In this paper,the existence uniqueness of solution for initial value problemsx′=f1(t,y)y′=f2(t,x) x(t0)=x0,y(t0)=y0of one order system of ordinary differential equations in Banach space is studied by means of cone theory. And the iterative algorithm of the solution for the above problem is given.
In the paper a method of identifying parameters a, b, c, d, and r in a kind of time-varying linear first-order differential equation system dx(t)dt=ax(t)+br -t y(t),dy(t)dt=cr tx(t)+dy(t) is introduced.
In this paper,the author use the method of Laplace transform to the differential equation system,which is M/M/1 queuing system satifies. So obtain the Laplace transform expression of the transient distribution P_n(t) of the length of M/M/1 queuing system.
To prove resolution existence and uniqueness theory of higher order linear differential equation with constant coefficient, it is first to change it into order linear differential equation group with constant coefficient, and secondly to change the order equation group into integral equation group, and then prove theory that integral equation group has only one group solution by using contraction mapping.
Fractal differential equations on the Sierpinski gasket
We study the analogs of some of the classical partial differential equations with Δ playing the role of the usual Laplacian.
Some applications are given to control theory for partial differential equations.
The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations
Originally introduced in the context of separation of variables for certain partial differential equations, PSWFs became an important tool for the analysis of band-limited functions after the famous series of articles by Slepian et al.
The problem for this control law and performance criterion is to find coefficients of a differential equation system with distributed delay, for which the chosen control is a control of optimal stabilization.
The differential equation system obtained has two singular points, in the vicinity of which nondegenerate transformation produces a system with a diagonal matrix which is then integrated.
The results of the analytical peak-shape equations were compared with those from a numerical solution of the partial differential equation system modeling the chromatographic reactor.
The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.
Singular perturbation of general boundary value problem for nonlinear differential equation system