带导数项的半正Right Focal边值问题单调正解的存在性

Existence of Monotone Positive Solutions for Semipositone Right Focal Boundary Value Problems with Dependence on the Derivatives

研究下列半正Right F0cal边值问题单调正解的存在性其中λ>0是一个参数,n≥3,1<k≤n-1固定,非线性项f允许下方无界.在没有任何单调性假设的情况下,利用锥中的不动点定理得到了一个和两个单调正解的存在性结果.

We study the existence of monotone positive solutions for the semipositone right focal boundary value problems {（-1）^（n-k）u^（n）（t）=λf（t,u（t）,u′,…u（k-1）（t））,t∈（0,1） u^（i）（0）=0,0≤i≤k-1,u（j）（1）=0,k≤j≤n-1 whereλ 〉0 is a parameter,n≥3,1 k≤n-1 is fixed,f may change sign for 0 〈t 〈1 and we allow f is both semipositone and lower unbounded.Without making any monotone type assumption,the existence results of at least one and two monotone positive solutions are obtained by means of the fixed point theorems in cones.