中文摘要：

运用分歧理论和拓扑度理论研究四阶两点半正边值问题{x″″（t）=λf（t,x（t））,t∈（0,1）,x（0）=x（1）=x″（0）=x″（1）=0正解的存在性,其中：λ〉0为参数;f：[0,1]×[0,＋∞）→R连续.获得了该问题在非线性项满足无穷远处渐近线性增长条件下正解存在性的新结果.

英文摘要：

Employing bifurcation theory and topological theory, we studied the positive solutions for the fourth-order two point semipositone boundary value problem {x″″（t）=λf（t,x（t））,t∈（0,1）,x（0）=x（1）=x″（0）=x″（1）=0 where λ is a positive parameter,f：[0,1]×[0,＋∞）→R is continuous, and we obtained a newexistence result of positive solutions with the nonlinearity satisfying asymptotically linear growth condition at infinity.