THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS

This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,the boundedness of the global classical solution is established in any dimensions(n≥1)provided that m>1.

Boundedness and liveness enforcement for labeled Petri nets using transition priority

This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condition is given and proven for the existence of a feasible priority-based controller based on the notions of liveness and transition invariants. Next, a cyclic behavior graph is constructed, which shows the reachable markings that guarantee the maximum liveness of the system within a given bound vector. Finally, an on-line control strategy is proposed to enforce boundedness and liveness to the given system by appending priority relations to transitions. The dynamic priority relation changes flexibly according to the current state of the system and enforces the system evolving in a bounded and live manner. In addition, numerical examples are studied to verify the validity of the proposed approach that remains the structure of the plant net and is efficient for on-line control.

Boundedness Types of Perturbations on the Growth of Semigroups

We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕj-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.

BOUNDEDNESS AND UNIFORM BOUNDEDNESS RESULTS FOR CERTAIN NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF FOURTH ORDER

Sufficient conditions have been obtained so that all solutions of a different fourth order differential equation are bounded and uniformly bounded.

ON BOUNDEDNESS OF SOLUTIONS OFIMPULSIVE INTEGRO-DIFFERENTIAL SYSTEMSWITH FIXED MOMENTS OF IMPULSE EFFECTS

Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.

BOUNDEDNESS OF THE HIGHER-DIMENSIONAL QUASILINEAR CHEMOTAXIS SYSTEM WITH GENERALIZED LOGISTIC SOURCE

This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.

BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES

For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRDINGER OPERATORS ON HEISENBERG GROUP

Let L = -△Hn ＋ V be a SchrSdinger operator on Heisenberg group Hn, where AHn is the sublaplacian and the nonnegative potential V belongs to the reverse HSlder class BQ/2 where Q is the homogeneous dimension of Hn. Let T1 = （--△Hn ＋V）-1V, T2 = （-△Hn ＋V）-1/2V1/2, and T3 = （--AHn ＋V）-I/2△Hn, then we verify that [b, Ti], i = 1, 2, 3 are bounded on some LP（Hn）, where b ∈ BMO（Hn）. Note that the kernel of Ti, i = 1, 2, 3 has no smoothness.

EXISTENCE, BOUNDEDNESS AND UNIQUENESS OF WEAK SOLUTION FOR THE THERMISTOR PROBLEM WITH MIXED BOUNDARV CONDITIONS

The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.

The Boundedness of Singular Integral Operator along an Open Curve

It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.

Boundedness and convergence of perturbed corrections for helium-like ions in ground states

Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.

THE BOUNDEDNESS OF CERTAIN OPERATORS ON HOLDER AND SOBOLEV SPACES

The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butzer deffereftital operators and differential equations.

L^p(R^n) BOUNDEDNESS FOR THE MARCINKIEWICZ INTEGRAL

Lp(Rn) boundedness is considered for the higher-dimensional Marcinkiewicz integral which was introduced by Stein. Some conditions implying the Lp(Rn) boundedness for the Marcinkiewicz integral are obtained.

BOUNDEDNESS AND EXPONENTIAL STABILIZATION IN A PARABOLIC-ELLIPTIC KELLER–SEGEL MODEL WITH SIGNAL-DEPENDENT MOTILITIES FOR LOCAL SENSING CHEMOTAXIS

In this paper we consider the initial Neumann boundary value problem for a degenerate Keller-Segel model which features a signal-dependent non-increasing motility function.The main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes unbounded.In the current work,we are interested in the boundedness and exponential stability of the classical solution in higher dimensions.With the aid of a Lyapunov functional and a delicate Alikakos-Moser type iteration,we are able to establish a time-independent upper bound of the concentration provided that the motility function decreases algebraically.Then we further prove the uniform-in-time boundedness of the solution by constructing an estimation involving a weighted energy.Finally,thanks to the Lyapunov functional again,we prove the exponential stabilization toward the spatially homogeneous steady states.Our boundedness result improves those in[1]and the exponential stabilization is obtained for the first time.

BOUNDEDNESS AND ASYMPTOTIC STABILITY IN A PREDATOR-PREY CHEMOTAXIS SYSTEM WITH INDIRECT PURSUIT-EVASION DYNAMICS

This work explores the predator-prey chemotaxis system with two chemicals {u_(t) = Δu + ∇ ・ (u∇v) + μ_(1)u(1 − u − α_(1)w), x ∈ Ω, t > 0,v_(t )= Δv −α_(1)v + β_(1)w, x ∈ Ω, t > 0,w_(t) = Δw − ξ∇ ・ (w∇z) + μ_(2)w(1 + α_(2)u − w), x ∈ Ω, t > 0,z_(t) =Δz −α_(2)z +β_(2)u, x ∈ Ω, t > 0, in an arbitrary smooth bounded domainΩ■R^(n) under homogeneous Neumann boundary conditions.The parameters in the system are positive.We first prove that if n≤3,the corresponding initial-boundary value problem admits a unique global bounded classical solution,under the assumption thatχ,ξ,μ_(i),a_(i),α_(i) andβ_(i)(i=1,2)satisfy some suitable conditions.Subsequently,we also analyse the asymptotic behavior of solutions to the above system and show that·when a_(1)<1 and bothμ1/χ^(2) andμ2/ξ^(2) are sufficiently large,the global solution(u,v,w,z)of this system exponentially converges to(1-a_(1)/1+a_(1)a_(2),β_(1)(1+a_(2))/α_(1)(1+a_(1)a_(2)),1+a_(2)/1+a_(1)a_(2),β_(2)(1-a_(1))/α_(2)(1+a_(1)a_(2)))as t→∞;·when a1>1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system exponentially converges to(0,α_(1)/β_(1),1,0)as t→∞;·when a1=1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system polynomially converges to(0,α_(1)/β_(1),1,0)as t→∞.

ON THE BOUNDEDNESS OF SPHERES IN F-SPACES

In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the .F*-space are presented. Moreover, some results about the compactness are also given.

Uniformly ultimate boundedness for discontinuous systems with time-delay

The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

BOUNDEDNESS AND CONVERGENCE FOR THE NON-LINARD TYPE DIFFERENTIAL EQUATION

In this article, the author studies the boundedness and convergence for the non-Liénard type differential equation {^·x=a（y）-f（x）,^·y=b（y）β（x）-g（x）＋e（t）,where a（y）, b（y）, f（x）, g（x）,β（x） are real continuous functions in y ∈ R or x ∈ R, β（x） ≥ 0 for all x and e（t） is a real continuous function on R^＋ = {t ： t ≥ 0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.

ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS VIA THE INTRINSIC METHOD

In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results.