四阶非线性特征值问题的多个正解

Multiple Positive Solutions of Fourth Order Singular Nonlinear Eigenvalue Problem

利用锥上的不动点定理,给出了四阶非线性特征值问题y(4)(x)-λh(x)f(y(x))=0,0<x<1,y(0)=y(1)=y′(0)=y′(1)=0至少有两个正解存在的结果,其中h允许在x=0及x=1处奇异。

Using fixed-point theorem in cone, we consider the fourth order nonlinear eigenvalue problem y^((4))(x)-λh(x)f(y(x))=0, 0<x<1,y(0)=y(1)=y′(0)=y′(1)=0, where f may be singular at both points x=0 and x=1, we obtain the results of at least two positive solutions.