The existence and uniqueness of a global smooth solution of this system with Cauchy problem and its stability and time decay rate are studied by means of an elementary energy method.
After proving the existence uniqueness of interpolation problems at center, vertex and partial center, we give the construction methods for these three interpolatiny functions.
By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved.
This paper proves local existence uniqueness and smoothness properties and improves, by essentially one order of differentiability, previous local existence results.
MacPherson posed the problem of unique existence of a bivariant Chern class—a Grothendieck transformation from the bivariant theory F of constructible functions to the bivariant homology theory H.
The existence and uniqueness of a global smooth solution of this system with Cauchy problem and its stability and time decay rate are studied by means of an elementary energy method.
In this paper, the existence and uniqueness of solutions for boundary value problemx?=f(t, x, x', x″),x(0)=A,x'(0)=B,g(x'(1),x″(1))=0 are studied by using Volterra type operator and upper and lower solutions.
Consider the real differential system dx/dt=P_3(x,y), dy/dt=Q_3(x,y)where P_3(x,y) and Q_3(x,y) are polynomials of the 3-rd degree. Suppose that the system has at lease one elementary critical point of index+1, and it can be written in the form dx/dt=-y+xF_1(x,y)+gy~2+hy~2 (1) dy/dt-x+yF_2(x,y)+rx~2+sx~3 where F_1(x,y)and F_2(x,y) are polynomials of the 2-nd degree. If g=h=r=s=0 and F_1(x,y)≡F_2(x,y), then systen(1)takes the form dx/dt=-y+xF(x,y),dy/dt=x+yF(x,y) (2)for which we have the following: Theorem. ...