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Title: Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms
Authors: Wong, Patricia Jia Yiing
Keywords: Sturm-Liouville Boundary Value Problems
DRNTU::Engineering::Electrical and electronic engineering
Issue Date: 2015
Source: Wong, P. J. Y. (2015). Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms. Boundary Value Problems, 2015, 12-. doi:10.1186/s13661-014-0227-y
Series/Report no.: Boundary Value Problems
Abstract: 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.
ISSN: 1687-2762
DOI: 10.1186/s13661-014-0227-y
Rights: © 2015 Wong; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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