Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms

• Main Author: Wong, Patricia Jia Yiing
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2018
• Subjects: Sturm-Liouville Boundary Value Problems; DRNTU::Engineering::Electrical and electronic engineering; Eigenvalues
• Online Access: https://hdl.handle.net/10356/88519; http://hdl.handle.net/10220/45848
• Institution: Nanyang Technological University

We shall consider the Sturm-Liouville boundary value problem y(m)(t)+λF(t,y(t),y′(t),…,y(q)(t))=0, t∈(0,1), y(k)(0)=0, 0≤k≤m−3, ζy(m−2)(0)−θy(m−1)(0)=0, ρy(m−2)(1)+δy(m−1)(1)=0 where m≥3, 1≤q≤m−2, and λ>0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained.