四阶超线性奇异微分方程正解存在的充分必要条件

A Necessary and Sufficient Condition for the Existence of Positive Solutions of Fourth Order Singular Superlinear Differential Equations

利用范数形式的锥拉伸与压缩不动点定理,对一类四阶奇异超线性微分方程边值问题做了研究,得到C^2[0,1]正解与C^3[0,1]正解存在的充分必要条件,也得到C^2[0,1]正解的不可比较性等解的性质.

This paper investigates a class of fourth order singular sublinear boundary value problems. A necessary and sufficient condition for the existence of C^2 [0, 1] positive solutions as well as C^3[0, 1] positive solutions is given by using fixed point theorem of cone expansion of norm type. We also obtaied the incomparability of C^2 [0, 1] positive solutions.