一类非线性二阶边值问题的解和正解的存在性

摘要

考察了非线性二阶两点边值问题:u''(t)+p(t)u'(t)+f(t,u(t),u'(t))＝0 0≤t≤1,u(0)＝A,u(1)＝B.通过转化为Sturm-Liouville问题并利用Leray-Schauder不动点定理,获得了若干解和正解的存在性结论.这些存在性结论表明该问题的解和正解的存在性,取决于非线性项在某个有界集合上的"高度".%The nonlinear second-order two-point boundaryvalue problem u''(t)+p(t)u'(t)+f(t,u(t),u'(t))=0,u(0)=A,u(1)=B is considered.By converting the problem into Sturm-Liouville problems and applying Leray-Schauder fixed point theorem,several existence results of solution and positive solution are obtained.The existence results show that the existence of solution and positive solution depends upon the "height" of nonlinear on certain bounded set.Our work extends previous results.