The theorem of the continuous dependence of the roots of a palynomial on itscoefficients is of great Importance in the qualitative theory of defferential equation.

By using the theory of the eigenvalue of completely continuous operators andα-concave (orα-convex) operators, we obtain several sufficient conditions which guarantee the existence and unique existence of positive periodic solutions and its continuous dependence on parameter for certain differential equations with piecewise constant argument.

In this paper the initial value problem of impulsive differential system is discussed and sufficient conditions for the continuous dependence of solution of the problem on the initial condition and the impulse effect are obtained.

In this paper,the stability robustness bounds for linear system with structured uncertainty are obtained according to the continuous dependence of the eigenvalues of Hermite matrix on its elements,which are constructed by some inequalities.

In chapter 2, we first discuss the complex Ginzurg-Landau equationsaccording to the conditions that solutions exist, we derive a prior estimates that indicate that solutions depend continuously on some parameters in the governing differential equation μ,ν,αSecondly, in chapter 3, continuous dependence on a modelling parameter is established for solutions of a problem for a complex Ginzurg-Landau equation with p-Laplacian.

Dependence of the algorithm solution on the disturbance of parameters that represent some characteristic numbers of industrial noises or process structure parameters is investigated.

With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial_boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated. The main results are: 1) there exists only one global weak solution which continuously depends on initial value;

With the method of prior estimate, the following results are obtained that: there exists unique smooth positive solution u(x, t) which dependents on initial value continuously in L1, ||u - u||L2 converges to a constant as t →∞.

In addition, the continuous dependence of the solution of this equation on the linear dispersive coefficient contained in the equation is obtained.

Spline approximation of experimental dependences of lnk on P is used to determine the continuous dependence of the activation volume ΔV# on P in the solvents cyclohexane, anisole, toluene, n-nonane, isopropylbenzene, and tert-butylbenzene.

Spline approximation of experimental dependences of lnk on P is used to determine the continuous dependence of the activation volume ΔV# on P in the solvents cyclohexane, anisole, toluene, n-nonane, isopropylbenzene, and tert-butylbenzene.

Continuous dependence of an element realizing the minimum of a convex functional on the set of admissible elements

Existence and continuous dependence of the solution of a system of operator equations

In this article, a mathematical method for calculation of model of a population Ⅱ star using high speed digital computer is discussed. The model used is the same as that which Hoyle and Schwarzschild have constructed and thereafter Kippenhahn and others have improved. It is suggested that the most simple and practical method to solve In ρ, In P_e, y, z_1, z_2, and In μ, from the view of programming, is the iterative method from (5)', (6)', (7)', (8)', (9)', (10)'. The corresponding condition of convergence is...

In this article, a mathematical method for calculation of model of a population Ⅱ star using high speed digital computer is discussed. The model used is the same as that which Hoyle and Schwarzschild have constructed and thereafter Kippenhahn and others have improved. It is suggested that the most simple and practical method to solve In ρ, In P_e, y, z_1, z_2, and In μ, from the view of programming, is the iterative method from (5)', (6)', (7)', (8)', (9)', (10)'. The corresponding condition of convergence is that the characteristic equation (11) and hence have characteristic roots with moduli less than unity. This is satisfied within the interested range of model compution. Since the characteristic root with the largest modulus is complex, the iterative process converges oscillatorially. Then the formulae (16) and (20) are used to accelerate the iterative process. It is shown from Table 2 that as theintegration is carried on toward the stellar interior, the largest modulus (|x_2|)~1/2 diminishes gradually step by step, and the iterative process ends more rapidly. The whole integration of the envelope solution proceeds by two ways: the improved Euler's method with a step length of Δ In P = 0.0125 and the Rung-Kutta method with changing interval. In integrating the partially degenerate isothermal core, we will require values of the Fermi-Dirac function at points between the pivotal values. For this, Newton's interpolation formulae with divided differences is used. The corresponding error formulae (30) leads to a maximum error of 10~(-6).

It has been studied in this paper that a control of distributed parameter systems is contained in coefficients of linear 2nd order elliptic or parabolic equations, which has beencalled the problem of control in the coefficients and applied to a numcer of mathemaitcal physics problems. We first give a sufficient condition under which thesystein state depends continuously on the control. And then we give conditions respectively for the systems governed by the mentioned equations. Under anyone of them the system...

It has been studied in this paper that a control of distributed parameter systems is contained in coefficients of linear 2nd order elliptic or parabolic equations, which has beencalled the problem of control in the coefficients and applied to a numcer of mathemaitcal physics problems. We first give a sufficient condition under which thesystein state depends continuously on the control. And then we give conditions respectively for the systems governed by the mentioned equations. Under anyone of them the system has the optimal control minimizing the given cost functional.

It has been studied in this paper that a control of distributed parameter systems is contained in coefficients of linear 2nd order elliptic or parabolic equations,which has been called the problem of control in the coefficients and applied to a numcer of mathemaitcal physics problems.We first give a sufficient condition under which thesystein state depends continuously on the control.And then we give conditions respectively for the systems governed by the mentioned equations.Under anyone of them the system has...

It has been studied in this paper that a control of distributed parameter systems is contained in coefficients of linear 2nd order elliptic or parabolic equations,which has been called the problem of control in the coefficients and applied to a numcer of mathemaitcal physics problems.We first give a sufficient condition under which thesystein state depends continuously on the control.And then we give conditions respectively for the systems governed by the mentioned equations.Under anyone of them the system has the optimal control minimizing the given cost functional.