一类四阶边值问题的正解的存在性与多重性

The Existence and Multiplicity of Positive Solutions for a Class of Fourth Order Boundary Value Problem

为了进一步发展和完善四阶边值问题正解的存在性理论,研究了下面的四阶边值问题u(4)=f(t,u(t),u'(t),u″(t),u'''(t)),0≤t≤1u'(0)=u″(0)=u'''(0)=0,ku(1)=u'''(1)其中,f:[0,1]×R4→[0,+∞)连续。利用锥上不动点定理得到了该四阶边值问题正解的存在性及多重性。推广了某些已知的结果。

In order to develop and improve the theory about existence of positive solutions of fourth order boundary value problem,the following fourth order boundary value problem {u（4）=f（t,u（t）,u′（t）,u″（t）,u＇＇＇（t））,0≤t≤1u′（0）=u″（0）=u＇＇＇（0）=0,ku（1）=u＇＇＇（1） is considered,where f：×R4→[0,＋∞） is continuous.By use of the fixed point theorem in cone,the existence and multiplicity of positive solutions are obtained to the above boundary value problem.The results generalize some recent ones.