Eigenvalue Intervals for 2mth Order Sturm—Liouville Boundary Value Problems

Values of λ are determined for which there exist positive solutions of the 2mth order differential equation on a measure chain, (-1)m x ▵2m (t)=λa(t)f(u(σ(t))), y∊ [0,1], satisfying α i+1 u ▵21(0)+0, γ i+1 u ▵21(σ(1))=0, 0≤i≤m−1 with αi,βi,γi,δi≥0, where a and f are positive valued, and both lim x-0+ (f(x)/x) and lim x-0+ (f(x)/x) exist.