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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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/103280 http://hdl.handle.net/10220/18604 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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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