On eigenvalue intervals and twin eigenfunctions of higher-order boundary value problems

On eigenvalue intervals and twin eigenfunctions of higher-order boundary value problems In this paper we shall consider the boundary value problem y (n) + λQ(t,y,y 1 ,…,y (n−2) ) = λP(t,y,y 1 ,…,y (n−2) ), n ⩾2, t∈(1,1), y (i) (0)=0, 0⩽i⩽n−3, αy (n−2) (0) − βy (n−1) (0)=0, yy (n−2) (1) + σy (n−1) (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. Intervals of γ are determined to ensure the existence of a positive solution of the boundary value problem. For γ = 1, we shall also offer criteria for the existence of two positive solutions of the boundary value problem. In addition, upper and lower bounds for these positive solutions are obtained for special cases. Several examples are included to dwell upon the importance of the results obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

On eigenvalue intervals and twin eigenfunctions of higher-order boundary value problems

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Publisher
Elsevier
Copyright
Copyright © 1998 Elsevier Ltd
ISSN
0377-0427
eISSN
1879-1778
D.O.I.
10.1016/S0377-0427(97)00202-1
Publisher site
See Article on Publisher Site

Abstract

In this paper we shall consider the boundary value problem y (n) + λQ(t,y,y 1 ,…,y (n−2) ) = λP(t,y,y 1 ,…,y (n−2) ), n ⩾2, t∈(1,1), y (i) (0)=0, 0⩽i⩽n−3, αy (n−2) (0) − βy (n−1) (0)=0, yy (n−2) (1) + σy (n−1) (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. Intervals of γ are determined to ensure the existence of a positive solution of the boundary value problem. For γ = 1, we shall also offer criteria for the existence of two positive solutions of the boundary value problem. In addition, upper and lower bounds for these positive solutions are obtained for special cases. Several examples are included to dwell upon the importance of the results obtained.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Feb 23, 1998

References

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