共振情形下周期边值问题正解的全局分歧

GLOBAL BIFURCATION OF POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS AT RESONANCE

考虑共振情形下二阶常微分方程周期边值问题{u''=f(t,u), t∈(0,2π), u(0)=u(2π), u'(0)=u'(2π)正解的全局分歧,其中f:[0,2π]×R→R(R=(-∞,+∞))为连续函数.运用Dancer全局分歧定理获得了上述问题至少存在一个正解的若干充分条件,这些充分条件中所涉及的值是最优的.

In this paper, we are concerned with the global bifurcation of positive solutions for the following second order periodic boundary value problem {u″=f（t,u）,t∈（0,2π） u（0）=u（2π）,u′（0）=u′（2π）wheref：[0,2π]×R→R（R=（-∞,＋∞））is continuous. By using Dancer＇s global bifurcation theorem, we obtain some optimal conditions such that the above problem has at least one positive solution.