渐近线性四阶半正边值问题正解的分歧结构

Bifurcation Structure of Positive Solutions for Asymptotically Linear Fourth-Order Semipositone Boundary Value Problems

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.

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.