1 Without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence and uniqueness of the equilibrium are obtained.

2 The linear controller ensures the boundedness of the input and output signals , and the nonlinear controller improves performance of the system.

3 We investigate the stability and the boundedness of the differential system. Stability criteria and boundedness criteria in terms of two measures employing the method of comparison are established.

4 Some boundedness theorems are given, and some simple atomic decompositions are also proved.

5 We discuss uniform extremely stable and uniform distances boundedness of solutions of nonautonomous equations.

6 Boundedness and unboundedness are the way people get to know the bounded concept of the outside world.

7 Moreover, some general conclusions about the boundedness of norms were given for the case that the coefficients of the equations form a square matrix.

8 The boundedness and stability of the solutions are established by the upper-lower solution method.

9 Lastly, we study the boundedness and dissipativity for functional differential equation.

10 By using the invertibility and boundedness of the operators in L2 space, the discussion of gradient-like of the system characterized by input output description is given.

11 Using the comparison principle, the positivity and the boundedness of the solution for the model were obtained and the uniform persistence of this system in given initial conditions was verified.

12 For doubling measure, the boundedness of the sub-linear operator plays an important role in many problems.

13 The positive invariant property, eventual boundedness, non-persistence, permanence, extinction, and globally asymptotic stability of the system was investigated.

14 In this paper we prove the boundedness of the θ - type Calder ? ? n - Zygmund Commutator on the Triebel - Lizorkin space.

15 In this paper, the equivalent relation of boundedness and continuity at zero for homogeneous operator in normal linear space is proved.

16 As special cases, we obtain the boundedness of fractional operators.

17 This paper deals with the boundedness of second-order functional differential equations, ar. d obtains sufficient criteria of the equation boundedness.

18 In this paper, we discuss uniform boundedness and uniform ultimate boundedness of differential systems with infinite delay.

19 In this paper, We obtained the boundedness of solution map for semilinear parabolic system with a Dirichlet boundary control using semigroup theory etc.

20 In this paper, I give a new proof of BMO - boundedness of Hardy - Littlewood maximal operator.

21 This project mainly dealt with the existence and multiplicity of periodic solutions and the boundedness (unboundedness) of solutions of nonlinear oscillations.

22 Applied to elemental analytic method and based on cognitive frame, this thesis wholly analyses this sentence pattern via boundedness and unboundedness theory.

23 The relationship between WTTPN and its underlying net is discussed, and it is proved that the WTTPN is equivalent to its underlying net about liveness, boundedness(safeness) and reversibility.

24 Discuss a growth model of Isochrysis galbana, obtain sufficient condition for boundedness, limiting quality, stability and bifurcation.

25 In this paper, We consider a class of degenerate elliptic systems in diagonal form and prove the global boundedness for generalized solutions.

26 This paper explores the linguistic representations of the cognitive concept of boundedness .

27 It is shown that the proposed controller can guarantee global uniform ultimate boundedness.

28 This paper deals with the second order functional differential equations with distributed delay. By using the inequality estimation we obtain the comparison theorem of the boundedness of solutions.

29 In this paper, using KAM theory, we obtain the boundedness of solutions as well as the existence of many invariant tori for jumping nonlinear oscilltions.

30 In general cases, we obtain some necessary and some sufficient conditions, which may not be same, for boundedness of matrix operators acting from a sequence space of Besov type to another one.