Some Researches In Nonlinear Order Differential Equations

The paper has five parts:1. two-point boundary value problem with nonlinear boundary condition for a class of second order nonlinear ODE. In this paper,we study a class of second order nonlinear ordinary equations.The existence of two-point boundary value problems with linear boundary conditions and nonlinear boundary conditions are proved.2. dichotomies of solutions for a class of second-order nonlinear differential equations.this paper considers the long-time behavior of solutions for the Cauchy problem of a class of second-order nonlinear differential equations:-x" + f(t,x,x')x' + g(x) = h(t). Under appropriate conditions it is shown that the solutions of the problem possess some dichotomy properties.3. Blow-up and oscillation phenomena of second-order nonlinear differential equations.4. On connective set-stability of large discrete system with respect to partial variables.The method of Liapunov function is used to study the connective set-stability of large discrete systems with respect to the partial variables.Some sufficient conditions for several basic theorem of the connective set-stability are derived,which are more tolerant and looser,and three significant elementary theorems are given,also.5. In this paper we do not impose such a restriction on /(i),and we proceed to give two oscillation criteria for Eq.(p(t)y')' + q{t)y = f(t),t ∈[0,∞).