Generalized multipoint conjugate eigenvalue problems

This paper considers the following boundary value problem: y(n)(t) = λP(t, y), t ∈ (0, 1), y(j)(ti)=0, j = 0, …, ni−1, i = 1, …, r, where r ⩾2,ni ⩾ 1 for i = 1,… r,∑i=1r ni = n and 0 = t1 < t2 < … < tr = 1 We shall determine those positive values of λ for which the boundary value problem has a solution that is “positive” in some sense. Specifically, criteria are developed for λ to constitute an interval, bounded as well as unbounded, more so explicit intervals of λ are presented. We also include examples to illustrate the importance of the results obtained.