Mathematical Problems in Engineering
Volume 2 (1996), Issue 5, Pages 401-434
doi:10.1155/S1024123X96000415

Eigenvalues of boundary value problems for higher order differential equations

Patricia J. Y. Wong1 and Ravi P. Agarwal2

1Division of Mathematics, Nanyang Technological University, Singapore
2Department of Mathematics, National University of Singapore, Singapore

Received 23 October 1995

Copyright © 1996 Patricia J. Y. Wong and Ravi P. Agarwal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We shall consider the boundary value problem y(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, where λ>0,α,β,γ and δ are constants satisfying αγ+αδ+βγ>0,β,δ≥0,β+α>0 and δ+γ>0 to characterize the values of λ so that it has a positive solution. For the special case λ=1, sufficient conditions are also established for the existence of positive solutions.