upper solutions for the problem uΔn(t)+∑lower limit j=1, upper limit n−1 MjuΔj(t)=ft,u(t), t∈[a,b],uΔi(a)=uΔiσ(b), i=0,…,n−1. Here f :[a,b]×R→R is such that f(· ,x) is rd-continuous in I for every x∈R and f(t,·) is continuous in R uniformly at t∈I, Mj∈R are given constants and [a,b]=Tκn for an arbitrary bounded time scale T. We obtain sufficient conditions in f to guarantee the existence and approximation of solutions lying between a pair of ordered lower and upper solutions α and β. To this end, given M>0, we study some maximum principles related with operators Tn±[M]u(t)≡uΔn(t)+∑lower limit j=1, upper limit n−1 MjuΔj(t)±Mu(t), in the space of periodic functions. [Copyright &y& Elsevier]

This paper deals with nonautonomous Lie´nard-type systems. Sufficient conditions are given for the zero solution of the systems to be globally asymptotically stable. The main result is proved by means of phase plane analysis with a Liapunov function. Examples are included to contrast our theorem with results which were presented by Hatvani and Cantarelli. Some global phase portraits are also attached. [Copyright &y& Elsevier]

In this paper, we consider the existence of at least three positive solutions for the 2nth order m-point boundary value problem y(2n)(t)=ft,y(t),y″(t),…,y(2(n−1))(t), 0&les;t&les;1,y(2i)(0)=0, y(2i)(1)=∑lower limit j=1, upper limit m−2 kijy(2i)(ξj), 0&les;i&les;n−1, where kij>0 (i=0,1,…,n−1; j=1,2,…,m−2), 0<ξ1<ξ2<⋯<ξm−2<1. The associated Green''s function for the higher order m-point boundary value problem is first given, and growth conditions are imposed on f which yield the existence of multiple positive solutions by using the Leggett–Williams fixed point theorem. [Copyright &y& Elsevier]

Gut and Spa˘taru (J. Math. Anal. Appl. 248 (2000) 233–246) proved a precise asymptotic theorem for random variables in the normal domain of attraction of some stable distribution with exponent α, 1<α&les;2. They also conjectured that the theorem should hold for the general case of the domain of attraction of a stable distribution. In this paper, we shall provide an example to deny their conjecture and study some further properties. [Copyright &y& Elsevier]

This paper deals with the global uniform exponential stability independent of delay of time-delay linear and time-invariant systems subject to point and distributed delays for the initial conditions being continuous real functions except possibly on a set of zero measure of bounded discontinuities. It is assumed that the delay-free system as well as an auxiliary one are globally uniformly exponentially stable and globally uniform exponential stability independent of delay, respectively. The auxiliary system is typically a part of the overall dynamics of the delayed system but not necessarily the isolated undelayed dynamics as usually assumed in the literature. Since there is a great freedom in setting such an auxiliary system, the obtained stability conditions are very useful in a wide class of practical applications. [Copyright &y& Elsevier]

This paper studies the global behaviors of the periodic logistic system with periodic impulsive perturbations. The results of D.D. Bainov and P.S. Simeonov (1993) are extended and dynamics different from the corresponding continuous system are found. It is shown that the system may have a unique positive periodic solution which is globally asymptotically stable, or go extinct when the two periods are rational dependent. When they are rational independent, the system has no periodic solutions, however, still has a global attractor or go extinct under some conditions. [Copyright &y& Elsevier]

In this paper we study the boundedness and the asymptotic behavior of the positive solutions of the system of difference equations xn+1=A+∑i=1kaixn−pi/∑j=1mbjyn−qj,yn+1=B+∑i=1kciyn−pi/∑j=1mdjxn−qj, yn+1=B+∑i=1kciyn−pi/∑j=1mdjxn−qj, where k,m∈{1,2,…}, A,B,ai,ci,bj,dj, i∈{1,…,k}, j∈{1,…,m}, are positive constants, pi, qj, i∈{1,…,k}, j∈{1,…,m}, are positive integers such that p1, q1 and the initial values xi,yi, i∈{−π,−π+1,…,0}, π=max{pk,qm} are positive numbers. [Copyright &y& Elsevier]