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Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms.
- Source :
-
Boundary Value Problems . 1/1/2015, Vol. 2015, p1-22. 22p. - Publication Year :
- 2015
-
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, ζ y(m-2)(0) - θy(m-1)(0) = 0, py(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? 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16872762
- Volume :
- 2015
- Database :
- Academic Search Index
- Journal :
- Boundary Value Problems
- Publication Type :
- Academic Journal
- Accession number :
- 102109233
- Full Text :
- https://doi.org/10.1186/s13661-014-0227-y