Eigenvalues of boundary value problems for higher order differential equations

[摘要] We shall consider the boundary value problemy(n)+λQ(t,y,y1,⋅⋅⋅,y(n−2))=λP(t,y,y1,⋅⋅⋅,y(n−1)),n≥2,t∈(0,1),y(i)(0)=0,0≤i≤n−3,αy(n−2)(0)−βy(n−1)(0)=0,γy(n−2)(1)+δy(n−1)=0,whereλ>0,α,β,γandδare constants satisfyingαγ+αδ+βγ>0,β,δ≥0,β+α>0andδ+γ>0to characterize the values ofλso that it has a positive solution. For the special caseλ=1, sufficient conditions are also established for the existence of positive solutions.

[学科分类] 工程和技术（综合）