Analysis for Some Fourth Order Boundary Value Problems
一类四阶边值问题的分析

This paper is concerned with a class of fourth-order boundary value problems. By some classical analysis methods, such as, defining an auxiliary truncation function, and Schauder fixed point theory, the authors develop the method of upper and lower solutions. Secondly, with the first eigenfunction of homogeneous boundary value problems, they construct a specific upper solution, and at the same time, 0 is taken as the corresponding lower one, thus the existence theorem of positive solutions is proved under more general assumptions. The case, when f(x,y,z) is singular at y=0 is discussed in the end.