In this paper,with the theory of trigonometrical series and contraction mapping principle,some sufficient conditions for the existence and uniqueness of periodic solution to Duffing equation ax″+bx+g(x(t～τ))=p(t) are obtained.
Second order nonlinear neutral difference equation Δ(a(n)Δ(x(n)+p(n)x(n-τ))+f(n,x(σ(n)))=0is discussed.Using Banach contraction mapping principle,the existence theorems for throughout positive solutions with some limit behavior of this equation is obtained.
In this paper, the stability and periodic solution of shunting inhibitory cellular neural networks and olfactory cortex neural networks are studied, a set of sufficient criteria are given by applying the theory of Brouwer degree and the principle of compressed mapping and contributing Lyapunov function.
Then using the contraction mapping principle and the extension theorem of the solution we prove the existence and uniqueness of the global generalized solutions and the existence and uniqness of the global classical solution.
By using the exponential dichotomy, its roughness theory and the contraction mapping principle, under some suitable conditions some sufficient conditions for the existence and uniqueness of almost periodic solutions and bounded solutions of these systems are obtained.
In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
Associated with the variational systems of non-perturbation systems, a kind of almost periodic perturbation system with deviating argument is investigated by using the contraction mapping principle. A set of sufficient conditions for the existence and uniqueness of the systems is obtained.
Based on contraction mapping theorem of analysis mathematics, the non-steady flow mathematical model of mine ventilation network was analyzed. The convergent condition of numerical solution to the mathematical model was obtained, and the selection scheme of circuit according to inertial coefficient searching the least spanning tree was put forward. Theoretical basis on the numerical solution convergence of the non-steady flow mathematical model is provided.