uniqueness. and asymptotic cstinlates of solLltions of singularly perturbed boundary value problems for a class of third order nonlinear diffcrellLial ecluatlonsεx' =f(t,x .x',ε),x(0) = A . g(X' (0),x'(0) .ε) = 0 .h (x (1). ε) = 0, by making use of Volterra type integral operator and differential inequality technique.
By using the limit method and iteration method of the analysis theory and inequality technique,the sufficient conditions are obtained for global attractivity of the positive equilibrium of the nonlinear difference equation.
Shows the existence and asymptotic estimates of singularly perturbed third order nonlinear boundary value problem by making use of volterra type integral operator and differential inequality technique.
Sufficient conditions for the existence 、 uniqueness and exponential stability of the periodic solutions are established by using the continuation theorem of coincidence degree theory, nonnegative matrices theory and differential inequality technique.
Based on the sufficient condition and the technique of parallel distributed compensator, a global controller ensuring the closed-loop system to be robust D-stable was designed by means of linear matrix inequality technique.
On the other hand, as to the time domain methods, based on Lyapunov-Krasovskii function method, Riccati equation method, linear matrix inequality technique, along with the skills of equality and inequality transformations, the robust stabilization and robust H controlproblems are studied via state feedback for some kinds of uncertain time-delay systems, and delay-independent as well as delay-dependent results are obtained.
Different from the normal approach, that's to say, without resorting to any Lyapunov function, these results are obtained by utilizing generalized Halanay inequality technique and combining the theory of exponential dichotomy with fixed point method.
Based on linear matrix inequality technique, a new method is developed for designing fuzzy stabilizing controllers via static output feedback.
In this paper we consider the singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations. The asymptotic expansions of the solutions are constructed by the method of boundary layer corrections. Moreover, the existence of the solution and the estimation of the remainder are simply derived by means of the higher order differential inequality techniques.
In this paper, we consider the boundary value problem: where ε is a small positive parameter. Under some suitable assumptions, using the method of "boundary layer corrections" and the differential inequality techniques, we obtain an uniformly efficient asymptotic solution which includes the boundary layer and can be approximated any times.
In the present paper, we study the general boundary value problems of nth-order nonlinear differential equations by means of differential inequality techniques and obtain the existence theorems of solutions for the boundary value problem (1. 2).