带积分边界条件的四阶边值问题的单调正解

运用单调迭代技巧研究了带积分边界条件的四阶边值问题{u⁽⁴⁾(t)=f(t,u(t),u'(t)), t∈(0,1),u(0)=u'(1)=u(1)=0,u″(0)=∫¹₀g(t)u″(t)dt单调正解的存在性,其中 f:［0,1］×［0,+∞)²→［0,+∞)连续, g:［0,1］→［0,+∞)连续,不仅获得了该问题正解的存在性,而且得出迭代列的初值是简单的零函数或一次函数。

Monotone positive solutions of fourth-order boundary value problems with integral boundary conditions

By using the monotone iterative technique, this article studies the existence of monotone positive solutions for fourth order boundary value problems with integral boundary conditions{u⁽⁴⁾(t)=f(t,u(t),u'(t)), t∈(0,1),u(0)=u'(1)=u(1)=0,u″(0)=∫¹₀g(t)u″(t)dt,where f:［0,1］×［0,+∞)2→［0,+∞) is continuous, g:［0,1］→［0,+∞) is continuous, not only the existence of the positive solution of the problem is obtained, but also the initial value of the iterative sequence is a simple zero function or a primary function.