In this paper, we consider a boundary problem of first order impulsive differential equation with a parameter and infinite delay. By using the method of upper and lower solutions, we get some sufficient conditions for...In this paper, we consider a boundary problem of first order impulsive differential equation with a parameter and infinite delay. By using the method of upper and lower solutions, we get some sufficient conditions for the existence of its solutions.展开更多
By using upper and lower solutions and fixed point theorem we give the existence theorem of non-linear second order ordinary differential equation with discontinuous terms in Banach Space.
The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterativ...The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analy- sis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.展开更多
基金Research supported by Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institute.
文摘In this paper, we consider a boundary problem of first order impulsive differential equation with a parameter and infinite delay. By using the method of upper and lower solutions, we get some sufficient conditions for the existence of its solutions.
文摘By using upper and lower solutions and fixed point theorem we give the existence theorem of non-linear second order ordinary differential equation with discontinuous terms in Banach Space.
文摘The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analy- sis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.
