Eigenvalues of complementary Lidstone boundary value problems
We consider the following complementary Lidstone boundary value problem (−1)my(2m+1)(t)=λF(t,y(t),y′(t)),t∈(0,1)y(0)=0,y(2k−1)(0)=y(2k−1)(1)=0,1≤k≤m where λ > 0. The values of λ are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit interval...
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sg-ntu-dr.10356-1032802020-03-07T14:00:36Z Eigenvalues of complementary Lidstone boundary value problems Agarwal, Ravi P. Wong, Patricia Jia Yiing School of Electrical and Electronic Engineering DRNTU::Engineering::Electrical and electronic engineering We consider the following complementary Lidstone boundary value problem (−1)my(2m+1)(t)=λF(t,y(t),y′(t)),t∈(0,1)y(0)=0,y(2k−1)(0)=y(2k−1)(1)=0,1≤k≤m where λ > 0. The values of λ are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit intervals of λ such that for any λ in the interval, the existence of a positive solution of the boundary value problem is guaranteed. Some examples are also included to illustrate the results obtained. Note that the nonlinear term F depends on y' and this derivative dependence is seldom investigated in the literature. Published version 2014-01-16T04:23:03Z 2019-12-06T21:08:59Z 2014-01-16T04:23:03Z 2019-12-06T21:08:59Z 2012 2012 Journal Article Agarwal, R. P., & Wong, P. J. (2012). Eigenvalues of complementary Lidstone boundary value problems. Boundary Value Problems, 2012(1), 49. 1687-2770 https://hdl.handle.net/10356/103280 http://hdl.handle.net/10220/18604 10.1186/1687-2770-2012-49 en Boundary value problems © 2012 Agarwal and Wong (Springer). This paper was published in Boundary Value Problems and is made available as an electronic reprint (preprint) with permission of Agarwal and Wong. The paper can be found at the following official DOI: http://dx.doi.org/10.1186/1687-2770-2012-49. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 21 p. application/pdf |
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DRNTU::Engineering::Electrical and electronic engineering Agarwal, Ravi P. Wong, Patricia Jia Yiing Eigenvalues of complementary Lidstone boundary value problems |
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We consider the following complementary Lidstone boundary value problem
(−1)my(2m+1)(t)=λF(t,y(t),y′(t)),t∈(0,1)y(0)=0,y(2k−1)(0)=y(2k−1)(1)=0,1≤k≤m
where λ > 0. The values of λ are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit intervals of λ such that for any λ in the interval, the existence of a positive solution of the boundary value problem is guaranteed. Some examples are also included to illustrate the results obtained. Note that the nonlinear term F depends on y' and this derivative dependence is seldom investigated in the literature. |
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School of Electrical and Electronic Engineering |
| author_facet |
School of Electrical and Electronic Engineering Agarwal, Ravi P. Wong, Patricia Jia Yiing |
| format |
Article |
| author |
Agarwal, Ravi P. Wong, Patricia Jia Yiing |
| author_sort |
Agarwal, Ravi P. |
| title |
Eigenvalues of complementary Lidstone boundary value problems |
| title_short |
Eigenvalues of complementary Lidstone boundary value problems |
| title_full |
Eigenvalues of complementary Lidstone boundary value problems |
| title_fullStr |
Eigenvalues of complementary Lidstone boundary value problems |
| title_full_unstemmed |
Eigenvalues of complementary Lidstone boundary value problems |
| title_sort |
eigenvalues of complementary lidstone boundary value problems |
| publishDate |
2014 |
| url |
https://hdl.handle.net/10356/103280 http://hdl.handle.net/10220/18604 |
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1681035874931834880 |